Approximation Ratio of LD Algorithm for Multi-Processor Scheduling and the Coffman-Sethi Conjecture
Abstract
Coffman and Sethi proposed a heuristic algorithm, called LD, for multi-processor scheduling, to minimize makespan over flowtime-optimal schedules. LD algorithm is a natural extension of a very well-known list scheduling algorithm, Longest Processing Time (LPT) list scheduling, to our bicriteria scheduling problem. Moreover, in 1976, Coffman and Sethi conjectured that LD algorithm has precisely the following worst-case performance bound: , where m is the number of machines. In this paper, utilizing some recent work by the authors and Huang, from 2013, which exposed some very strong combinatorial properties of various presumed minimal counterexamples to the conjecture, we provide a proof of this conjecture. The problem and the LD algorithm have connections to other fundamental problems (such as the assembly line-balancing problem) and to other algorithms.
Cite
@article{arxiv.1505.01005,
title = {Approximation Ratio of LD Algorithm for Multi-Processor Scheduling and the Coffman-Sethi Conjecture},
author = {Peruvemba Sundaram Ravi and Levent Tuncel},
journal= {arXiv preprint arXiv:1505.01005},
year = {2015}
}
Comments
This paper, building on the intermediate results in arXiv:1312.3345 (by the authors and Huang) proves that the Coffman-Sethi conjecture holds. As a result, this paper and arXIv:1312.3345 (cited in the current paper) have many definitions and mathematical statements in common, some of them in free-style text