On polynomial-time approximation algorithms for the variable length scheduling problem

  • Authors:

  • Artur Czumaj;Leszek Gasieniec;Daya Ram Gaur;Ramesh Krishnamurti;Wojciech Rytter;Michele Zito

  • Affiliations:

  • Department of Computer Science, New Jersey Institute of Technology, Newark, NJ;Department of Computer Science, University of Liverpool, Peach Street, L69 7ZF, UK;Department of Math & Computer Science, University of Lethbridge, Lethbridge, AB, Canada, T1K 3M4;School of Computing Science, Simon Fraser University, Burnaby, BC, Canada V5A 1S6;Department of Computer Science, New Jersey Institute of Technology, Newark, NJ;Department of Computer Science, University of Liverpool, Peach Street, L69 7ZF, UK

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2003

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Abstract

This paper may be viewed as a corrigendum as well as an extension of the paper by (Czumaj et al., Theoret. Comput. Sci. 262 (1-2), (2001) 569-582) where they deal with the variable length scheduling problem (VLSP) with parameters k1,k2, denoted VLSP(k1,k2). In the current paper, we first discuss an error in the analysis of one of the approximation algorithms described in (Czumaj et al., Theoret. Comput. Sci. 262 (1-2), (2001) 569-582), where an approximation algorithm for VLSP(k1,k2), k1 k2, was presented and it was claimed that the algorithm achieves the approximation ratio of 1 + (k1(k2-k1))/k2. In this paper we give a problem instance for which the same algorithm obtains the approximation ratio ≈ k2/k1. We then present two simple approximation algorithms, one for the case k1 = 1 with an approximation ratio of 2, and one for the case k1 1 with an approximation ratio of 2 + (k2/2k1). This corrects the result claimed in (Czumaj et al., Theoret. Comput. Sci. 262 (1-2), (2001) 569-582).