Distributed Algorithms

 Conflict prevention. Read-modify-write can be thought as a particular
Distributed Algorithms in NoSQL Databases case of transaction, so distributed locking or consensus protocols like
Scalability is one of the main drivers of the NoSQL movement. As such, it PAXOS [20, 21] are both a solution. This is a generic technique
encompasses distributed system coordination, failover, resource management that can support both atomic read-modify-write semantics and
and many other capabilities. It sounds like a big umbrella, and it is. Although it arbitrary isolated transactions. An alternative approach is to prevent
can hardly be said that NoSQL movement brought fundamentally new distributed concurrent writes entirely and route all writes of a
techniques into distributed data processing, it triggered an avalanche of particular data item to a single node (master). To prevent conflicts,
practical studies and real-life trials of different combinations of protocols and a database must sacrifice availability in case of network partitioning
algorithms. These developments gradually highlight a system of relevant and stop all but one partition.
database building blocks with proven practical efficiency. In this article I’m  Conflict detection. A database track concurrent conflicting updates
trying to provide more or less systematic description of techniques related to and either rollback one of the conflicting updates or preserve both
distributed operations in NoSQL databases. versions for resolving on the client side. Concurrent updates are
In the rest of this article we study a number of distributed activities like typically tracked by using vector clocks [19] (which can be though as
replication of failure detection that could happen in a database. These activities, a generalization of the optimistic locking) or by preserving an entire
highlighted in bold below, are grouped into three major sections: version history. This approach is used in systems like Riak,
 Data Consistency. Historically, NoSQL paid a lot of attention to Voldemort, CouchDB.
tradeoffs between consistency, fault-tolerance and performance to serve Now let’s take a closer look at commonly used replication techniques and
geographically distributed systems, low-latency or highly available classify them in accordance with the described properties. The first figure
applications. Fundamentally, these tradeoffs spin around data consistency, so below depicts logical relationships between different techniques and their
this section is devoted data replication and data repair. coordinates in the system of the consistency-scalability-availability-latency
 Data Placement. A database should accommodate itself to different data tradeoffs. The second figure illustrates each technique in detail.
distributions, cluster topologies and hardware configurations. In this section
we discuss how to distribute or rebalance data in such a way that failures
are handled rapidly, persistence guarantees are maintained, queries are
efficient, and system resource like RAM or disk space are used evenly
throughout the cluster.
 System Coordination. Coordination techniques like leader election are
used in many databases to implements fault-tolerance and strong data
consistency. However, even decentralized databases typically track their
global state, detect failures and topology changes. This section describes
several important techniques that are used to keep the system in a coherent
state.
Data Consistency
It is well known and fairly obvious that in geographically distributed systems or
other environments with probable network partitions or delays it is not
generally possible to maintain high availability without sacrificing consistency
because isolated parts of the database have to operate independently in case of
network partition. This fact is often referred to as the CAP theorem. However,
consistency is a very expensive thing in distributed systems, so it can be traded
not only to availability. It is often involved into multiple tradeoffs. To study
these tradeoffs, we first note that consistency issues in distributed systems are
induced by the replication and the spatial separation of coupled data, so we
have to start with goals and desired properties of the replication:
 Availability. Isolated parts of the database can serve read/write requests
in case of network partition.
 Read/Write latency. Read/Write requests are processes with a minimal
latency.
 Read/Write scalability. Read/Write load can be balanced across multiple
nodes.
 Fault-tolerance. Ability to serve read/write requests does not depend on
availability of any particular node.
 Data persistence. Node failures within certain limits do not cause data
loss.
 Consistency. Consistency is a much more complicated property than the
previous ones, so we have to discuss different options in detail. It beyond this
article to go deeply into theoretical consistency and concurrency models, so
we use a very lean framework of simple properties.
o Read-Write consistency. From the read-write perspective, the basic goal
of a database is to minimize a replica convergence time (how long does it
take to propagate an update to all replicas) and guarantee eventual
consistency. Besides these weak guarantees, one can be interested in
stronger consistency properties:
 Read-after-write consistency. The effect of a write operation on data item
X, will always be seen by a successive read operation on X.
