A Parallel Algorithm Template for Updating Single-Source Shortest Paths in Large-Scale Dynamic Networks : NOTES

1
A Parallel Algorithm Template for Updating
Single-Source Shortest Paths in Large-Scale
Dynamic Networks
Arindam Khanda, Sriram Srinivasan, Sanjukta Bhowmick, Boyana Norris, and Sajal K. Das
Abstract—The Single Source Shortest Path (SSSP) problem is a classic graph theory problem that arises frequently in various
practical scenarios; hence, many parallel algorithms have been developed to solve it. However, these algorithms operate on static
graphs, whereas many real-world problems are best modeled as dynamic networks, where the structure of the network changes with
time. This gap between the dynamic graph modeling and the assumed static graph model in the conventional SSSP algorithms
motivates this work. We present a novel parallel algorithmic framework for updating the SSSP in large-scale dynamic networks and
implement it on the shared-memory and GPU platforms. The basic idea is to identify the portion of the network affected by the changes
and update the information in a rooted tree data structure that stores the edges of the network that are most relevant to the analysis.
Extensive experimental evaluations on real-world and synthetic networks demonstrate that our proposed parallel updating algorithm is
scalable and, in most cases, requires significantly less execution time than the state-of-the-art recomputing-from-scratch algorithms.
Index Terms—Dynamic Networks, Single Source Shortest Path (SSSP), Shared-Memory Parallel Algorithm, GPU Implementation
F
1 INTRODUCTION
NEtworks (or graphs) are mathematical models of com-
plex systems of interacting entities arising in diverse
disciplines, e.g., bioinformatics, epidemic networks, social
sciences, communication networks, cyber-physical systems,
and cyber-security. The vertices of the network represent en-
tities and the edges represent dyadic relations between pairs
of entities. Network analysis involves computing structural
properties, which in turn can provide insights to the charac-
teristics of the underlying complex systems.
Many networks arising from real-world applications are
extremely large (order of millions of vertices and order of
billions of edges). They are also often dynamic, in that their
structures change with time. Thus, fast analysis of network
properties requires (i) efficient algorithms to quickly update
these properties as the structure changes, and (ii) parallel
implementations of these dynamic algorithms for scalability.
We posit that the design of the parallel algorithm for
updating the network properties should ideally be indepen-
dent of the implementation platforms. However, most of the
existing literature compound these two aspects by creating
algorithms that are closely tied to the parallel platform. This
lack of flexibility of applying algorithms across platforms
becomes even more critical for exascale computing, which
is generally achieved through a combination of multi-core,
many-core machines as well as accelerators, such as GPUs.
• A. Khanda and S. K. Das are with the Department of Computer Science,
Missouri University of Science and Technology, Rolla, MO 65409. E-mail:
{akkcm, sdas}@mst.edu
• Sriram Srinivasan is with the Department of Radiation Oncology, Vir-
ginia Commonwealth University, Richmond, V
A 23284. E-mail: sri-
ram.srinivasan@vcuhealth.org
• Sanjukta Bhowmick is with the Department of Computer Science and
Engineering, University of North Texas, Denton, TX 76201. E-mail:
sanjukta.bhowmick@unt.edu
• Boyana Norris is with the Dept. of Computer and Information Science,
Univ. of Oregon, Eugene, OR 97403. E-mail: norris@cs.uoregon.edu
This motivated us to develop a framework for updating Single
Source Shortest Path (SSSP) in large dynamic networks on GPUs
and multicore CPUs, which is an important first step in
achieving exascale capability.
The SSSP is a fundamental problem of network anal-
ysis that has applications in transportation networks [1],
communication (wireline, wireless, sensor) [2], social net-
works [3], and many others. It is also the building block
for computing other important network analysis properties
such as closeness and betweenness centrality. While numer-
ous algorithms can compute the SSSP in static networks and
sequentially update the SSSP on dynamic networks [4], [5],
[6], few parallel SSSP update algorithms have been created.
Because most of the real-world networks are large, unstruc-
tured and sparse, developing efficient update algorithms
becomes extremely challenging.
In this paper, we present a novel parallel algorithmic
framework for updating the SSSP in large-scale dynamic
networks. The key idea is to first identify the subgraphs
that are affected by the changes, and then update only
these subgraphs. The first step is trivially parallel. Each
changed edge is processed in parallel to identify the affected
subgraphs. The second step is challenging as it requires
synchronization when the SSSP tree is altered. We propose
an iterative method that converges to the smallest distance,
thereby eliminating explicit and expensive synchronization
constructs such as critical sections.
In our framework, these two steps can be designed
and implemented independently of the parallel architecture
platforms. We efficiently implement the proposed parallel
SSSP update algorithm on both the GPU platform and the
shared-memory platform (the latter extends our previous
implementation [7] to handle changes in batches).
We experimentally demonstrate the efficacy of our paral-
lel algorithm by comparing our GPU implementation with

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state-of-the-art GPU based recomputing-from-scratch SSSP
implementation provided by Gunrock [8]. Experimental re-
sults exhibit that our implementation most often outper-
forms Gunrock, achieving up to 5.6x speedup. We also
compare our shared-memory implementation with state-
of-the-art shared memory based recomputing-from-scratch
SSSP algorithm implementation provided by Galois. Our
shared memory implementation shows up to 5.X speed up
when compared to the Galois.
Our Contributions. The main contributions of this paper
are as follows:
• We propose a common framework for efficiently up-
dating SSSP that can be implemented for both CPU and
GPU architectures. Our novel framework leverages a
rooted tree based data structure to address challenges
in load balancing and synchronization
• We implement our parallel algorithm on two platforms
– NVIDIA GPUs and shared memory. The latter imple-
mentation significantly extends our previous version [9]
by handling changes in batches, thus allowing to run up
to 100M changes (i.e., 10 times more than in [9]).
• For the GPU implementation, we introduce a novel
functional block based approach that breaks a complex
function into several simple similar blocks and reduces
the redundant computation.
2 BACKGROUND
This section discusses preliminaries on SSSP and sequential
algorithms for computing and updating SSSPs.
Graphs and SSSP. A graph is denoted as G(V, E), where
V represents the set of vertices (nodes) and E the set
of edges. In this paper, we assume the graphs have non-
negative edge weights.
