Approximation Algorithms for Time Constrained Scheduling

In this paper we consider the following time constrained scheduling problem. Given a set of jobsJwith execution timese(j)?(0, 1] and an undirected graphG=(J, E), we consider the problem to find a schedule for the jobs such that adjacent jobs (j, j?)?Eare assigned to different machines and that the total execution time for each machine is at most 1. The goal is to find a minimum number of machines to execute all jobs under this time constraint. This scheduling problem is a natural generalization of the classical bin-packing problem. We propose and analyse several approximation algorithms with constant absolute worst case ratio for graphs that can be colored in polynomial time.

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