 Read-after-read consistency. If some client reads the value of a data item
X, any successive read operation on X will always return that same or a
more recent value.
o Write-Write consistency. Write-write conflicts appear in case of database
partition, so a database should either handle these conflicts somehow or
guarantee that concurrent writes will not be processed by different partitions.
From this perspective, a database can offer different consistency models:
 Atomic Writes. If a database provides an API where a write request can
only be an independent atomic assignment of a value, one possible way
to avoid write-write conflicts is to pick the “most recent” version of each
entity. This guarantees that all nodes will end up with the same version
of data irrespectively to the order of updates which can be affected by
network failures and delays. Data version can be specified by a
timestamps or application-specific metric. This approach is used for
example in Cassandra.
 Atomic Read-modify-write. Applications often do a read-modify-write
sequence instead of independent atomic writes. If two clients read the
same version of data, modify it and write back concurrently, the latest
update will silently override the first one in the atomic writes model.
This behavior can be semantically inappropriate (for example, if both
clients add a value to a list). A database can offer at least two solutions:

Replication factor 4. It is assumed that read/write coordinator can be either an becomes visible to the readers as soon as it appears on at least one node.
external client or a proxy node within a database. Network partitions of course can lead to violation of this guarantee.
Let’s go through all these techniques moving from weak to strong consistency  (G, Master-Slave) The techniques above are often used to provide either
guarantees: Atomic Writes or Read-modify-write with Conflict Detection consistency
 (A, Anti-Entropy) Weakest consistency guarantees are provided by the levels. To achieve a Conflict Prevention level, one has to use a kind of
following strategy. Writer updates any arbitrary selected replica. Reader reads
any replica and sees the old data until a new version is not propagated via centralization or locking. A simplest strategy is to use master-slave
background anti-entropy protocol (more on anti-entropy protocols in the next asynchronous replication. All writes for a particular data item are routed to a
section). The main properties of this approach are: central node that executes write operations sequentially. This makes master a
o High propagation latency makes it quite impractical for data bottleneck, so it becomes crucial to partition data into independent shards to
synchronization, so it is typically used only as an auxiliary background be scalable.
process that detects and repairs unplanned inconsistencies. However,  (H, Transactional Read Quorum Write Quorum and Read One Write All)
databases like Cassandra use anti-entropy as a primary way to propagate Quorum approach can also be reinforced by transactional techniques to
information about database topology and other metadata. prevent write-write conflicts. A well-known approach is to use two-phase
o Consistency guarantees are poor: write-write conflicts and read-write commit protocol. However, two-phase commit is not perfectly reliable
discrepancies are very probable even in absence of failures.
o Superior availability and robustness against network partitions. This because coordinator failures can cause resource blocking. PAXOS commit
schema provides good performance because individual updates are replaced protocol [20, 21] is a more reliable alterative, but with a price or performance
by asynchronous batch processing. penalty. A small step forward and we end up with the Read One Write All
o Persistence guarantees are weak because new data are initially stored on approach where writes update all replicas in a transactional fashion. This
a single replica. approach provides strong fault-tolerant consistency but with a price of
 (B) An obvious improvement of the previous schema is to send an performance and availability.
update to all (available) replicas asynchronously as soon as the update request It is worth noting that the analysis above highlights a number of tradeoffs:
hits any replica. It can be considered as a kind of targeted anti-entropy.  Consistency-availability tradeoff. This strict tradeoff is formalized by
o In comparison with pure anti-entropy, this greatly improves consistency the CAP theorem. In case of network partition, a database should either stop
with a relatively small performance penalty. However, formal consistency
and persistence guarantees remain the same. all partitions except one or accept the possibility of data conflicts.