A path between two vertices u and v is called a shortest
path, if the sum of the weights of edges between these two
vertices is the smallest. The Single Source Shortest Path
(SSSP) problem is to compute shortest paths from a source
vertex s to all other vertices in the graph. The output is a
spanning tree, called the SSSP tree. We store the SSSP as
a rooted tree by maintaining the distance from the root to
every vertex and maintaining a parent-child relationship to
capture the tree structure. If there exists an edge between u
and v in the SSSP tree and the distance of u from the root is
lower than that of v, then u is called the parent of vertex v.
Computing SSSP. The most well known sequential al-
gorithms to compute SSSP is due to Dijkstra [10]. It creates
the SSSP tree with the source vertex as its root. For a given
graph G(V, E), where all edge weights are non-negative,
this algorithm maintains two sets of vertices, Set1 and
Set2 = V − {Set1}, where Set1 contains all the vertices,
whose shortest path weight from the source have already
been calculated. The algorithm selects the vertex from Set2
having the minimum shortest-path estimate, and adds it to
Set1 and relaxes all outgoing edges of the selected vertex.
This is repeated until Set2 becomes empty.
Relaxing an edge e(u, v) involves checking if the esti-
mated path distance of v from the source can be decreased
by going through vertex u. The implementation of Dijkstra’s
algorithm using a min-priority queue with a Fibonacci heap
requires O(|E|+|V | log |V |) time. There also exist a plethora
of sequential SSSP algorithms (including Bellman-Ford) and
their variants [10].
2.1 Sequential Algorithms for Updating SSSP
The structural changes in a dynamic network can be in
the form of edge or vertex insertion and deletion as well
as changing edge weights. In this paper, we only apply
changes in the form of edge addition or deletion, since
vertex insertion/deletion can be represented as changes to
edges, given that the upper bound on the number of vertices
that can be added is known. For a single edge insertion or
deletion scenario, the first step is to identify the affected
vertices in the graph, and enter them to a priority queue.
In the next phase, using state-of-the-art implementation of
Dijkstra’s algorithm the distance of the vertices in the queue
are updated. This continues until the queue is empty or
all the affected nodes and their neighbors from the source
have the shortest paths. The sequential approach involves
redundant computation as the same set of vertices can be
updated multiple times and therefore cannot scale to large
networks. Algorithm 1 presents how to update SSSP given
an input undirected graph G, initial SSSP tree and a changed
edge ∆E = e(u, v). (An algorithm to update the SSSP tree
in a similar sequential manner is proposed in [4].)
Algorithm 1: Updating SSSP for a Single Change
Input: Weighted Graph G(V, E), SSSP Tree T,
Changed edge ∆E = e(u, v)
Output: Updated the SSSP Tree Tu
1 Function SingleChange(∆E, G, T):
// Find the affected vertex, x
2
3 if Distu[u] > Distu[v] then
4 x ← u, y ← v
5 else
6 x ← v, y ← u
// Initialize Priority Queue PQ and
update Distu[x]
7 PQ ← x
8 if E is inserted then
9 Distu[x] ← Distu[y] + W(u, v)
10 if E is deleted then
11 Distu[x] ← infinity
// Update the subgraph affected by x
12 while (PQ not empty) do
13 Updated ← False
14 z ← PQ.top()
15 PQ.dequeue()
16 Updated ← SSSP(z,G,T)
// Calculate the shortest distance
from source vertex to the z
17 if Updated = True then
18 for n where n is the neighbor of z do
19 PQ.enqueue(n)
Over the last 30 years, many sequential implementations
of updating or incremental algorithms for dynamic net-
works have been developed. The authors in [5] developed
complexity models for the sequential update of dynamic
networks. The algorithms in [6] suggest techniques to up-
date the SSSP tree. An implementation to update SSSP in

3
batches is propsoed in [11]. The dynamic SSSP algorithm
due to [12] is one of the most recent sequential update
algorithms, aiming to reduce the complexity of updates.
3 RELATED WORK
This section highlights related work on parallel implemen-
tations for computing SSSP on static and dynamic networks.
3.1 GPU-based Implementation
Gunrock [8] is a high-performance graph library that pro-
vides a data-centric abstraction on a set of vertices or edges
and develops a three-step architecture (advance, filter, and
compute) to compute SSSP on GPU. The authors in [13]
proposed an efficient implementation of the Bellman-Ford
algorithm using two queues on the Kepler GPU. Although
this algorithm exploits dynamic parallelism, a feature of
modern Kepler GPU, it also uses atomic operation that
makes part of the code serial.
In [14], a detailed study is proposed on the performance
of various graph algorithms, including SSSP on temporal
graphs, on different multicore architectures and GPU ac-
celerator. In [15] is implemented a dynamic incremental
and decremental SSSP algorithm in JavaScript. This is the
only GPU implementation we found for updating dynamic
networks in GPU. Results show the algorithm performs
well, only if the number of changed edges is less than 10%.
3.2 CPU-based Implementation
In [7] we developed the first shared-memory algorithm for
updating SSSP on dynamic networks, and implemented it
using OpenMP. To the best of our knowledge, this is the
only shared-memory parallel implementation for updating
SSSP on dynamic networks. The ones mentioned below
operate on static networks or are sequential implementa-
tions on dynamic networks. For example, a Spark-based
implementation to update SSSP on dynamic networks is
reported in [16], while [17] implemented the Bellman-Ford
algorithm using parallel hypergraph algorithms and [18]
provided two implementations of ∆–stepping algorithm on
static graph in shared memory multicore architecture.
Galois [19] is a shared-memory based amorphous data-
parallelism programming model for graph algorithms. It
supports priority scheduling and processes on active ele-
ments comprised of a subset of vertices. Galois provides
a shared-memory parallel implementation of Dijkstra’s al-
gorithm. Havoqgt [20] is a software to compute SSSP on
a distributed platform; it only allows re-computation from
scratch, with no support for dynamic networks. Approxi-
mations for streaming graphs are proposed in [21].
4 OUR PARALLEL DYNAMIC SSSP ALGORITHM
In this section, we propose a novel framework for updating
SSSP in parallel for dynamic networks. We maintain the
SSSP values as a tree, which is rooted at the starting vertex.
Our algorithm involves efficiently traversing and updating
the weights or the structure of the tree. A sketch of the
framework is given in Figure 1
Problem Description. Let Gk(Vk, Ek) denotes the graph at
time step k. Since SSSP results are non-unique, several SSSP
trees are possible. Let Tk be one such SSSP tree of Gk.
Let ∆Ek be the set of edges changed from the time step
k − 1 to time step k. This set consists of two subsets; the set
of inserted edges Insk and the set of deleted edges Delk.
