TY - GEN

T1 - On-line and off-line approximation algorithms for vector covering problems

AU - Alon, Noga

AU - Csirik, János

AU - Sevastianov, Sergey V.

AU - Vestjens, Arjen P.A.

AU - Woeginger, Gerhard J.

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1996.
Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.

PY - 1996

Y1 - 1996

N2 - This paper deals with vector covering problems in ddimensional space. The input to a vector covering problem consists of a set X of d-dimensional vectors in [0, 1] d. The goal is to partition X into a maximum number of parts, subject to the constraint that in every part the sum of all vectors is at least one in every coordinate. This problem is known to be NP-complete, and we are mainly interested in its on-line and off-line approximability. For the on-fine version, we construct approximation algorithms with worst case guarantee arbitrarily close to 1/(2d) in d ≥ 2 dimensions. This result contradicts a statement of Csirik and Freak (1990) in [5] where it is claimed that for d ≥ 2, no on-line algorithm can have a worst case ratio better than zero. For the off-fine version, we derive polynomial time approximation algorithms with worst case guarantee Ω (1/log d). For d = 2, we present a very fast and very simple off-line approximation algorithm that has worst case ratio 1/2. Moreover, we show that a method from the area of compact vector summation can be used to construct off-line approximation algorithms with worst case ratio 1/d for every d ≥ 2.

AB - This paper deals with vector covering problems in ddimensional space. The input to a vector covering problem consists of a set X of d-dimensional vectors in [0, 1] d. The goal is to partition X into a maximum number of parts, subject to the constraint that in every part the sum of all vectors is at least one in every coordinate. This problem is known to be NP-complete, and we are mainly interested in its on-line and off-line approximability. For the on-fine version, we construct approximation algorithms with worst case guarantee arbitrarily close to 1/(2d) in d ≥ 2 dimensions. This result contradicts a statement of Csirik and Freak (1990) in [5] where it is claimed that for d ≥ 2, no on-line algorithm can have a worst case ratio better than zero. For the off-fine version, we derive polynomial time approximation algorithms with worst case guarantee Ω (1/log d). For d = 2, we present a very fast and very simple off-line approximation algorithm that has worst case ratio 1/2. Moreover, we show that a method from the area of compact vector summation can be used to construct off-line approximation algorithms with worst case ratio 1/d for every d ≥ 2.

KW - Approximation algorithm

KW - Covering problem

KW - On-line algorithm

KW - Packing problem

KW - Worst case ratio

UR - http://www.scopus.com/inward/record.url?scp=0344750918&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0344750918&partnerID=8YFLogxK

U2 - 10.1007/3-540-61680-2_71

DO - 10.1007/3-540-61680-2_71

M3 - Conference contribution

AN - SCOPUS:0344750918

SN - 3540616802

SN - 9783540616801

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 406

EP - 418

BT - Algorithms - ESA 1996 - 4th Annual European Symposium, Proceedings

A2 - Diaz, Josep

A2 - Serna, Maria

PB - Springer Verlag

T2 - 4th European Symposium on Algorithms, ESA 1996

Y2 - 25 September 1996 through 27 September 1996

ER -