o If some replica is temporary unavailable due to network failures or node  Consistency-scalability tradeoff. One can see that even read-write
failure/replacement, updates should be eventually delivered to it by the consistency guarantees impose serious limitations on a replica set scalability,
anti-entropy process. and write-write conflicts can be handled in a relatively scalable fashion only
 (C) In the previous schema, failures can be handled better using the in the Atomic Writes model. The Atomic Read-modify-write model
hinted handoff technique [8]. Updates that are intended for unavailable nodes introduces short casual dependencies between data and this immediately
are recorded on the coordinator or any other node with a hint that they should requires global locking to prevent conflicts. This shows that even a slight
be delivered to a certain node as soon as it will become available. This spatial or casual dependency between data entries or operations could kill
improves persistence guarantees and replica convergence time.
 (D, Read One Write One) Since the carrier of hinted handoffs can fail scalability, so separation of data into independent shards and careful data
before deferred updates were propagated, it makes sense to enforce modeling is extremely important for scalability.
consistency by so-called read repairs. Each read (or randomly selected reads)  Consistency-latency tradeoff. As it was shown above, there exists a
triggers an asynchronous process that requests a digest (a kind of tendency to Read-All and Write-All techniques when strong consistency or
signature/hash) of the requested data from all replicas and reconciles persistence guarantees are provides by a database. These guarantees are
inconsistencies if detected. We use term ReadOne-WriteOne for combination clearly in inverse proportion to requests latency. Quorum techniques are a
of techniques A, B, C and D – they all do not provide strict consistency middle ground.
guarantees, but are efficient enough to be used in practice as an self-contained  Failover-consistency/scalability/latency tradeoff. It is interesting that
approach. contention between failover and consistency/scalability/latency is not really
 (E, Read Quorum Write Quorum) The strategies above are heuristic severe. Failures of up to N/2 nodes can often be tolerated with reasonable
enhancements that decrease replicas convergence time. To provide guarantees
beyond eventual consistency, one has to sacrifice availability and guarantee performance/consistency penalty. However, this tradeoff is visible, for
an overlap between read and write sets. A common generalization is to write example, in the difference between 2-phase commit and PAXOS protocols.
synchronously W replicas instead of one and touch R replicas during reading. Another example of this tradeoff is ability to lift certain consistency
o First, this allows one to manage persistence guarantees setting W>1. guarantees like read-your-writes using sticky sessions which complicate
o Second, this improves consistency for R+W>N because synchronously failover [22].
written set will overlap with the set that is contacted during reading (in the
figure above W=2, R=3, N=4), so reader will touch at least one fresh replica Anti-Entropy Protocols, Gossips
and select it as a result. This guarantees consistency if read and write Let us start our study with the following problem statement:
requests are issued sequentially (e.g. by one client, read-your-writes There is a set of nodes and each data item is replicated to a subset of nodes.
consistency), but do not guarantee global read-after-read consistency. Each node serves update requests even if there is no network connection to
Consider an example in the figure below to see why reads can be other nodes. Each node periodically synchronizes its state with other nodes is
inconsistent. In this example R=2, W=2, N=3. However, writing of two such a way that if no updates take place for a long time, all replicas will
replicas is not transactional, so clients can fetch both old and new values
gradually become consistent. How this synchronization should be organized –
until writing is not completed:
when synchronization is triggered, how a peer to synchronize with is chosen,
what is the data exchange protocol? Let us assume that two nodes can always
merge their versions of data selecting a newest version or preserving both
versions for further application-side resolution.
This problem appears both in data consistency maintenance and in
synchronization of a cluster state (propagation of the cluster membership
information and so on). Although the problem above can be solved by means of
a global coordinator that monitors a database and builds a global
synchronization plan or schedule, decentralized databases take advantage of
more fault-tolerant approach. The main idea is to use well-studied epidemic
protocols [7] that are relatively simple, provide a pretty good convergence time,
o Different values of R and W allows to trade write latency and persistence and can tolerate almost any failures or network partitions. Although there are
to read latency and vice versa. different classes of epidemic algorithms, we focus on anti-entropy protocols
o Concurrent writers can write to disjoint quorums if W<=N/2. Setting because of their intensive usage in NoSQL databases.
