The task allocation problem with constant communication Original Research Article

In the module allocation problem we are given n tasks t1,…,tn, to be executed by m processors P1,…,Pm, subject to both execution and communication costs. The cost of any assignment of the tasks to the processors is defined as the sum of the corresponding execution costs, and the communication costs for any pair of tasks assigned to distinct processors. We consider the case where all the tasks communicate with communication costs all equal to a constant c0. When the number of processors is bounded, we give two exact, polynomial-time algorithms, an elementary one for the case where the execution costs take only two distinct values and one for the general case. When the number of processors is not bounded, we obtain a polynomial-time approximation scheme. We obtain a similar algorithm when the communication graph is the edge union of a bounded number of cliques and complete bipartite graphs