Deadlock Detection Algorithm

Introduction
What are Deadlocks ? ‘ Any blocked process which cannot be
resolved unless there is some outside intervention’.
In operating system deadlocks can be visualized where processes
have some resources held by them and are waiting for some resources
to fulfill their completion which are instead being held by some other
blocked process.
A very simple real-world example is of the two cars halted on
both sides of a bridge which has only width for one car to pass. As both
cars are holding each end of the bridge so neither can pass unless and
until one car backs up and clears the road so that the other car pass and
vice versa.

Deadlock Classification
Mutual Exclusion : If one process is holding a resource required by other
processes that resource must wait until it is released by the process.
Hold and Wait : Processes are allowed to hold one or more resources and
waiting for additional resources held by other processes.
No Pre-Emption : Resources are released voluntarily, neither another process
nor the OS can force a process to release a resource.
Circular Wait : There may exist a set of waiting processes such that P0 is
waiting for a resource held by P1, P1 is waiting for a resource held by P2,… Pn-
1 is waiting for a resource held by Pn, and Pn is waiting for a resource held by
P0.

Resource Allocation Graph
We can model deadlock conditions using a directed graph called a Resource Allocation Graph (RAG).
Lets understand some basics:
Two Kinds of Nodes :
Boxes : Represent Resources
Circles : Represent Processes
Two Kinds of (Directed) Edges:
Request Edge : from thread to resource, indicates that the thread has requested the resource and is
waiting to acquire it.
Assignment Edge : from resource instance to thread, indicates the thread is holding the resource
instance.
When a request is made, a request edge is added
On fulfillment the request edge is transformed into and assignment edge.
When a resource is released by a process, the assignment edge is deleted.

RAG with Single Resource Instance
R1 R2 R1 R2
P1 P2 P3
R3 R4
P1 P2 P3
R3 R4
A closed cycle in RAG with single resource instance is mandatory for deadlock.

RAG with Multiple Resource Instances
R1 R2 R1 R2
P1 P2 P3
R3 R4
P1 P2 P3
R3 R4
A Knot is mandatory for a deadlock. (Knot is created when strongly connected
subgraphs with no outgoing edges are formed).

Prevention and Avoidance
Prevention by eliminating one of the four conditions
Acquire all resources before proceeding (No wait while Hold)
Allow Preemption (Eliminate 3d Condition)
Prioritize Processes and Assign Resources in order of Priorities (No Circular
Wait)
Avoidance can be done by allowing resource requests only if they don’t lead to
deadlock condition. In other words, Safe state : An order to entertain resource
requests so that all processes can be completed.
Drawbacks:
Resource requirements for all processes must be known in advance.
Resource request set is known and fixed,
Complex Analysis for every request.

Deadlock Detection
Detection :
Issues
Maintenance of WFG (Wait for Graphs)
Search of WFG for deadlocks
Requirements
Progress No undetected deadlocks
Safety No false(phantom) deadlocks
Resolution
Roll Back one or more processes to break dependencies in WFG to resolve the
situation.

Single Instance for Each
Resource Type
Maintain wait-for Graph
Nodes are processes
Pi-> Pj if Pi is waiting for Pj
Periodically invoke an algorithm that searches for a cycle in the graph. If
there is a cycle then there is or will be a deadlock.
An algorithm to detect a cycle in graph requires an order of n2
Operations, where n is the number of vertices in the graph.

RAG& WFG
R1 R4
P1 P2 P3
P5
R3
P4 R5
R2
P1 P2 P3
P5
P4
Corresponding Wait for Graph
Resource Allocation Graph

Several Instances of a Resource
Type
Available : A vector of length m indicates the number of available
resources of each type.
Allocation: An n x m matrix defines the number of resources of each type
currently allocated to each process.
Request: An n x m matrix indicates the current request of each process.
If Request[ij]=k, then process Pi is requesting k more instances of
resource type Rj.

Detection Algorithm
1. Let Work and Finish be vectors of length m and n, respectively
Initialize :
(a) Work=Available
(b) For i=1,2,…,n if Allocationi ≠ 0, then
Finish[i]=false; otherwise, Finish[i]=true.
2. Find an index i such that both:
(a) Finish[i]==false
(b) Requesti≤ Work
3. Work = Work +Allocationi
Finish[i]=true
go to step 2.
4. If Finish[i]==false, for some i, 1 ≤i ≤n, then the system is in the deadlock
state. Moreover, if Finish[i]==false, then Piis deadlocked.
Algorithm requires an order of O(m x n2) operations to detect whether the system is in
deadlocked state.

Example of Detection Algorithm
Five processes Po through P4; three resource types A(7 instances), B(2
instances), and C(6 instances).
Snapshot at time T0:
Allocation Request Available
A B C A B C A B C
P0 0 1 0 0 0 0 0 0 0
P1 2 0 0 2 0 2
P2 3 0 3 0 0 0
P3 2 1 1 1 0 0
P4 0 0 2 0 0 2
Sequence <P0,P1,P2,P3,P4>will result in Finish[i]=true for all i.

P2 request an additional instance of type C.
Request
A B C
P0 0 0 0
P1 2 0 1
P2 0 0 1
P3 1 0 0
P4 0 0 2
State of System?
Can reclaim resources held by process P0, but insufficient
resources to fulfill other processes; requests.
Deadlock exists, consisting of processes P1,P2,P3 and P4.

Detection-Algorithm Usage
When, and how often, to invoke depends on:
How often a deadlock is likely to occur?
How many processes will need to be rolled back?
One for each disjoint cycle.
If detection algorithm is invoked arbitrarily, there may be many cycles in
the resource graph and so we would not be able to tell which of the
many deadlocked processes “caused” the deadlock.

Deadlock Detection Algorithm

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