Thus, Ek = ((Ek−1 ∪ Insk) Delk.
Our goal is to compute the SSSP tree Tk at time step k,
based on the structure and edge weights of the tree Tk−1at
time step k − 1 and the changed edge set ∆Ek.
Iden�fy 1st level
Inser�on and Dele�on
affected ver�ces
Iden�fy ver�ces in sub
tree under 1st
level
Dele�on affected
ver�ces in Tk-1
Tk-1 ΔEk
Adjust the distance of all
affected ver�ces
Iden�fy affected
neighbor ver�ces
Tk
Gk-1
Update Edge
List
Itera�vely iden�fy all affected ver�ces
and adjust distance
Step
1
Step
2
Fig. 1: A Parallel framework to update SSSP in dynamic
networks
4.1 A Parallel Framework for Updating SSSP
Our framework for updating SSSP consists of two steps;
Step 1: Identify the subgraph (a set of vertices) affected by
changes (Algorithm 2); and Step 2: Update this subgraph to
create a new SSSP tree (Algorithm 3).
Data Structures: We store the SSSP tree as an adjacent list.
Since the number of edges in a tree is one less than the
number of vertices, thus the memory would be of order
V . Each vertex, except the root, is associated with four
variables; Parent– its parent in the tree, Dist– its shortest
distance from the root , Affected Del–whether the vertex has
been affected due to deletion, and Affected– whether the
vertex has been affected by any changed edge. Each of these
variables are stored as arrays of length V , with the each
index associated with the corresponding vertex.
Step 1: Identifying Subgraphs Affected by the Changed
Edge: In this step we process each edge in parallel and
identify the vertices affected by these changes. Note that
a vertex can be affected due to multiple changes. However,
this step determines whether a vertex is affected by at least
one changed edge. Due to this criterion, no synchronization
is required and each changed edge can be potentially be
processed in parallel.

4
In practice, however, the computation is expedited if part
of the new SSSP tree is formed in Step 1. This includes
removing deleted edges (that can result in some subtrees
being disconnected) and changing the parent of affected ver-
tices whose distance to the root is lowered due to insertions.
Edge Deletion. Given two vertices u and v, let the edge
between them be e(u, v). In the case of deletion, we first
check whether this edge was part of the SSSP tree (Algo-
rithm 2, line 5). If it is not, then it does not affect any vertex,
and no further processing is needed.
For the case where the edge e(u, v) is part of the SSSP
tree, let us assume that u is the parent of v. Thus only
the shortest distance of v is affected. We change Dist[v] to
infinity and Parent[v] to null, to indicate that vertex v is
now disconnected from the parent tree. We further change
Affected Del[v] and Affected[v] to true to indicate that
this vertex is affected by deletion (Algorithm 2; lines 7, 8).
Edge Insertion. Let the weight of an inserted edge
e(u, v) be W(u, v). The edge will affect the SSSP tree only if
Dist[u] + W(u, v) is less than Dist[v].
If this condition holds, then we set Dist[v] to Dist[u] +
W(u, v), update the parent of v, Parent[v] to u, and mark
Affected[v] to true to mark that vertex v has been affected
(Algorithm 2, lines 15-18 ).
Algorithm 2: Identify Affected Vertices
1 Function ProcessCE(G, T, ∆E, Parent, Dist):
2 Initialize Boolean arrays Affected Del and
Affected to false
3 Gu ← G
4 for each edge e(u, v) ∈ Delk in parallel do
5 if e(u, v) ∈ T then
6 y ← argmaxx∈{u,v}(Dist[x])
7 Change Dist[y] to infinity
8 Affected Del[y] ← True
Affected[y] ← True
9 Mark e(u, v) as deleted
10 for each edge e(u, v) ∈ Insk in parallel do
11 if Dist[u] > Dist[v] then
12 x ← v, y ← u
13 else
14 x ← u, y ← v
15 if Dist[y] > Dist[x] + W(x, y) then
16 Dist[y] ← Dist[x] + W(x, y)
17 Parent[y] ← x
18 Affected[y] ← True
19 Add e(u, v) to Gu
Step 2: Updating the Affected Subgraph: Note that when
a vertex gets disconnected from the SSSP tree due to edge
deletion, then its descendants would also get disconnected.
Thus their distance from the root would be infinity. In the
first part of Step 2, we update these distances by traversing
through the subtree rooted at the vertices affected by dele-
tion. The distances of all the vertices in these disconnected
subtrees are set to infinity. We set the Affected variable for
each of these vertices as true. Since the subtrees can be of
different sizes, we use a dynamic scheduler for balancing
the workload. The pseudo code in given in Algorithm 3,
lines 2-8.
A
F
B
D E
C
5
2 3
4
2
2
1
1
A
F
B
D E
C
2 3
2
1
1
a. Original Network b. SSSP Tree
0
3
5
6
3
2
A
F
B
D E
C
3
2
1
inf
2
f. Step 2B: Connec�ng
disconnected nodes
A
F
B
D E
C
3
2
1
inf
inf
e. Step2A: Processing dele�on
aﬀected nodes in Parallel and
disconnec�ng subtrees
0
3
5
4
0
3
5
4
7
A
F
B
D E
C
3
2
1
2
1
h. End of Step 2: Final
updated SSSP tree
A
F
B
D E
C
3
2
1
2
1
g. Step 2C: Connec�ng disconnected
nodes and upda�ng neighbor’s Dist
8
0
3
5
4
7
8
0
3
5
4
7
A
F
B
D E
C
3
2
1
1
Change Set
A:E:7(Ins)
C:F:1(Ins)
A:B:2(Del)
A:D:5(Del)
inf
c. Step1A: Processing Edge dele�on
in Parallel
A
F
B
D E
C
3
2
1
1
inf
d. Step1B: Processing Edge inser�on in
Parallel
0
3
5
6
3
3
3
0
4
5
Fig. 2: Illustration of updating SSSP tree
In the second part, we update the distances of the
affected vertices. For each vertex marked as Affected and
its neighbors, we check whether the distance is reduced. If
the distance of a neighbor, n is reduced by passing through
an affected vertex v, then the distance of n, Dist[n], is
updated and Parent[n] is set to v. On the other hand if
the distance of v is reduced by passing through a neighbor,
n, then Dist[v] is updated and Parent[v] is updated to n.
