Deadlock Detection Algorithm in Operating System

If a system does not employ either a deadlock prevention or deadlock avoidance algorithm then a deadlock situation may occur. In this case- 

• Apply an algorithm to examine state of system to determine whether deadlock has occurred or not.
• Apply an algorithm to recover from the deadlock. For more refer- Deadlock Recovery

Deadlock Avoidance Algorithm/ Bankers Algorithm:
The algorithm employs several times varying data structures: 

• Available – 
  A vector of length m indicates the number of available resources of each type.
• Allocation – 
  An n*m matrix defines the number of resources of each type currently allocated to a process. Column represents resource and rows represent process.
• Request – 
  An n*m matrix indicates the current request of each process. If request[i][j] equals k then process P_i is requesting k more instances of resource type R_j.

This algorithm has already been discussed here 

Now, Bankers algorithm includes a Safety Algorithm / Deadlock Detection Algorithm 
The algorithm for finding out whether a system is in a safe state can be described as follows:

Steps of Algorithm:

1. Let Work and Finish be vectors of length m and n respectively. Initialize Work= Available. For i=0, 1, …., n-1, if Request_i = 0, then Finish[i] = true; otherwise, Finish[i]= false.
2. Find an index i such that both 
   a) Finish[i] == false
   b) Request_i <= Work
   If no such i exists go to step 4.
3. Work= Work+ Allocation_i
   Finish[i]= true
   Go to Step 2.
4. If Finish[i]== false for some i, 0<=i<n, then the system is in a deadlocked state. Moreover, if Finish[i]==false the process P_i is deadlocked.

For example, 

1. In this, Work = [0, 0, 0] & 
   Finish = [false, false, false, false, false]
   
2. i=0 is selected as both Finish[0] = false and [0, 0, 0]<=[0, 0, 0].
   
3. Work =[0, 0, 0]+[0, 1, 0] =>[0, 1, 0] & 
   Finish = [true, false, false, false, false].
   
4. i=2 is selected as both Finish[2] = false and [0, 0, 0]<=[0, 1, 0].
5. Work =[0, 1, 0]+[3, 0, 3] =>[3, 1, 3] & 
   Finish = [true, false, true, false, false].
   
6. i=1 is selected as both Finish[1] = false and [2, 0, 2]<=[3, 1, 3].
7. Work =[3, 1, 3]+[2, 0, 0] =>[5, 1, 3] & 
   Finish = [true, true, true, false, false].
   
8. i=3 is selected as both Finish[3] = false and [1, 0, 0]<=[5, 1, 3].
9. Work =[5, 1, 3]+[2, 1, 1] =>[7, 2, 4] & 
   Finish = [true, true, true, true, false].
   
10. i=4 is selected as both Finish[4] = false and [0, 0, 2]<=[7, 2, 4].
    
11. Work =[7, 2, 4]+[0, 0, 2] =>[7, 2, 6] & 
    Finish = [true, true, true, true, true].
    
12. Since Finish is a vector of all true it means there is no deadlock in this example.

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