### 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 k_{1},k_{2}, denoted VLSP(k_{1},k_{2}). 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(k_{1},k_{2}), k_{1} <k_{2}, was presented and it was claimed that the algorithm achieves the approximation ratio of 1 + (k_{1}(k_{2} - k_{1}))/k_{2}. In this paper we give a problem instance for which the same algorithm obtains the approximation ratio ≈ k_{2}/k_{1}. We then present two simple approximation algorithms, one for the case k_{1} = 1 with an approximation ratio of 2, and one for the case k_{1} > 1 with an approximation ratio of 2 + (k_{2}/2k_{1}). This corrects the result claimed in (Czumaj et al., Theoret. Comput. Sci. 262 (1-2), (2001) 569-582).

Original language | English (US) |
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Pages (from-to) | 489-495 |

Number of pages | 7 |

Journal | Theoretical Computer Science |

Volume | 302 |

Issue number | 1-3 |

DOIs | |

State | Published - Jun 13 2003 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Theoretical Computer Science*,

*302*(1-3), 489-495. https://doi.org/10.1016/S0304-3975(03)00141-5