This process is continued iteratively until there is no vertex
whose distance can be updated. Since the vertices are always
moving towards lower distance, the iterations will converge.
At the end of Step 2, we obtain an SSSP tree with
updated distance for every vertex from the root at time tk.
Figure 2 shows an example of SSSP tree update, where Dist
values of the vertices are shown in red color and the affected
vertices at each step are shown in green color. Figures 2(c -
g) show the step and the sub-steps of the algorithm.
4.2 Challenges in Achieving Scalability
We discuss the challenges that arise in making the code
scalable and how we address these challenges;
Load Balancing In Step 2 of our algorithm, the number of
operations depends on the size of the subgraph rooted at

5
Algorithm 3: Update Affected Vertices
1 Function UpdateAffectedVertices(Gu, T,
Dist, Parent Affected Del and Affected):
2 while Affected Del has true values do
3 for each vertex v ∈ V such that
Affected Del[v] = true in parallel do
4 Affected Del[v] ← false
5 for all vertex c, where c is child of v in the
SSSP tree T do
6 Set Dist[c] as infinity
7 Affected Del[c] ← True
8 Affected[c] ← True
9 while Affected has true values do
10 for each vertex v ∈ V such that
Affected[v] = true in parallel do
11 Affected[v] ← False
12 for vertex n, where n ∈ V and n is neighbor
of v do
13 if Dist[n] > Dist[v] + W(v, n) then
14 Dist[n] ← Dist[v] + W(v, n)
15 Parent[n] ← v
16 Affected[n] ← True
17 else if Dist[v] > Dist[n] + W(n, v)
then
18 Dist[v] ← Dist[n] + W(n, v)
19 Parent[v] ← n
20 Affected[v] ← True
the affected vertices. Since the subgraphs can be of different
sizes, the work done by each processing unit can be imbal-
anced.
While several complicated load balancing techniques can
be applied, such as knowing the size of the subtrees apriori
and then distributing the vertices according to the size of
the subtrees, our experiments show that by simple using
dynamic scheduling provide good scalability with much
lower overhead.
Synchronization. Since multiple processors are updating
the affected vertices, thus race conditions can occur where
these vertices may not be updated to their minimum dis-
tance from the root. The traditional method to resolve this
problem is by using locking constructs. However using
these constructs reduces the scalability of the implementa-
tion.
In our algorithm, instead of using locking constructs, we
iteratively update the distances of the vertices to a lower
value. Over the iterations the vertices thus converge to their
minimum distance from the source node or root of the tree.
Although multiple iterations add to the computation time,
the overhead is much lower than using locking constructs.
Avoiding Cycle Formation Our updating algorithm is
based on the assumption that the underlying data structure
is a tree. However, when multiple edges are inserted in
parallel cycles can be formed.
Consider an edge e(u, v) which is deleted, and v is the
affected vertex. Then as per Step 1, the parent of vertex v is
set to null to indicate it is disconnected from the main tree.
Let a be a descendant of vertex v, that is it is a node in
the disconnected subtree rooted at v. At the end of step 1,
the distance of a is not yet updated to infinity. Now if there
is an inserted edge e(a, v) from a to v, then the distance of
v will be lower after passing through a. Thus a will be set
as the parent of v creating a cycle. Figure 3 illustrates the
formation of this kind of cycle.
To avoid this cycle formation, in Step 2, we first process
the subtrees of the vertices affected by deletion to mark their
distances as infinity. Then the edge between two discon-
nected vertices in the tree are not processed.
Fig. 3: Type 2 cycle formation
4.3 Algorithm Analysis
We now prove that our algorithm indeed forms a correct
SSSP tree for the graph at time step k, and also compute
the analytical scalability of our method. These results are
reproduced from our earlier paper [7]
Lemma 1. The parent-child relation between vertices assigned by
our parallel updating algorithm produces tree(s).
Proof. To prove this, we first create a directed graph where
the parent vertices point to their children. Now consider a
path in this graph between any two vertices a and b. The
path goes from vertex a to vertex b. This means that a is
an ancestor of b. As per our parallel updating algorithm, a
vertex v is assigned as a parent of vertex u only if Dist[v] <
Dist[u], therefore transitively the distance of an ancestor
vertex will be less than its descendants. Thus, Dist[a] <
Dist[b].
Since G has non-zero edge weights, it is not possible
that Dist[b] < Dist[a]. Thus, there can be no path from b
to a. Hence, all connected components are DAGs, and thus
trees.
Lemma 2. The tree obtained by our parallel algorithm will be a
valid SSSP tree for Gk.
Proof. Let Tk be a known SSSP tree of Gk and let Talg be the
tree obtained by our algorithm. If Talg is not a valid SSSP
tree, then there should be at least one vertex a for which
the distance of a from the source in Talg is greater than the
distance of a from the source vertex in Tk.
I also read about these cycles in routing algorithms

6
Consider a subset of vertices, S, such that all vertices in
S have the same distance in Tk and Talg. This means that
∀v ∈ S, DistTk
[v] = DistTalg
[v]. Clearly, such a set S can be
trivially constructed by including only the source vertex.
Now consider a vertex a for which DistTk
[v] <
DistTalg
[v] and the parent of a is connected to a vertex in S.
Let the parent of a in Tk (Talg) be b (c).
Consider the case where b=c. We know that the
DistTk
[b] = DistTalg
[b]. Also, the distance of a child node is
the distance of its parent plus the weight of the connecting
edge. Therefore, DistTalg
[a] = DistTalg
[b] + W(a, b) =
DistTk
[b] + W(a, b) = DistTk
[a].
Now consider when b 6= c. Since the edge (b, a) exists
in Tk, it also exists in Gk. Since DistTk
[v] 6= DistTalg
[v],
the distance of a was updated either in Tk or in Talg, or in
both, from the original SSSP tree. Any of these cases imply
that a was part of an affected subgraph. Therefore, at some
iteration(s) in Step 2, a was marked as an affected vertex.
Because the edge (b, a) exists in Gk and a is an affected
vertex, in Step 2, the current distance of a would have been
compared with DistTalg
[b]+W(a, b). Since this is the lowest
distance of a according to the known SSSP tree Tk, either the
current distance would have been updated to the value of
DistTalg
[b] + W(a, b) or its was already equal to the value.
Therefore, DistTk
[a] = DistTalg
[a].
Scalability of the Algorithm Assume that we have p pro-
cessing units, and m changed edges to process, out of which
there are a insertions and b deletions that affect the SSSP.