W>N/2 guarantees immediate conflict detection in Atomic Anti-entropy protocols assume that synchronization is performed by a fixed
Read-modify-write with rollbacks model. schedule – every node regularly chooses another node at random or by some
o Strictly speaking, this schema is not tolerant to network partitions, rule and exchanges database contents, resolving differences. There are three
although it tolerates failures of separate nodes. In practice, heuristics like flavors of anti-entropy protocols: push, pull, and push-pull. The idea of the
sloppy quorum [8] can be used to sacrifice consistency provided by a push protocol is to simply select a random peer and push a current state of data
standard quorum schema in favor of availability in certain scenarios. to it. In practice, it is quite silly to push the entire database, so nodes typically
 (F, Read All Write Quorum) The problem with read-after-read work in accordance with the protocol which is depicted in the figure below.
consistency can be alleviated by contacting all replicas during reading (reader
can fetch data or check digests). This ensures that a new version of data

and C and increment operation was applied 3 times, once per node. If A pulls
value from B and adds it to the local copy, C pulls from B, C pulls from A, then
C ends up with value 4 which is incorrect. One possible way to overcome these
issues is to use a data structure similar to vector clock [19] and maintain a pair
of counters for each node [1]:
class Counter {
int[] plus
int[] minus
int NODE_ID
increment() plus[NODE_ID]++
decrement() minus[NODE_ID]++
get() return sum(plus) – sum(minus)
merge(Counter other)
for i in 1..MAX_ID {
plus[i] = max(plus[i], other.plus[i])
minus[i] = max(minus[i], other.minus[i])
}
}
Cassandra uses a very similar approach to provide counters as a part of its
functionality [11]. It is possible to design more complex eventually consistent
data structures that can leverage either state-based or operation-based
replication principles. For example, [1] contains a catalog of such structures
that includes:
 Counters (increment and decrement operations)
Node A which is initiator of synchronization prepares a digest (a set of  Sets (add and remove operations)
checksums) which is a fingerprint of its data. Node B receives this digest,  Graphs (addEdge/addVertex, removeEdge/removeVertex operations)
determines the difference between the digest and its local data and sends a  Lists (insertAt(position) and removeAt(position) operations)
digest of the difference back to A. Finally, A sends an update to B and B However, eventually consistent data types are often limited in functionality and
updates itself. Pull and push-pull protocols work similarly, as it shown in the impose performance overheads.
figure above.
Anti-entropy protocols provide reasonable good convergence time and
Data Placement
This section is dedicated to algorithms that control data placement inside a
scalability. The following figure shows simulation results for propagation of an
distributed database. These algorithms are responsible for mapping between
update in the cluster of 100 nodes. On each iteration, each node contacts one
data items and physical nodes, migration of data from one node to another and
randomly selected peer.
global allocation of resources like RAM throughout the database.
Rebalancing
Let us start with a simple protocol that is aimed to provide outage-free data
migration between cluster nodes. This task arises in situations like cluster
expansion (new nodes are added), failover (some node goes done), or
rebalancing (data became unevenly distributed across the nodes). Consider a
situation that is depicted in the section (A) of the figure below – there are three
nodes and each node contains a portion of data (we assume a key-value data
model without loss of generality) that is distributed across the nodes according
to an arbitrary data placement policy:

One can see that the pull style provides better convergence than the push, and
this can be proven theoretically [7]. Also, push has a problem with a
“convergence tail” when a small percent of nodes remains unaffected during
many iterations, although almost all nodes are already touched. The Push-Pull
approach greatly improves efficiency in comparison with the original push or
pulls techniques, so it is typically used in practice. Anti-entropy is scalable
because the average conversion time grows as a logarithmic function of the
cluster size.
