Worst-Case Analysis of LPT Scheduling on Small Number of Non-Identical Processors

TL;DR

This paper determines tight approximation ratios for the LPT scheduling algorithm on small sets of non-identical processors, specifically for three, four, and five processors, extending known results from identical processors.

Contribution

It provides the first tight approximation ratios for LPT on 3, 4, and 5 non-identical processors, matching the lower bounds by Gonzalez, Ibarra, and Sahni.

Findings

Approximate ratios: 1.38 for 3 processors

Approximate ratios: 1.43 for 4 processors

Approximate ratios: 1.46 for 5 processors

Abstract

The approximation ratio of the longest processing time (LPT) scheduling algorithm has been studied in several papers. While the tight approximation ratio is known for the case when all processors are identical, the ratio is not yet known when the processors have different speeds. In this work, we give a tight approximation ratio for the case when the number of processors is 3,4, and 5. We show that the ratio for those cases are no more than the lower bound provided by Gonzalez, Ibarra, and Sahni (SIAM J. Computing 1977). They are approximately 1.38 for three processors, 1.43 for four processors, and 1.46 for five processors.