For Step 1, each changed edge can be processed in parallel,
requiring time O(m/p).
For Step 2, the parallelism depends on the number of
affected vertices, and the size of the subgraph that they
alter. At each iteration, an affected vertex goes through its
neighbors, so the work is proportional to its degree.
Assuming that x vertices are affected, x ≤ m, and the
average degree is a vertex is d, then the time per iterations
is O(xd/p). The maximum number of iteration required
would be the diameter of the graph D. Thus an upper bound
time complexity for Step 2 is D ∗ O(xd/p).
Taken together, the complexity of the complete updating
algorithm is O(m
p )+O(Dxd
p ). The term Dxd represents the
number of edges processed. Let this be equal to Ex. The
number of edges processed in the recomputing method
would be E + m. Therefore for the updating method to be
effective, we require Ex < (E + m).
5 IMPLEMENTATION DETAILS
In this Section we discuss how we implemented the updat-
ing algorithm in shared memory architectures and in GPUs.
5.1 Shared-Memory Implementation
We implemented the proposed algorithm on the shared
memory platform where the input consists of a graph
G(V, E), changed edges ∆E(Delk, Insk), source vertex s,
and SSSP tree T.
We use pragma omp parallel for directive to leverage the
shared memory parallelism. The implementation processes
the set of Delk in parallel before processing the set of Insk
in parallel. In case of deletion, Delk is first validated by
searching if the edge is available in key edges stored in T; if
it belongs to the key edges it is processed further, otherwise
it is ignored. If the changed edge e(u, v) is marked for
insertion, the next step is to check if the addition of this edge
helps to reduce the distance of vertex v from the source; if it
does, then the edge is marked for update.
In this implementation, each vertex has a Boolean Af-
fected flag which is true when it is identified that the SSSP of
the vertex needs to be recalculated. Now for all the affected
vertices, SSSP is computed using the unaffected adjacent
vertices and their distances as mentioned in the last part
of Algorithm 3. The computation of affected vertices is done
in parallel and this process continues until there is no vertex
left with the Affected flag set to true.
Since a vertex can be set to affected multiple times, this
process incurs some redundancy of computation. However,
the alternate process of using locking constructs to syn-
chronize lead to reduced scalability. We therefore allow for
some redundancy in the operations. The shared memory
implementation uses C++ and OpenMP library.
Asynchronous Updates:
In Step 2 of our updating algorithm, the threads syn-
chronize at the while loop. This synchronization occurs after
each vertex accesses its neighbors. However the synchro-
nization can be made less frequent if the vertices access their
distance d neighbors for a given value of d. Increasing this
level of asynchrony can lead to more redundant computa-
tions and increased iterations, but reduced number of syn-
chronizations. In the experimental study (see Section 6), we
discuss how changing the levels of synchronization affects
performance. The pseudocode in Algorithm 4 demonstrates
how asynchronous updates can be implemented for Step 2
of our algorithm.
Processing Batches of Changes: The original implementa-
tion discussed in [7] processes all changed edges together. In
order to improve the load balancing and avoid having mem-
ory hotspot we processed the changed edges in batches.
We experimented with different batch sizes to study the
performance. Section 6 shows how processing in batches of
different size gives a boost in the performance.
5.2 GPU Implementation
To leverage the Single Instruction Multiple Threads (SIMT)
execution model of modern NVIDIA GPU, in our imple-
mentation we create an array of operands where a single
CUDA (Compute Unified Device Architecture) thread is
assigned to a single element of the operand array to execute
some user defined function. In this architecture a large
number of threads (divided into thread, block and grid
at the programming level) are executed simultaneously to
achieve data-parallelism. Commonly, Grid-Stride Loops are
used to cover the whole operand array when the size of the
array is larger than the number of CUDA threads available.
Compressed sparse row (CSR) and its variants like Dy-
namic CSR-based (DCSR) data structure [22] or Packed
Compressed Sparse Row (PCSR) [23] are potentially suitable
for storing input graphs depending on the application. Here,
we consider simple CSR format to store the graph. To store
the SSSP tree structure and its properties, we define a data
structure T, which is an array of size |V |, where the element

7
Algorithm 4: Asynchronous Update of SSSP
Input: G(V, E), T, Dist,Parent, source vertex s,
∆E(Delk, Insk)
Output: Updated SSSP Tree Tk
1 Function AsynchronousUpdating(∆E, G, T):
2 Set Level of Asynchrony to A.
3 Change ← True
4 while Change do
5 Change ← False
6 pragma omp parallel schedule (dynamic)
7 for v ∈ V do
8 if Affected Del[v] = True then
9 Initialize a queue Q
10 Push v to Q
11 Level ← 0
12 while Q is not empty do
13 Pop x from top of Q
14 for c where c is child of x in T do
15 Mark c as affected and change
distance to infinite
16 Change ← True
17 Level ← Level + 1
18 if Level ≤ A then
19 Push c to Q
20 Change ← True
21 while Change do
22 Change ← False
23 pragma omp parallel schedule (dynamic)
24 for v ∈ V do
25 if Affected[v] == True then
26 Affected[v] ← false
27 Initialize a queue Q
28 Push v to Q
29 Level ← 0
30 while Q is not empty do
31 Pop x from top of Q
32 for n where n is neighbor of x in G
do
33 Level ← Level + 1
34 if Dist[x] > Dist[n]+W(x, n)
then
35 Change ← True
36 Dist[x]=Dist[n]+W(x, n)
37 Parent[x]=n
38 Affected[x] ← True
40 Push x to Q
41 if Dist[n] > Dist[x]+W(n, x)
then
42 Change ← True
43 Dist[n]=Dist[n]+W(n, x)
44 Parent[n]=x
45 Affected[n] ← True
47 Push n to Q
at index i denotes the properties of vertex i in the SSSP tree.
Each element of T contains three variables: Parent (stores
the parent of the vertex), Dist (stores the distance of the
vertex from the source), and Flag (a Boolean variable to
denote the affected vertex).
Synchroniza�on
Filter
Asynchronous Vertex marking
Vertex marking
thread block
thread block
0
0
1 2 3 4
0 n-1 n
0 1 1 0 1
Flags array
1 2
|Aff |
0
1 2 4
i
size =
Array of
marked
ver�ces
All marked ver�ces
CUDA threads
1
2
0
3
1
2
0
k
k-2
k-1
k-3
Operand array
Fig. 4: Vertex-Marking Functional Block (VMFB)
5.2.1 Functional Block
When numerous threads are operating on shared variables
and attempting to write concurrently, it may lead to race
condition or erroneous update. To avoid this situation,
CUDA atomic operations are used. However, the use of
atomic operation makes the computation serial and in-
creases the overall execution time. Therefore, we define a
functional block, which minimizes the use of atomic operation
while maintaining the correctness of the algorithm.