Although these techniques look pretty simple, there are many studies [5]
regarding performance of anti-entropy protocols under different constraints.
One can leverage knowledge of the network topology to replace a random peer
selection by a more efficient schema [10]; adjust transmit rates or use advanced
rules to select data to be synchronized if the network bandwidth is limited [9]. If one does not have a database that supports data rebalancing internally, he
Computation of digest can also be challenging, so a database can maintain a probably will deploy several instances of the database to each node as it is
journal of the recent updates to facilitate digests computing. shown in the section (B) of the figure above. This allows one to perform a
manual cluster expansion by turning a separate instance off, copying it to a new
Eventually Consistent Data Types node, and turning it on, as it is shown in the section (C). Although an automatic
In the previous section we assumed that two nodes can always merge their database is able to track each record separately, many systems including
versions of data. However, reconciliation of conflicting updates is not a trivial MongoDB, Oracle Coherence, and upcoming Redis Cluster use the described
task and it is surprisingly difficult to make all replicas to converge to a technique internally, i.e. group records into shards which are minimal units of
semantically correct value. A well-known example is that deleted items can migration for sake of efficiency. It is quite obvious that a number of shards
resurface in the Amazon Dynamo database [8]. should be quite large in comparison with the number of nodes to provide the
Let us consider a simple example that illustrates the problem: a database even load distribution. An outage-free shard migration can be done according to
maintains a logically global counter and each database node can serve the simple protocol that redirects client from the exporting to the importing
increment/decrement operations. Although each node can maintain its own node during a migration of the shard. The following figure depicts a state
local counter as a single scalar value, but these local counters cannot be merged machine for get(key) logic as it going to be implemented in Redis Cluster:
by simple addition/subtraction. Consider an example: there are 3 nodes A, B,

Consistent hashing is basically a mapping schema for key-value store – it maps
keys (hashed keys are typically used) to physical nodes. A space of hashed keys
is an ordered space of binary strings of a fixed length, so it is quite obvious that
each range of keys is assigned to some node as it depicted in the figure (A) for
3 nodes, namely, A, B, and C. To cope with replication, it is convenient to close
a key space into a ring and traverse it clockwise until all replicas are mapped, as
it shown in the figure (B). In other words, item Y should be placed on node B
because its key corresponds to B’s range, first replica should be placed on C,
second replica on A and so on.
The benefit of this schema is efficient addition and removal of a node because it
causes data rebalancing only in neighbor sectors. As it shown in the figures (C),
addition of the node D affects only item X but not Y. Similarly, removal (or
failure) of the node B affects Y and the replica of X, but not X itself. However,
as it was pointed in [8], the dark side of this benefit is vulnerability to overloads
– all the burden of rebalancing is handled by neighbors only and makes them to
replicate high volumes of data. This problem can be alleviated by mapping each
node not to a one range, but to a set of ranges, as it shown in the figure (D).
This is a tradeoff – it avoids skew in loads during rebalancing, but keeps the
total rebalancing effort reasonably low in comparison with module-based
mapping.
It is assumed that each node knows a topology of the cluster and is able to map Maintenance of a complete and coherent vision of a hashing ring may be
any key to a shard and a shard to a cluster node. If the node determines that the problematic in very large deployments. Although it is not a typical problem for
requested key belongs to a local shard, then it looks it up locally (the upper databases because of relatively small clusters, it is interesting to study how data
square in the picture above). If the node determines that the requested key placement was combined with the network routing in peer-to-peer networks. A
belongs to another node X, than it sends a permanent redirection command to good example is the Chord algorithm [2] that trades completeness of the ring
the client (the lower square in the figure above). Permanent redirection means vision by a single node to efficiency of the query routing. The Chord algorithm
that the client is able to cache the mapping between the shard and the node. If is similar to consistent hashing in the sense that it uses a concept of a ring to
the shard migration is in progress, the exporting and the importing nodes mark
map keys to nodes. However, a particular node maintains only a short list of
this shard accordingly and start to move its records locking each record
separately. The exporting node first looks up the key locally and, if not found, peers with exponentially growing offset on the logical ring (see the picture
redirects the client to the importing node assuming that key is already migrated. below). This allows one to locate a key in several network hops using a kind of
This redirect is a one-time and should not be cached. The importing node binary search:
processes redirects locally, but regular queries are permanently redirected until
migration is not completed.
