Worst-Case Performance Analysis of Some Approximation Algorithms for Minimizing Makespan and Flow-Time
Data Structures and Algorithms
2013-12-18 v1 Discrete Mathematics
Combinatorics
Optimization and Control
Abstract
In 1976, Coffman and Sethi conjectured that a natural extension of LPT list scheduling to the bicriteria scheduling problem of minimizing makespan over flowtime optimal schedules, called LD algorithm, has a simple worst-case performance bound: (5m-2)/(4m-1), where m is the number of machines. We study structure of potential minimal counterexamples to this conjecture and prove that the conjecture holds for the cases (i) n > 5m, (ii) m = 2, (iii) m = 3, and (iv) m greater than or equal to 4, n less than or equal to 3m, where n is the number of jobs. We further conclude that to verify the conjecture, it suffices to analyze the following case: for every m greater than or equal to 4, n is either equal to 4m or 5m.
Keywords
Cite
@article{arxiv.1312.3345,
title = {Worst-Case Performance Analysis of Some Approximation Algorithms for Minimizing Makespan and Flow-Time},
author = {Peruvemba Sundaram Ravi and Levent Tuncel and Michael Huang},
journal= {arXiv preprint arXiv:1312.3345},
year = {2013}
}