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**Fast Separation Algorithms for Three-Index Assignment Problems.** / Dokka, Trivikram; Mourtos, I; Spieksma, Frits C.r.

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter

Dokka, T, Mourtos, I & Spieksma, FCR 2012, Fast Separation Algorithms for Three-Index Assignment Problems. in A Ridha Mahjoub, V Markakis, I Milis & VT Paschos (eds), *Combinatorial optimization: Second International Symposium, ISCO 2012, Athens, Greece, April 19-21, 2012, revised selected papers.* Lecture Notes in Computer Science, vol. 7422, Springer Berlin Heidelberg, New York, pp. 189-200. https://doi.org/10.1007/978-3-642-32147-4_18

Dokka, T., Mourtos, I., & Spieksma, F. C. R. (2012). Fast Separation Algorithms for Three-Index Assignment Problems. In A. Ridha Mahjoub, V. Markakis, I. Milis, & V. T. Paschos (Eds.), *Combinatorial optimization: Second International Symposium, ISCO 2012, Athens, Greece, April 19-21, 2012, revised selected papers *(pp. 189-200). (Lecture Notes in Computer Science; Vol. 7422). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-32147-4_18

Dokka T, Mourtos I, Spieksma FCR. Fast Separation Algorithms for Three-Index Assignment Problems. In Ridha Mahjoub A, Markakis V, Milis I, Paschos VT, editors, Combinatorial optimization: Second International Symposium, ISCO 2012, Athens, Greece, April 19-21, 2012, revised selected papers. New York: Springer Berlin Heidelberg. 2012. p. 189-200. (Lecture Notes in Computer Science). https://doi.org/10.1007/978-3-642-32147-4_18

@inbook{08205b0b5af94135bb9adc373b156b41,

title = "Fast Separation Algorithms for Three-Index Assignment Problems",

abstract = "In polyhedral combinatorics, the polytope related to a combinatorial optimization problem is examined in order to obtain families of valid inequalities. To incorporate such families of inequalities within a {\textquoteleft}Branch & Cut{\textquoteright} algorithm requires one further step: that of deriving an algorithm which determines whether an inequality of a specific family is violated by a given vector (the separation problem). The idea put forward in this work is to consider a compact representation of the given vector, and measure the complexity of a separation algorithm in terms of this compact representation. We illustrate the idea on the separation of known inequalities for the three index assignment polytope. It turns out that we find new separation algorithms with better complexities than the current ones (that were called best possible).",

author = "Trivikram Dokka and I Mourtos and Spieksma, {Frits C.r.}",

year = "2012",

doi = "10.1007/978-3-642-32147-4_18",

language = "English",

isbn = "9783642321467",

series = "Lecture Notes in Computer Science",

publisher = "Springer Berlin Heidelberg",

pages = "189--200",

editor = "{Ridha Mahjoub}, A. and Vangelis Markakis and Ioannis Milis and Paschos, {Vangelis Th.}",

booktitle = "Combinatorial optimization",

}

TY - CHAP

T1 - Fast Separation Algorithms for Three-Index Assignment Problems

AU - Dokka, Trivikram

AU - Mourtos, I

AU - Spieksma, Frits C.r.

PY - 2012

Y1 - 2012

N2 - In polyhedral combinatorics, the polytope related to a combinatorial optimization problem is examined in order to obtain families of valid inequalities. To incorporate such families of inequalities within a ‘Branch & Cut’ algorithm requires one further step: that of deriving an algorithm which determines whether an inequality of a specific family is violated by a given vector (the separation problem). The idea put forward in this work is to consider a compact representation of the given vector, and measure the complexity of a separation algorithm in terms of this compact representation. We illustrate the idea on the separation of known inequalities for the three index assignment polytope. It turns out that we find new separation algorithms with better complexities than the current ones (that were called best possible).

AB - In polyhedral combinatorics, the polytope related to a combinatorial optimization problem is examined in order to obtain families of valid inequalities. To incorporate such families of inequalities within a ‘Branch & Cut’ algorithm requires one further step: that of deriving an algorithm which determines whether an inequality of a specific family is violated by a given vector (the separation problem). The idea put forward in this work is to consider a compact representation of the given vector, and measure the complexity of a separation algorithm in terms of this compact representation. We illustrate the idea on the separation of known inequalities for the three index assignment polytope. It turns out that we find new separation algorithms with better complexities than the current ones (that were called best possible).

U2 - 10.1007/978-3-642-32147-4_18

DO - 10.1007/978-3-642-32147-4_18

M3 - Chapter

SN - 9783642321467

T3 - Lecture Notes in Computer Science

SP - 189

EP - 200

BT - Combinatorial optimization

A2 - Ridha Mahjoub, A.

A2 - Markakis, Vangelis

A2 - Milis, Ioannis

A2 - Paschos, Vangelis Th.

PB - Springer Berlin Heidelberg

CY - New York

ER -