Date: 02 Jun 2005

Improved scheduling algorithms for minsum criteria

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We consider the problem of finding near-optimal solutions for a variety of NP-hard scheduling problems for which the objective is to minimize the total weighted completion time. Recent work has led to the development of several techniques that yield constant worst-case bounds in a number of settings. We continue this line of research by providing improved performance guarantees for several of the most basic scheduling models, and by giving the first constant performance guarantee for a number of more realistically constrained scheduling problems. For example, we give an improved performance guarantee for minimizing the total weighted completion time subject to release dates on a single machine, and subject to release dates and/or precedence constraints on identical parallel machines. We also give improved bounds on the power of preemption in scheduling jobs with release dates on parallel machines.

We give improved on-line algorithms for many more realistic scheduling models, including environments with parallelizable jobs, jobs contending for shared resources, tree precedence-constrained jobs, as well as shop scheduling models. In several of these cases, we give the first constant performance guarantee achieved on-line. Finally, one of the consequences of our work is the surprising structural property that there are schedules that simultaneously approximate the optimal makespan and the optimal weighted completion time to within small constants. Not only do such schedules exist, but we can find approximations to them with an on-line algorithm.

Supported partly by ARPA/DOD (DABT63-92-C-0026), DOE (DE-FG03-94ER25206), and NSF (CCR-9210260, CDA-8722788 and CDA-9401156). Part of the work was done while visiting IBM T. J. Watson Research Center.
This work was performed under U.S. Department of Energy contract number DE-AC04-76AL85000.
Supported by the graduate school Algorithmische Diskrete Mathematik (DFG), grant We 1265/2-1.
Research partially supported by NSF grant CCR-9307391.
Research partially supported by NSF Award CCR-9308701, a Walter Burke Research Initiation Award and a Dartmouth College Research Initiation Award.
Research partially supported by NSF Research Initiation Award CCR-9211494 and a grant from the New York State Science and Technology Foundation, through its Center for Advanced Technology in Telecommunications.