Two semi-online scheduling problems on two uniform machines

Chi To Ng, Zhiyi Tan, Yong He, Edwin Tai Chiu Cheng

Research output: Journal article publicationJournal articleAcademic researchpeer-review

13 Citations (Scopus)

Abstract

This paper considers two semi-online scheduling problems, one with known optimal value and the other with known total sum, on two uniform machines with a machine speed ratio of s ≥ 1. For the first problem, we provide an optimal algorithm for s ∈ [frac(1 + sqrt(3), 2), frac(1 + sqrt(21), 4)], and improved algorithms or/and lower bounds for s ∈ [frac(1 + sqrt(21), 4), sqrt(3)], over which the optimal algorithm is unknown. As a result, the largest gap between the competitive ratio and the lower bound decreases to 0.02192. For the second problem, we also present algorithms and lower bounds for s ≥ 1. The largest gap between the competitive ratio and the lower bound is 0.01762, and the length of the interval over which the optimal algorithm is unknown is 0.47382. Our algorithms and lower bounds for these two problems provide insights into their differences, which are unusual from the viewpoint of the known results on these two semi-online scheduling problems in the literature.
Original languageEnglish
Pages (from-to)776-792
Number of pages17
JournalTheoretical Computer Science
Volume410
Issue number8-10
DOIs
Publication statusPublished - 1 Mar 2009

Keywords

  • Analysis of algorithm
  • Competitive ratio
  • Scheduling
  • Semi-online

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this