Our functional block, called the Vertex-Marking Func-
tional Block (VMFB), is created solely for graph-related op-
erations. It can accept an operand array Arrayoperand, a
function Fx, an array (Flags) of size |V | to store flags for
each vertex of a graph G(V, E) and a predicate P as input.
The VMFB has three main functional steps, as described
below.
Vertex Marking: The VMFB allocates parallel CUDA
thread for each element of Arrayoperand, while each thread
performs Fx and alters the flag values in the shared array,
Flags. It is considered that Fx is capable of doing other
computations along with changing the flag values (primary
function). Here, all the CUDA threads operate without any
guaranteed synchronization (no control over synchroniza-
tion at this stage) without using any atomic operation. They
update Flags with a constant value (e.g. updating to 1) only
when some specified condition mentioned in Fx is satisfied.
Although, in this step multiple threads can asyn-
chronously update the same element of the array Flags,
the correctness is preserved as all threads update a flag with
a single constant value. More specifically, the process is one
directional and a vertex can be marked in the process, but
cannot be unmarked.
Synchronization: This step puts a global barrier for all
the threads, and the code execution halts here for all threads
to complete their execution before going further.

8
Filter: This step stores the index value from the array
Flags using CUDA ballot sync when the predicate P
is true. In general, the predicate simply states comparison
between flag value and a given constant. The filter step
identifies and stores all marked vertices in an array without
duplication. Moreover, this operation reduces the redundant
computation due to overlapping affected subgraphs.
Figure 4 depicts the VMFB, in which only the filter
operation uses the CUDA atomicAdd operation while main-
taining the dimension of the list of marked vertices.
5.2.2 SSSP Update Using Vertex Marking Functional Block
The idea of implementing a graph algorithm using VMFB is
simple. We write a function which takes a single vertex or
a single edge and operates on it and marks some vertices
in the flag array depending on user defined clauses. Let
our function can work on a vertex, then we pass an array
of vertices(as operand array), the function we have written
and an associated flag array to a VMFB. VMFB executes
the user defined function on every element of the operand
array in parallel and generates an array of marked vertices.
Therefore, to implement SSSP update we first write four
functions named ProcessIns, ProcessDel, DisconnectC
and ChkNbr. The functionality of these are given in Table 1.
TABLE 1: Notation used for GPU implementation.
Used Notation Detail
VMFB Vertex Marking Functional Block
ProcessIns()
Operate on an edge being inserted and
finds 1st level insertion affected vertices
ProcessDel()
Operate on an edge being deleted and
finds 1st level deletion affected vertices
DisconnectC()
Operate on a deletion affected vertex
and disconnects child neighbors
ChkNbr()
Operate on an affected vertex to connect
disconnected vertices and update neighbors
P Predicate to find if a flag is raised
Reset() Function to reset all values of an array to 0
Algorithm 5 presents the pseudocode for GPU imple-
mentation using VMFB blocks and the notations used in the
pseudocode are listed in Table 1.
Step 1: We implement the first step of the SSSP update
algorithm using two VMFBs. The first VMFB (Line 3 in
Algorithm 5) accepts the array of deleted edges as the
operand array and marks the first-level affected vertices
due to edge deletion. As additional function, it disconnects
the first-level deletion affected vertices from their parent
vertices in the SSSP tree. This block mainly implements lines
5–9 in Algorithm 2.
The second block takes the array of inserted edges as
Arrayoperand and identifies the first-level insertion affected
vertices by processing them using ProcIns function, which
is actually the implementation of lines 11–19 in Algorithm 2.
As in VMFB, the parallel threads are distributed across
the operand array, every changed edge is processed by
different CUDA thread in Step 1.
Step 2: The second step of the SSSP update algorithm
has two main parts. The first part iteratively disconnects the
subtrees under every first-level deletion-affected vertex (us-
ing the DisconnectC function) by passing the function and
affected vertices to a VMFB. Specifically, the DisconnectC
function implements lines 4–8 in Algorithm 3. The VMFB
here uses the output of the first VMFB (an array of first
Algorithm 5: GPU implementation
Input: G(V, E), T(Dist, Parent), ∆E(Delk, Insk)
Output: Updated SSSP Tree Tu
1 Function GPUimplementation(G, T, ∆E):
2 Initialize a flag array of size |V | named Flags
with all values 0
/* Process Delk in parallel */
3 Affdel ←
V MFB(Delk, ProcessDel(G, T), Flags, P)
/* Process Insk in parallel */
4 Reset(Flags)
5 Affins ←
V MFB(Insk, ProcessIns(G, T), Flags, P)
/* Mark all vertices in deletion
affected sub-tree */
6 AffAlldel ← Affdel
7 while Affdel is not empty do
8 Reset(Flags)
9 Affdel ←
V MFB(Affdel, DisconnectC(T), Flags, P)
10 AffAlldel ← AffAlldel ∪ Affdel
/* Connect disconnected vertices and
update neighbor distance */
11 AffAll ← AffAlldel ∪ Affins
12 while AffAll is not empty do
13 Reset(Flags)
14 AffAll ←
V MFB(AffAll, ChkNbr(G, T), Flags, P)
level deletion-affected vertices) as input Arrayoperand and
marks all the children of the first-level deletion-affected
vertices in the SSSP tree and then disconnects them. In the
next iteration, the newly affected vertices are used as the
operand array for the same VMFB, and all the deletion-
affected vertices are marked and disconnected iteratively
(Algorithm 5, lines 7-10).
The last part of the implementation, connects the dis-
connected vertices and updates the distance of all affected
vertices. The set of all deletion affected vertices and first-
level insertion affected vertices are combined (via set union
operation) to form an array of all affected vertices (both
deletion and insertion affected) and is used as initial input
operand array for the last VMFB (line 14 in Algorithm 5).
