Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter (peer-reviewed) › peer-review

Published

Integer Programming and Combinatorial Optimization: Proceedings of the 7th International IPCO Conference. ed. / Gérard Cornuéjols; Rainer E. Burkard; Gerhard J. Woeginger. Berlin: Springer, 1999. p. 87-98 (Lecture Notes in Computer Science ; Vol. 1610).

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter (peer-reviewed) › peer-review

Caprara, A, Fischetti, M & Letchford, AN 1999, On the separation of maximally violated mod-k cuts. in G Cornuéjols, RE Burkard & GJ Woeginger (eds), *Integer Programming and Combinatorial Optimization: Proceedings of the 7th International IPCO Conference.* Lecture Notes in Computer Science , vol. 1610, Springer, Berlin, pp. 87-98, 7th International IPCO Conference , Graz, Austria, 9/06/99. https://doi.org/10.1007/3-540-48777-8_7

Caprara, A., Fischetti, M., & Letchford, A. N. (1999). On the separation of maximally violated mod-k cuts. In G. Cornuéjols, R. E. Burkard, & G. J. Woeginger (Eds.), *Integer Programming and Combinatorial Optimization: Proceedings of the 7th International IPCO Conference *(pp. 87-98). (Lecture Notes in Computer Science ; Vol. 1610). Springer. https://doi.org/10.1007/3-540-48777-8_7

Caprara A, Fischetti M, Letchford AN. On the separation of maximally violated mod-k cuts. In Cornuéjols G, Burkard RE, Woeginger GJ, editors, Integer Programming and Combinatorial Optimization: Proceedings of the 7th International IPCO Conference. Berlin: Springer. 1999. p. 87-98. (Lecture Notes in Computer Science ). doi: 10.1007/3-540-48777-8_7

@inbook{1f59082c3e0f4f8fa76107f6482c9ad8,

title = "On the separation of maximally violated mod-k cuts",

abstract = "Separation is of fundamental importance in cutting-plane based techniques for Integer Linear Programming (ILP). In recent decades, a considerable research effort has been devoted to the definition of effective separation procedures for families of well-structured cuts. In this paper we address the separation of Chvatal rank-1 inequalities in the context of general ILP's of the form min c^Tx : Ax <= b; x integer, where A is an m x n integer matrix and b an m-dimensional integer vector. In particular, for any given integer k we study mod-k cuts of the form (lambda^TA)x <= floor lambda^Tb floor¸ for any lambda in {0,1/2}^m such that lambda^TA is integer. Following the line of research recently proposed for mod-2 cuts by Applegate, Bixby, Chvatal and Cook, and Fleischer and Tardos, we restrict to maximally violated cuts, i.e., to inequalities which are violated by (k-1)/k by the given fractional point. We show that, for any given k, such a separation requires O(mn min{m,n}) time. Applications to the TSP are discussed.",

keywords = "integer programming, cutting planes, travelling salesman problem",

author = "A Caprara and M Fischetti and Letchford, {A N}",

note = "The full version of this paper appeared as: A. Caprara, M. Fischetti & A.N. Letchford (2000) On the separation of maximally violated mod-k cuts. Math. Program., 87(1), 37-56.; 7th International IPCO Conference ; Conference date: 09-06-1999 Through 11-06-1999",

year = "1999",

doi = "10.1007/3-540-48777-8_7",

language = "English",

isbn = "978-3-540-66019-4",

series = "Lecture Notes in Computer Science ",

publisher = "Springer",

pages = "87--98",

editor = "Cornu{\'e}jols, {G{\'e}rard } and Burkard, {Rainer E. } and Woeginger, {Gerhard J. }",

booktitle = "Integer Programming and Combinatorial Optimization",

}

TY - CHAP

T1 - On the separation of maximally violated mod-k cuts

AU - Caprara, A

AU - Fischetti, M

AU - Letchford, A N

N1 - The full version of this paper appeared as: A. Caprara, M. Fischetti & A.N. Letchford (2000) On the separation of maximally violated mod-k cuts. Math. Program., 87(1), 37-56.

PY - 1999

Y1 - 1999

N2 - Separation is of fundamental importance in cutting-plane based techniques for Integer Linear Programming (ILP). In recent decades, a considerable research effort has been devoted to the definition of effective separation procedures for families of well-structured cuts. In this paper we address the separation of Chvatal rank-1 inequalities in the context of general ILP's of the form min c^Tx : Ax <= b; x integer, where A is an m x n integer matrix and b an m-dimensional integer vector. In particular, for any given integer k we study mod-k cuts of the form (lambda^TA)x <= floor lambda^Tb floor¸ for any lambda in {0,1/2}^m such that lambda^TA is integer. Following the line of research recently proposed for mod-2 cuts by Applegate, Bixby, Chvatal and Cook, and Fleischer and Tardos, we restrict to maximally violated cuts, i.e., to inequalities which are violated by (k-1)/k by the given fractional point. We show that, for any given k, such a separation requires O(mn min{m,n}) time. Applications to the TSP are discussed.

AB - Separation is of fundamental importance in cutting-plane based techniques for Integer Linear Programming (ILP). In recent decades, a considerable research effort has been devoted to the definition of effective separation procedures for families of well-structured cuts. In this paper we address the separation of Chvatal rank-1 inequalities in the context of general ILP's of the form min c^Tx : Ax <= b; x integer, where A is an m x n integer matrix and b an m-dimensional integer vector. In particular, for any given integer k we study mod-k cuts of the form (lambda^TA)x <= floor lambda^Tb floor¸ for any lambda in {0,1/2}^m such that lambda^TA is integer. Following the line of research recently proposed for mod-2 cuts by Applegate, Bixby, Chvatal and Cook, and Fleischer and Tardos, we restrict to maximally violated cuts, i.e., to inequalities which are violated by (k-1)/k by the given fractional point. We show that, for any given k, such a separation requires O(mn min{m,n}) time. Applications to the TSP are discussed.

KW - integer programming

KW - cutting planes

KW - travelling salesman problem

U2 - 10.1007/3-540-48777-8_7

DO - 10.1007/3-540-48777-8_7

M3 - Chapter (peer-reviewed)

SN - 978-3-540-66019-4

T3 - Lecture Notes in Computer Science

SP - 87

EP - 98

BT - Integer Programming and Combinatorial Optimization

A2 - Cornuéjols, Gérard

A2 - Burkard, Rainer E.

A2 - Woeginger, Gerhard J.

PB - Springer

CY - Berlin

T2 - 7th International IPCO Conference

Y2 - 9 June 1999 through 11 June 1999

ER -