Sharding and Replication in Dynamic Environments
The next question we have to address is how to map records to physical nodes.
A straightforward approach is to have a table of key ranges where each range is
assigned to a node or to use procedures like NodeID = hash(key) % TotalNodes.
However, modulus-based hashing does not explicitly address cluster
reconfiguration because addition or removal of nodes causes complete data
reshuffling throughout the cluster. As a result, it is difficult to handle
replication and failover.
There are different ways to enhance the basic approach from the replication and
failover perspectives. The most famous technique is a consistent hashing. There
are many descriptions of the consistent hashing technique in the web, so I
provide a basic description just for sake of completeness. The following figure
depicts the basic ideas of consistent hashing:

This figure depicts a cluster of 16 nodes and illustrates how node A looks up a
key that is physically located on node D. Part (A) depicts the route and part (B)
depicts partial visions of the ring for nodes A, B, and C. More information
about data replication in decentralized systems can be found in [15].
Multi-Attribute Sharding
Although consistent hashing offers an efficient data placement strategy when
data items are accessed by a primary key, things become much more complex
when querying by multiple attributes is required. A straightforward approach
(that is used, for example, in MongoDB) is to distribute data by a primary key
regardless to other attributes. As a result, queries that restrict the primary key
can be routed to a limited number of nodes, but other queries have to be
processed by all nodes in the cluster. This skew in query efficiency leads us to
the following problem statement:
There is a set of data items and each item has a set of attributes along with
their values. Is there a data placement strategy that limits a number of nodes
that should be contacted to process a query that restricts an arbitrary subset of
the attributes?
One possible solution was implemented in the HyperDex database. The basic
idea is to treat each attribute as an axis in a multidimensional space and map
blocks in the space to physical nodes. A query corresponds to a hyperplane that
intersects a subset of blocks in the space, so only this subset of blocks should
be touched during the query processing. Consider the following example from
[6]:

Each data item is a user account that is attributed by First Name, Last Name,
and Phone Number. These attributes are treated as a three-dimensional space
and one possible data placement strategy is to map each octant to a dedicated
physical node. Queries like “First Name = John” correspond to a plane that
intersects 4 octants, hence only 4 nodes should be involved into processing.
Queries that restrict two attributes correspond to a line that intersects two
octants as it shown in the figure above, hence only 2 nodes should be involved The gray arrows highlight replication of shards from node #2. Shards from the
into processing. other nodes are replicated symmetrically. The red arrows depict how the
The problem with this approach is that dimensionality of the space grows as an passivated replicas will be loaded into RAM in case of failure of node #2. Even
exponential function of the attributes count. As a result, queries that restrict distribution of replicas throughout the cluster allows one to have only a small
only a few attributes tend to involve many blocks and, consequently, involve memory reserve that will be used to activate replicas in case of failure. In the
many servers. One can alleviate this by splitting one data item with multiple figure above, the cluster is able to survive a single node failure having only 1/3
attributes into multiple sub-items and mapping them to the several independent of RAM in reserve. It is worth noting that replica activation (loading from disk
subspaces instead of one large hyperspace: to RAM) takes some time and cause temporally performance degradation or
outage of the corresponding data during failure recovery.