The last VMFB block connects the disconnected vertices (ap-
plicable to deletion affected vertices) and updates the Dist
value of neighbors (applicable to both deletion and insertion
affected vertices) using ChkNbr function (implementation
of lines 11–20 in Algorithm 3). Vertices are marked as
affected whenever their Dist values are changed and the
filter operation in the block gathers all affected vertices in
an iteration as an output array of marked vertices. In the
next iterations, the output of the last iteration is input into
the VMFB. This process ends when the updated Dist is
computed for all affected vertices and there is no marked
vertex left for further processing.

9
TABLE 2: Networks in Our Test Suite
Name Num. of Vertices Num. of Edges
BHJ2015-M87101049(BHJ-1) 1,827,148 193,540,306
BHJ2015-M87101705(BHJ-2) 1,827,168 202,250,875
soc-Orkut 2,997,166 106,349,209
LiveJournal 12,693,249 161,021,950
graph500-scale23-ef16 4,606,315 258,503,995
RMAT24 G 16,777,215 134,511,383
BHJ: bn-human-Jung
6 EXPERIMENTAL RESULTS
For the experiments, we choose five large graphs from
the network-repository collection [24]; and one synthetic
R-MAT graph generated with probability (a=0.45, b=0.15,
c=0.15, d=0.25), labeled as G, which is a random network
with scale-free degree distribution. Table 2 lists the names,
the number of vertices and edges of our graph datasets.
All GPU experiments have been conducted on a NVIDIA
Tesla V100 GPU with 32GB memory. The host processor
was dual 32 core AMD EPYC 7452. For the shared memory
experiments we used Intel(R) Xeon(R) Gold 6148 CPU with
384GB memory.
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Fig. 5: Execution time of proposed GPU implementation for
networks in Table 2 with 50M and 100M changed edges
consisting of p = 100%, 95%, 90%, 85%, 75%, 50%, 25%, and
0% insertions and (100 − p)% deletions.
6.1 GPU Implementation Results
Figure 5 shows the execution time of CUDA implementation
of our SSSP update algorithm. We present the time for
updating the shortest path following a 50-million and 100-
million edge updates. The edge updates consist of different
mixes of edge deletions and insertions. Specifically, edge
insertion percentage means that if the dataset contains p%
insertions then there is (100 − p)% edge deletion. For all of
our experiments, only the execution time is used instead
of TEPS (Traversed Edges per Second). This is because,
for dynamic networks update, we typically aim to traverse
fewer edges; thus maximizing TEPS is not the right metric.
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Fig. 6: Comparison of our GPU implementation of the
SSSP update algorithm for dynamic networks with Gun-
rock implementation computing SSSP from scratch on static
networks. The Y-axis is the speedup; the X-axis is the graph
input. The speedup is measured for all networks with 50M
and 100M changed edges for 0%, 25%, 50%, 75%, 85%, 90%,
95% and 100% edge insertions (the rest of the edge changes
are deletions).
The execution time mainly depends on the total number
of affected vertices, which in turn depends on the network
structure and location of changes. The changes and net-
work structure are random in our experiments. Therefore,
the affected subgraph size and its location are also ran-
dom. In general, for p = 100% edge insertions (i.e., no
edge deletion), the GPU implementation skips the part of
the algorithm where all vertices in the deletion affected
subgraph get disconnected and require comparatively less
time. We observe that the execution time increases when
the percentage of edge insertions is decreased from 100%,
i.e., the percentage of edge deletions is increased. This is
because, for edge deletion, the algorithm disconnects all
deletion affected vertices at first and then tries to reconnect
them with the actual SSSP tree. However, when one deletion
affected subgraph overlaps with another deletion affected
subgraph, the Filter operation in VMFB combines them to
avoid rework. Therefore, in Figure 5 we notice that most
of the time, the execution time decreases when the percent-
age of insertions is further reduced (i.e., the percentage of
deletions is increased) below 75%. Although, an exception
to this trend occurs when the change edges are random and
the affected subgraphs do not overlap.
6.2 GPU Performance Comparison
We compare the GPU implementation of our SSSP update
algorithm with other available GPU implementation for
computing SSSP. The implementation reported in [15] is
not appropriate for comparison because because it is useful
only if the edge updates are less than 10% of the total

10
Fig. 7: Speedup of our shared-memory update algorithm
compared to the recomputation approach in Galois.
number of edges. To the best of our knowledge, there is
no other implementation of updating SSSP on dynamic
networks on GPUs. Therefore, we compare the time taken
by our algorithm to update the SSSP with the time taken
to recompute the SSSP from scratch by using Gunrock [8],
a widely used tool for (static) graph analytics on GPUs.
The Gunrock implementation shows good speedups when
compared to other GPU graph analytics packages.
Figure 6 shows the speedup of the SSSP update algo-
rithm compared with the Gunrock SSSP implementation on
the networks discussed in Table 2. The changed edges are
added to the original network and used as an input to the
Gunrock software. We only consider the time taken by Gun-
rock to compute SSSP for the modified network, ignoring
the time to create the input network with new changes. Each
comparison experiment was repeated six times; we took the
average and measured the improvement.
Figure 6 clearly shows that, in most of the cases, our
implementation achieves good speedup (up to 8.5x for
50 million changed edges and up to 5.6x for 100 million
changed edges) when the percentage of insertion is more
than 25%. When the percentage of insertion is below 25%
(i.e., the deletion percentage is above 75%), it implies 75% or
more of the total 50 million (or 100 million) changed edges
are deleted from the original set of edges and the rest of
the edges (which is very small) is supplied to Gunrock as
input. This is why at lower percentage of insertion (i.e., high
deletion), Gunrock performs better than our approach.
We observed that if the number of total changed edges is
greater than 50% of the network size and the majority (more
than 50%) of the changed edges involve edge deletion, it is
better to recompute from scratch rather than updating. Our
proposed implementation works better in most cases when
the majority of the changed edges are marked for insertion.
6.3 Shared-Memory Implementation Results
We compare our shared-memory implementation with the
state-of-the-art CPU based shared memory recomputation
approach [25] on a dual 40-core Intel(R) Xeon(R) Gold
6148 CPU @ 2.40GHz with 384GB DDR4 2666 RAM. Fig-
ure 7 provides a comparison between the proposed shared
memory implementation and Galois [25] for all graphs. We
have used 100M edge changes with different combinations
of edge insertion percentage. For the recomputation based
approach we modify the network by adding the changes
and then re-run the SSSP from scratch. We ignore the time
it takes to add those changes to the original network. We
observe that in most cases, the proposed shared-memory
implementation performs better than the recomputing ap-
proach. We performed this experiment for all networks three
times with three different set of changed edges generated for
each network. The average speed up for each network for
different edge percentage is used for comparison. We didn’t
see much difference in the speedup for all 3 runs. We did
observe that speed up is not consistent for networks such as
Graph-500, we noticed that the speedup is less than 1 when
more than 85% percentage of total nodes affected for the
given changes. We believe that if the changes affect more
than a certain threshold percentage which varies for each
network than recomputation is recommended than using
the update algorithm. For the networks used in this paper
for scalability experiments in Figure 8 the threshold ranges
were around 75-85%.
