Efficient algorithms for integer programs with two variables per constraint

Reuven Bar-Yehuda; Dror Rawitz

doi:10.1007/3-540-48481-7_11

Efficient algorithms for integer programs with two variables per constraint

Reuven Bar-Yehuda, Dror Rawitz

Technion-Israel Institute of Technology

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Given a bounded integer program with n variables and m constraints each with 2 variables we present an O(mU) time and O(m) space feasibility algorithm for such integer programs (where U is the maximal variable range size). We show that with the same complexity we can find an optimal solution for the positively weighted minimization problem for monotone systems. Using the localratio technique we develop an O(nmU) time and O(m) space 2-approximation algorithm for the positively weighted minimization problem for the general case. We further generalize all results to non linear constraints (called axis-convex constraints) and to non linear (but monotone) weight functions. Our algorithms are not only better in complexity than other known algorithms, but they are also considerably simpler, and contribute to the understanding of these very fundamental problems.

Original language	English
Title of host publication	Algorithms - ESA 1999 - 7th Annual European Symposium, Proceedings
Editors	Jaroslav Nešetřil
Publisher	Springer Verlag
Pages	116-126
Number of pages	11
ISBN (Print)	3540662510, 9783540662518
DOIs	https://doi.org/10.1007/3-540-48481-7_11
State	Published - 1999
Externally published	Yes
Event	7th Annual European Symposium on Algorithms, ESA 1999 - Prague, Czech Republic Duration: 16 Jul 1999 → 18 Jul 1999

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	1643
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	7th Annual European Symposium on Algorithms, ESA 1999
Country/Territory	Czech Republic
City	Prague
Period	16/07/99 → 18/07/99

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1999.

Keywords

2SAT
Approximation algorithm
Combinatorial optimization
Integer programming
Local ratio technique
Vertex cover

Access to Document

10.1007/3-540-48481-7_11

Cite this

Bar-Yehuda, R., & Rawitz, D. (1999). Efficient algorithms for integer programs with two variables per constraint. In J. Nešetřil (Ed.), Algorithms - ESA 1999 - 7th Annual European Symposium, Proceedings (pp. 116-126). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1643). Springer Verlag. https://doi.org/10.1007/3-540-48481-7_11

Bar-Yehuda, Reuven ; Rawitz, Dror. / Efficient algorithms for integer programs with two variables per constraint. Algorithms - ESA 1999 - 7th Annual European Symposium, Proceedings. editor / Jaroslav Nešetřil. Springer Verlag, 1999. pp. 116-126 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Bar-Yehuda, R & Rawitz, D 1999, Efficient algorithms for integer programs with two variables per constraint. in J Nešetřil (ed.), Algorithms - ESA 1999 - 7th Annual European Symposium, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1643, Springer Verlag, pp. 116-126, 7th Annual European Symposium on Algorithms, ESA 1999, Prague, Czech Republic, 16/07/99. https://doi.org/10.1007/3-540-48481-7_11

Efficient algorithms for integer programs with two variables per constraint. / Bar-Yehuda, Reuven; Rawitz, Dror.
Algorithms - ESA 1999 - 7th Annual European Symposium, Proceedings. ed. / Jaroslav Nešetřil. Springer Verlag, 1999. p. 116-126 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1643).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Bar-Yehuda R, Rawitz D. Efficient algorithms for integer programs with two variables per constraint. In Nešetřil J, editor, Algorithms - ESA 1999 - 7th Annual European Symposium, Proceedings. Springer Verlag. 1999. p. 116-126. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-48481-7_11

Efficient algorithms for integer programs with two variables per constraint

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