System Coordination
In this section we discuss a couple of techniques that relates to system
coordination. Distributed coordination is an extremely large area that was a
subject of intensive study during several decades. In this article, we, of course,
consider only a couple of applied techniques. A comprehensive description of
distributed locking, consensus protocols and other fundamental primitives can
be found in numerous books or web resources [17, 18, 21].
Failure Detection
Failure detection is a fundamental component of any fault tolerant distributed
system. Practically all failure detection protocols are based on a heartbeat
messages which are a pretty simple concept – monitored components
periodically send a heartbeat message to the monitoring process (or the
monitoring process polls monitored components) and absence of heartbeat
messages for a long time is interpreted as a failure. However, real distributed
systems impose a number of additional requirements that should be addressed:
 Automatic adaptation. Failure detection should be robust to the
temporary network failures and delays, dynamic changes in the cluster
topology, workload or bandwidth. This is a fundamentally difficult problem
because there is no way to distinguish crashed process from a slow one [13].
As a result, failure detection is always a tradeoff between a failure detection
time (how long does it take to detect a real failure) and the false-alarm
probability. Parameters of this tradeoff should be adjusted dynamically and
automatically.
 Flexibility. At first glance, failure detector should produce a boolean
This provides more narrowed query-to-nodes mapping, but complicates output, a monitored process considered to be either live or dead. Nevertheless,
coordination because one data item becomes scattered across several it can be argued that boolean output is insufficient in practice. Let us consider
an example from [12] that resembles Hadoop MapReduce. There is a
independent subspaces with their own physical locations and transactional
distributed application that consists of a master and several workers. The
updates become required. More information about this technique and master has a list of jobs and submits them to the workers. The master can
implementation details can be found in [6]. distinguish different “degrees of failure”. If the master starts to suspect that
Passivated Replicas some worker went down, it stops to submit new jobs to this worker. Next, as
time goes by and there are no heartbeat messages, the master resubmits jobs
Some applications with heavy random reads can require all data to fit RAM. In
that were running on this worker to the other workers. Finally, the master
these cases, sharding with independent master-slave replication of each replica becomes completely confident that the worker is down and releases all
(like in MongoDB) typically requires at least double amount of RAM because corresponding resources.
each chunk of data is stored both on a master and on a slave. A slave should  Scalability and robustness. Failure detection as a system process should
have the same amount of RAM as a master in order to replace the master in scale up as well as the system does. It also should be robust and consistent, i.e.
case of failure. However, shards can be placed in such a way that amount of all nodes in the system should have a consistent view of running and failed
required RAM can be reduced, assuming that the system tolerates short-time processes even in case of communication problems.
outages or performance degradation in case of failures. A possible way to address the first two requirements is so-called Phi Accrual
The following figure depicts 4 nodes that host 16 shards, primary copies are Failure Detector [12] that is used with some modifications in Cassandra [16].
The basic workflow is as follows (see the figure below):
stored in RAM and replicas are stored on disk:
 For each monitored resource, Detector collects arrival times Ti of
heartbeat messages.
 Mean and variance are constantly computed for the recent arrival times
(on a sliding window of size W) in the Statistics Estimation block.

 Assuming that distribution of arrival times is known (the figure below 1. Initially five nodes are in the cluster and node 5 is a globally accepted
contains a formula for normal distribution), one can compute the probability coordinator.
of the current heartbeat delay (difference between the current time t_now and 2. Let us assume that node 5 goes down and nodes 3 and 2 detect this
the last arrival time Tc). This probability is a measure of confidence in a simultaneously. Both nodes start election procedure and send election
failure. As suggested in [12], this value can be rescaled using the logarithmic
messages to the nodes with greater IDs.
function for sake of usability. In this case output 1 means that the likeness of
the mistake is about 10%, output 2 means 1% and so on. 3. Node 4 kicks out nodes 2 and 3 from the competition by sending OK.
Node 3 kicks out node 2.
4. Imagine that node 1 detects failure of 5 now and an election message to
the all nodes with greater IDs.
