Semi on-line algorithms for the partition problem

  • Authors:

  • Hans Kellerer;Vladimir Kotov;Maria Grazia Speranza;Zsolt Tuza

  • Affiliations:

  • Institut für Statistik, Ökonometrie und Operations Research, Universität Graz, Universitätsstraíe 15, A-8010 Graz, Austria;Faculty of Applied Mathematics and Computer Science, University of Minsk, Minsk, 220080, Byelarussia, Russia;Dipartimento Metodi Quantitativi, Universití degli Studi di Brescia, Facoltí di Economia e Commercio, Corso Mameli 27, I-25122 Brescia, Italy;Computer and Automation Institute, Hungarian Academy of Sciences, H-1111 Budapest, Kende u. 13-17, Hungary

  • Venue:
  • Operations Research Letters
  • Year:
  • 1997

Quantified Score

Hi-index 0.01

Visualization

Abstract

The partition problem is one of the basic NP-complete problems. While an efficient heuristic for the optimization version, which is equivalent to minimizing the makespan on two identical machines, is known with worst-case ratio 1211, no deterministic heuristic for the on-line problem can have a worst-case ratio lower than 32. In this paper we investigate three different semi on-line versions of the partition problem. In the first case, we assume that a buffer of length k is available to maintain k items. In the second case, two parallel processors are available which assign each item independently to the partition sets. The best of the two produced solutions is chosen. Finally, in the third problem the total sum of the items is known in advance. For each version we propose a heuristic and investigate its worst-case ratio. All algorithms have a worst-case ratio of 43 which is shown to be the best possible worst-case ratio.