Hard equality constrained integer knapsacks

K.I. Aardal, A.K. Lenstra

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

18 Citations (Scopus)
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We consider the following integer feasibility problem: "Given positive integer numbers a 0, a 1,..., a n, with gcd(a 1,..., a n) = 1 and a = (a 1,..., a n), does there exist a nonnegative integer vector x satisfying ax = a 0?" Some instances of this type have been found to be extremely hard to solve by standard methods such as branch-and-bound, even if the number of variables is as small as ten. We observe that not only the sizes of the numbers a 0, a 1,..., a n, but also their structure, have a large impact on the difficulty of the instances. Moreover, we demonstrate that the characteristics that make the instances so difficult to solve by branch-and-bound make the solution of a certain reformulation of the problem almost trivial. We accompany our results by a small computational study.
Original languageEnglish
Title of host publicationProceedings 9th IPCO (Cambridge MA, USA, May 27-29, 2002)
EditorsW.J. Cook, A.S. Schulz
Place of PublicationBerlin
ISBN (Print)3-540-43676-6
Publication statusPublished - 2002

Publication series

NameLecture Notes in Computer Science
ISSN (Print)0302-9743


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