Scheduling in the presence of processor networks : complexity and approximation.
RAIRO-OPERATIONS RESEARCH(2012)
Abstract
In this paper, we study the problem of makespan minimization for the multiprocessor scheduling problem in the presence of communication delays. The communication delay between two tasks i and j depends on the distance between the two processors on which these two tasks are executed. Lahlou shows that a simple polynomial-time algorithm exists when the length of the schedule is at most two (the problem becomes NP-complete when the length of the schedule is at most three). We prove that there is no polynomial-time algorithm with a performance guarantee of less than 4/3 (unless P = NP) to minimize the makespan when the network topology is a chain or ring and the precedence graph is a bipartite graph of depth one. We also develop two polynomial-time approximation algorithms with constant ratio dedicated to cases where the processor network admits a limited or unlimited number of processors.
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Key words
Scheduling,non-approximability,processor network model
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