Task assignment approach
- 1. There are two nodes, {N1, n2} and six tasks {T1, t2, T3, t4, t5, t6}. There are two task assignment parameters – the task execution cost (xab the cost of executing task a on node b) and the inter-task communication cost (cij the inter-task communication cost between tasks i and j). Inter-task communication cost Execution costs T1 T1 0 t2 6 T3 4 t4 0 t5 0 t6 12 Nodes N1 n2 t2 6 0 8 12 3 0 T1 5 10 T3 4 8 0 0 11 0 t2 2 ∞ t4 0 12 0 0 5 0 T3 4 4 t5 0 3 11 5 0 0 t4 6 3 t6 12 0 0 0 0 0 t5 5 2 t6 ∞ 4 Task t6 cannot be executed on node N1 and task t2 cannot be executed on node n2 since the resources they need are not available on these nodes.
- 2. Serial assignment, where tasks T1, t2, T3 are assigned to node N1 and tasks t4, t5, t6 are assigned to node n2: Execution cost: x = x11 + x21 + x31 + x42 + x52 + x62 = 5 + 2 + 4 + 3 + 2 + 4 = 20 Communication cost,: c = c14 + c15 + c16 + c24 + c25 + c26 + c34 + c35 + c36 = 0 + 0 + 12 + 12 + 3 + 0 + 0 + 11 + 0 = 38. Hence total cost =20+38= 58. Optimal assignment, where tasks T1, t2, t3, t4, t5 are assigned to node n1 and task t6 is assigned to node n2. Execution cost: x = x11 + x21 + x31 + x41 + x51 + x62= 5 + 2 + 4 + 6 + 5 + 4 = 26 Communication cost: c = c16 + c26 + c36 + c46 + c56= 12 + 0 + 0 + 0 + 0 = 12 Total cost = 38
- 3. • Optimal assignments are found by first creating a static assignment graph. • In this graph, the weights of the edges joining pairs of task nodes represent inter- task communication costs. • The weight on the edge joining a task (say t1)to node n1 represents the execution cost of that task on node n2 (say 10)and vice-versa. • Then we determine a minimum cutset in this graph. A cutset is defined to be a set of edges such that when these edges are removed, the nodes of the graph are partitioned into two disjoint subsets such that nodes in one subset are reachable from N1 and the nodes in the other are reachable from n2. Each task node is reachable from either N1 or n2. The weight of a cutset is the sum of the weights of the edges in the cutset. This sums up the execution and communication costs for that assignment. An optimal assignment is found by finding a minimum cutset.