On the Complexity of Separation: The Three-Index Assignment Problem

25 Pages Posted: 23 Oct 2012

See all articles by Trivikram Dokka

Trivikram Dokka

Katholieke Universiteit Leuven - Faculty of Business and Economics (FBE)

Ioannis Mourtos

Athens University of Economics and Business - Department of Management Science and Technology

Frits Spieksma

Catholic University of Leuven (KUL)

Date Written: 2012

Abstract

A fundamental step in any cutting plane algorithm is separation: deciding whether a violated inequality exists within a certain class of inequalities. It is customary to express the complexity of a separation algorithm in n, the number of variables. Here, we argue that the input to a separation algorithm can be expressed in jsup(x)j, where sup(x) denotes the vector containing the positive components of x. This input measure allows one to take sparsity into account. We apply this idea to two known classes of valid inequalities for the three-index assignment problem, and we find separation algorithms with a better complexity than the ones known in literature. We also show empirically the performance of our separation algorithms.

Suggested Citation

Dokka, Trivikram and Mourtos, Ioannis and Spieksma, Frits, On the Complexity of Separation: The Three-Index Assignment Problem (2012). Available at SSRN: https://ssrn.com/abstract=2165756 or http://dx.doi.org/10.2139/ssrn.2165756

Trivikram Dokka (Contact Author)

Katholieke Universiteit Leuven - Faculty of Business and Economics (FBE) ( email )

Naamsestraat 69
Leuven, B-3000
Belgium

Ioannis Mourtos

Athens University of Economics and Business - Department of Management Science and Technology ( email )

Athens GR-11362
Greece

Frits Spieksma

Catholic University of Leuven (KUL) ( email )

Leuven, B-3000
Belgium

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