The task allocation problem with constant communication

• Published in: Discrete Applied Mathematics Vol. 131; no. 1; pp. 169 - 177
• Main Authors: Fernandez de la Vega, W., Lamari, M.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Lausanne Elsevier B.V 06.09.2003; Amsterdam Elsevier; New York, NY
• Subjects: Applied sciences; Combinatorics; Combinatorics. Ordered structures; Computer science; control theory; systems; Computer systems performance. Reliability; Exact sciences and technology; Graph theory; Mathematics; Operational research and scientific management; Operational research. Management science; Polynomial time approximation scheme; Scheduling; Scheduling, sequencing; Sciences and techniques of general use; Software; Polynomial time approximation scheme; Scheduling; Polynomial; Costs; Processor; Scheme; Polynomial approximation; Complete; Constant; Numerical approximation; Assignment; Allocation; Number; Optimal allocation; Bipartite graph; Communication; Edge(graph); Approximation; Complete graph; Graph clique; Graph theory; Algorithm; Cost control; Polynomial time; Problem; Communication graph; Module; Edge; Graph algorithm
• ISSN: 0166-218X; 1872-6771
• DOI: 10.1016/S0166-218X(02)00423-7

In the module allocation problem we are given n tasks t 1,…, t n , to be executed by m processors P 1,…, P m , 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 c 0. 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.