New Competitive Analysis Results of Online List Scheduling Algorithm

TL;DR

This paper presents new upper bounds on the competitive ratio of Graham's online list scheduling algorithm for independent jobs, improving understanding of its performance in specific input scenarios.

Contribution

It introduces two novel upper bounds on the competitive ratio of LSA for particular classes of input sequences, advancing theoretical analysis.

Findings

Upper bound of 2 - 2/m on competitive ratio

Upper bound of 2 - (m^2 - m + 1)/m^2 on competitive ratio

Results motivate designing improved online scheduling algorithms

Abstract

Online algorithm has been an emerging area of interest for researchers in various domains of computer science. The online $m$-machine list scheduling problem introduced by Graham has gained theoretical as well as practical significance in the development of competitive analysis as a performance measure for online algorithms. In this paper, we study and explore the performance of Graham's online \textit{list scheduling algorithm(LSA)} for independent jobs. In the literature, \textit{LSA} has already been proved to be $2-\frac{1}{m}$ competitive, where $m$ is the number of machines. We present two new upper bound results on competitive analysis of \textit{LSA}. We obtain upper bounds on the competitive ratio of $2-\frac{2}{m}$ and $2-\frac{m^2-m+1}{m^2}$ respectively for practically significant two special classes of input job sequences. Our analytical results can motivate the practitioners to design improved competitive online algorithms for the $m$-machine list scheduling problem by characterization of real life input sequences.