5. Nodes 2, 3, and 4 kick out node 1.
6. Node 4 sends an election message to node 5.
7. Node 5 does not respond, so node 4 declares itself as a coordinator and
announce this fact to all other peers.

Coordinator election process can count a number of nodes that participate in it
The scalability requirement can be addressed in significant degree by and check that at least a half of cluster nodes are attend. This guarantees that
hierarchically organized monitoring zones that prevent flooding of the network only one partition can elect a coordinator in case of network partition.
with heartbeat messages [14] and synchronization of different zones via gossip
protocol or central fault-tolerant repository. This approach is illustrated below
References
1. M. Shapiro et al. A Comprehensive Study of Convergent and
(there are two zones and all six failure detectors talk to each other via gossip Commutative Replicated Data Types
protocol or robust repository like ZooKeeper): 2. I. Stoica et al. Chord: A Scalable Peer-to-peer Lookup Service for
Internet Applications
3. R. J. Honicky, E.L.Miller. Replication Under Scalable Hashing: A
Family of Algorithms for Scalable Decentralized Data Distribution
4. G. Shah. Distributed Data Structures for Peer-to-Peer Systems
5. A. Montresor, Gossip Protocols for Large-Scale Distributed Systems
6. R. Escriva, B. Wong, E.G. Sirer. HyperDex: A Distributed, Searchable
Key-Value Store
7. A. Demers et al. Epidemic Algorithms for Replicated Database
Maintenance
8. G. DeCandia, et al. Dynamo: Amazon’s Highly Available Key-value
Store
9. R. van Resesse et al. Efficient Reconciliation and Flow Control for
Anti-Entropy Protocols
10. S. Ranganathan et al. Gossip-Style Failure Detection and Distributed
Consensus for Scalable Heterogeneous Clusters
11. http://www.slideshare.net/kakugawa/distributed-counters-in-cassandra-c
assandra-summit-2010
12. N. Hayashibara, X. Defago, R. Yared, T. Katayama. The Phi Accrual
Coordinator Election Failure Detector
Coordinator election is an important technique for databases with strict 13. M.J. Fischer, N.A. Lynch, and M.S. Paterson. Impossibility of
consistency guarantees. First, it allows one to organize failover of a master Distributed Consensus with One Faulty Process
node in master-slave systems. Second, it allows one to prevent write-write 14. N. Hayashibara, A. Cherif, T. Katayama. Failure Detectors for
conflicts in case of network partition by terminating partitions that do not Large-Scale Distributed Systems
15. M. Leslie, J. Davies, and T. Huffman. A Comparison Of Replication
include a majority of nodes.
Strategies for Reliable Decentralised Storage
Bully algorithm is a relatively simple approach to coordinator election. 16. A. Lakshman, P.Malik. Cassandra – A Decentralized Structured Storage
MongoDB uses a version of this algorithm to elect leaders in replica sets. The System
main idea of the bully algorithm is that each member of the cluster can declare 17. N. A. Lynch. Distributed Algorithms
itself as a coordinator and announce this claim to other nodes. Other nodes can 18. G. Tel. Introduction to Distributed Algorithms
either accept this claim or reject it by entering the competition for being a 19. http://basho.com/blog/technical/2010/04/05/why-vector-clocks-are-hard/
coordinator. Node that does not face any further contention becomes a 20. L. Lamport. Paxos Made Simple
coordinator. Nodes use some attribute to decide who wins and who loses. This 21. J. Chase. Distributed Systems, Failures, and Consensus
attribute can be a static ID or some recency metric like the last transaction ID 22. W. Vogels. Eventualy Consistent – Revisited
23. J. C. Corbett et al. Spanner: Google’s Globally-Distributed Database
(the most up-to-date node wins).
An example of the bully algorithm execution is shown in the figure below.
Static ID is used as a comparison metric, a node with a greater ID wins.

Distributed Algorithms

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