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

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 disc...

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Vydané v:Theoretical computer science Ročník 302; číslo 1; s. 489 - 495
Hlavní autori: Czumaj, Artur, Ga̧sieniec, Leszek, Gaur, Daya Ram, Krishnamurti, Ramesh, Rytter, Wojciech, Zito, Michele
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Amsterdam Elsevier B.V 13.06.2003
Elsevier
Predmet:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Computer science; control theory; systems
Computer systems performance. Reliability
Exact sciences and technology
Software
Theoretical computing
Scheduling
Error analysis
Computer theory
Approximation algorithm
VLSP problem
Polynomial time
ISSN:0304-3975, 1879-2294
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Shrnutí: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 2/2 k 1). This corrects the result claimed in (Czumaj et al., Theoret. Comput. Sci. 262 (1–2), (2001) 569–582).
ISSN:0304-3975
1879-2294
DOI:10.1016/S0304-3975(03)00141-5