Scheduling intervals using independent sets in claw-free graphs

Authors:
Daya Ram Gaur;Ramesh Krishnamurti
Affiliations:
Dept. of Math & Computer Sc., University of Lethbridge, Lethbridge, AB, Canada;School of Computing Science, Simon Fraser University, Burnaby, BC, Canada
Venue:
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartI
Year:
2003

Citing 5
Cited 0

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Abstract

The Variable Length Scheduling Problem has been studied in the context of web searching, where the execution time for a task depends on the start time for the task. The objective is to minimize the total completion time of all the tasks. It is known that the problem is NP-Hard to approximate within a factor of nO(1). For the case when the execution times are from the set {1, 2}, the optimal execution sequence can be determined in polynomial time. Also, when the execution times are from the set {k1, k2} the problem is NP-complete and can be approximated within a ratio of 2 + k2/2k1. Here we note that the approximation ratio for the case when the execution times are from the set {k1, k2} can be improved to 2 + 2k2/5k1.