Efficient Algorithms for Integer Programs with Two Variables per Constraint

Authors:
Reuven Bar-Yehuda;Dror Rawitz
Affiliations:
-;-
Venue:
ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
Year:
1999

Citing 2
Cited 1

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A graph based simplex method for the integer minimum perturbation problem with sum and difference constraints

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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.