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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| Published in: | Theoretical computer science Vol. 302; no. 1; pp. 489 - 495 |
|---|---|
| Main Authors: | , , , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Amsterdam
Elsevier B.V
13.06.2003
Elsevier |
| Subjects: | |
| ISSN: | 0304-3975, 1879-2294 |
| Online Access: | Get full text |
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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
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). |
|---|---|
| AbstractList | 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). |
| Author | Zito, Michele Czumaj, Artur Krishnamurti, Ramesh Gaur, Daya Ram Rytter, Wojciech Ga̧sieniec, Leszek |
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| Keywords | Scheduling Error analysis Computer theory Approximation algorithm VLSP problem Polynomial time |
| Language | English |
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| References | Cai, Deng, Wang (BIB1) 2003; 290 Czumaj, Finch, Ga̧sieniec, Gibbons, Leng, Rytter, Zito (BIB2) 2001; 262 Czumaj (10.1016/S0304-3975(03)00141-5_BIB2) 2001; 262 Cai (10.1016/S0304-3975(03)00141-5_BIB1) 2003; 290 |
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| Title | On polynomial-time approximation algorithms for the variable length scheduling problem |
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