Abstract
This paper considers the minimization of the maximum lateness for a set of dependent tasks with unit duration, unit communication delays release times and due dates. The number of processors is limited, and each task requires one processor for its execution. A time window built from an upper bound of the minimum maximum lateness is associated to each task. The parameter considered is the pathwidth of the associated interval graph. A fixed-parameter algorithm based on a dynamic programming approach is developed to solve this optimization problem. This is, as far as we know, the first fixed-parameter algorithm for a scheduling problem with communication delays and a limited number of processors.
Subject
Management Science and Operations Research,Computer Science Applications,Theoretical Computer Science
Reference26 articles.
1. New MIP model for multiprocessor scheduling problem with communication delays
2. W[2]-hardness of precedence constrained K-processor scheduling
3. Chrétienne P. and Picouleau C., Scheduling with communication delays: a survey, in Scheduling Theory and its Applications. John Wiley & Sons, New York (1995) 65–90.
4. Cygan M., Fomin F.V., Kowalik Ł., Lokshtanov D., Marx D., Pilipczuk M., Pilipczuk M. and Saurabh S., Parameterized Algorithms, 1st edition. Springer Publishing Company, Incorporated (2015).