Worst-case performance analysis of some approximation algorithms for minimizing makespan and flowtime

• Published in: Journal of scheduling Vol. 19; no. 5; pp. 547 - 561
• Main Authors: Ravi, Peruvemba Sundaram, Tunçel, Levent, Huang, Michael
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.10.2016; Springer Nature B.V
• Subjects: Algorithms; Approximation; Artificial Intelligence; Business and Management; Calculus of Variations and Optimal Control; Optimization; Employment; Job shops; Lists; Mathematical analysis; Operations Research/Decision Theory; Optimization; Packing problem; Production scheduling; Schedules; Scheduling; Scheduling algorithms; Studies; Supply Chain Management; Texts; Work in process; Makespan; Approximation algorithms for scheduling; Total completion time; Parallel identical machines
• ISSN: 1094-6136; 1099-1425
• DOI: 10.1007/s10951-015-0467-4

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 the LD algorithm, has a simple worst-case performance bound: 5 m - 2 4 m - 1 , where m is the number of machines. We study the structure of potential minimal counterexamples to this conjecture, provide some new tools and techniques for the analysis of such algorithms, and prove that to verify the conjecture, it suffices to analyze the following case: for every m ≥ 4 , n ∈ { 4 m , 5 m } , where n is the number of jobs.