Figure 8 shows the performance of the shared memory
implementation with different combinations of edge inser-
tion percentages. For this experiment, we ran the proposed
implementation on four networks with 100 M changes on
different thread counts. As we increase the number of
threads, the time for updating decreases in most cases. We
ran the proposed implementation on five different sets of
changed edges (generated for each network) for the four
networks and with different combinations of edge insertion
percentage and averaged the time of five runs for each
configuration. There are few cases where time to update
doesn’t show significant improvement when we increase
the thread count. For example the Live Journal network
for 25 and 50% edge insertion, Orkut Network for 0%. Our
investigations revealed that the given changes did not affect
more than 10-15% of the nodes (for each run) where as for
the networks which didn’t show this trend around 55%–60%
of the nodes were affected during the multiple runs. We did
also notice few spikes for Live journal and RMAT 24, but
when we took average of five runs, there were only two
occasions where we observed spikes for those networks.
We believe this could be due to load imbalance, however
the remaining three times with the same input network and
change edges the time to update decreased and there were
no spikes.
The proposed implementation is sensitive to changes
and the overall percentage of nodes being affected due to
the changes. If the percentage of nodes affected is above 80,
we do see time to update decreases but the change is not
very significant.
In Figure 9, we explore how increasing the level of
asynchrony impacts the execution time. The definition of
asynchrony is provided in Section 47. We observed that for
both 50M and 100M changes on two networks, Orkut and
RMAT-24, with edge insertion percentages of 100% and 75%,
increasing the level of asynchrony reduces the execution

11
Fig. 8: Shared-memory implementation scalability plot for the four networks: BHJ-2, Orkut, Live Journal, and RMAT-24.
Here the X-axis is the number of threads and the Y-axis is the runtime in log scale. For this experiment, we used 100M
changes and different combinations of edge insertion percentages.
Fig. 9: Shared-memory asynchronous implementation for
100M and 50M changes with different levels of asynchrony.
The X-axis is the level or length to be traversed before
synchronization, and the Y-axis is the execution time in log
scale. For this experimental setup, we used 8 threads; we
tried different thread combinations and the execution with
8 threads gave good performance.
time in all cases except for the Orkut network where 75%
of changed edges are marked for insertion.
In Figure 10, we explore how processing changed edges
in batches can help improve the performance of the pro-
posed implementation. For this experiment we took 100M
changed edges and we choose one BHJ-1 and graph-500
network and processed changed edges with (25,50, and
100)% edge insertion in batches of different sizes (15, 30, and
Fig. 10: Shared-memory implementation performance im-
provement when edges are processed in batches.
50). We compared this with our original implementation
[7], which doesn’t use any batch processing for the same
networks, change edges, and for 64 and 72 threads. We re-
peated this experiment 10 times and then took the average.
We observe that processing changed edges in batches does
show performance improvement for higher thread counts,
such as 64 and 72. For lower thread counts we did not
see significant performance improvement when edges are
processed in parallel.
7 CONCLUSION
In this paper we proposed a novel parallel framework to
update SSSP graph property for dynamic networks. The
framework was implemented on two different HPC envi-
ronments, namely a CPU-based shared memory implemen-
tation and an NVIDIA GPU-based implementation. Our
experiments on real-world and synthetic networks show
that the proposed framework performs well compared to
the re-computation based approaches (e.g., Galois for CPU
and Gunrock for GPU) when the edge insertion percentage
is 50% or more of the total changed edges. Our observation
also shows that as the number of deletions increases beyond
50%, the recomputing approach performs well.

12
In future we plan to extend our framework with a hybrid
approach where the changes for a given batch can deter-
mine which approach—recomputing or updating—would
provide faster results. Investigation of the performance for
non-random batches is one of our future interests. We also
plan to explore predictive algorithms, where knowing the
changed set apriori can lead to more optimized updates.
ACKNOWLEDGMENTS
This work is supported by the NSF OAC grants 1725755,
1725566, and 1725585 for the collaborative SANDY project.
It is also supported in part by the NSF OAC grant 1919789.
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Arindam Khanda received the BTech degree in
ECE from Institute of Engineering and Manage-
ment and the MTech degree in Software Sys-
tems from BITS Pilani in 2015 and 2019, re-
spectively. He is working toward the PhD degree
at the Missouri University of Science and Tech-
nology. His research interests include parallel
programming models, dynamic graphs and HPC.
Sriram Srinivasan obtained his Ph.D. from the University of Nebraska,
Omaha. His current research is on developing parallel scalable dynamic
graph algorithms.
Sanjukta Bhowmick is an Associate Professor
in the Computer Science and Engineering de-
partment at the University of North Texas. She
obtained her Ph.D. from the Pennsylvania State
University. She had a joint postdoc at Columbia
University and Argonne National Lab. Her cur-
rent research is on understanding change in
complex network analysis, with a focus on de-
veloping scalable algorithms for large dynamic
networks and developing uncertainty quantifica-
tion metrics for network analysis.
Boyana Norris is an Associate Professor at
the Department of Computer and Information
Science at the University of Oregon. Her re-
search interests include parallel algorithms, per-
formance modeling, automated performance op-
timization (autotuning) of parallel scientific ap-
plications, embedding of domain-specific lan-
guages into legacy codes, adaptive algorithms
for HPC, and component-based software engi-
neering for HPC.
Sajal K. Das is a professor of computer science
and Daniel St. Clair Endowed Chair at Missouri
University of Science and Technology. His re-
search interests include parallel and cloud com-
puting, sensor networks, mobile and pervasive
computing, cyber-physical systems, IoT, smart
environments, cybersecurity, biological and so-
cial networks. He serves as the Editor-in-Chief
of Pervasive and Mobile Computing journal, and
as Associate Editor of the IEEE Transactions of
Mobile Computing, IEEE Transactions on De-
pendable and Secure Computing, and ACM Transactions on Sensor
Networks. He is an IEEE Fellow.

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