# Semidefinite Programming Based Algorithms for the Sparsest Cut Problem

Luis A.A. Meira; Flávio K. Miyazawa

RAIRO - Operations Research (2011)

- Volume: 45, Issue: 2, page 75-100
- ISSN: 0399-0559

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topMeira, Luis A.A., and Miyazawa, Flávio K.. "Semidefinite Programming Based Algorithms for the Sparsest Cut Problem." RAIRO - Operations Research 45.2 (2011): 75-100. <http://eudml.org/doc/276365>.

@article{Meira2011,

abstract = {
In this paper we analyze a known relaxation for the Sparsest Cut
problem based on positive semidefinite constraints, and we present a
branch and bound algorithm and heuristics based on this relaxation.
The relaxed formulation and the algorithms were tested on small and moderate
sized instances. It leads to values very close to the
optimum solution values. The exact algorithm could obtain solutions
for small and moderate sized instances, and the best heuristics
obtained optimum or near optimum solutions for all tested
instances. The semidefinite relaxation gives a lower bound
$\frac\{C\}\{W\}$ and each heuristic produces a cut S with a ratio
$\frac\{c_S\}\{w_S\}$, where either cS is at most a factor of C or
wS is at least a factor of W. We solved the semidefinite
relaxation using a semi-infinite cut generation with a commercial
linear programming package adapted to the sparsest cut problem. We
showed that the proposed strategy leads to a better performance
compared to the use of a known semidefinite programming solver.
},

author = {Meira, Luis A.A., Miyazawa, Flávio K.},

journal = {RAIRO - Operations Research},

keywords = {Semidefinite programming; Sparsest Cut; combinatorics; semidefinite programming; sparsest cut},

language = {eng},

month = {6},

number = {2},

pages = {75-100},

publisher = {EDP Sciences},

title = {Semidefinite Programming Based Algorithms for the Sparsest Cut Problem},

url = {http://eudml.org/doc/276365},

volume = {45},

year = {2011},

}

TY - JOUR

AU - Meira, Luis A.A.

AU - Miyazawa, Flávio K.

TI - Semidefinite Programming Based Algorithms for the Sparsest Cut Problem

JO - RAIRO - Operations Research

DA - 2011/6//

PB - EDP Sciences

VL - 45

IS - 2

SP - 75

EP - 100

AB -
In this paper we analyze a known relaxation for the Sparsest Cut
problem based on positive semidefinite constraints, and we present a
branch and bound algorithm and heuristics based on this relaxation.
The relaxed formulation and the algorithms were tested on small and moderate
sized instances. It leads to values very close to the
optimum solution values. The exact algorithm could obtain solutions
for small and moderate sized instances, and the best heuristics
obtained optimum or near optimum solutions for all tested
instances. The semidefinite relaxation gives a lower bound
$\frac{C}{W}$ and each heuristic produces a cut S with a ratio
$\frac{c_S}{w_S}$, where either cS is at most a factor of C or
wS is at least a factor of W. We solved the semidefinite
relaxation using a semi-infinite cut generation with a commercial
linear programming package adapted to the sparsest cut problem. We
showed that the proposed strategy leads to a better performance
compared to the use of a known semidefinite programming solver.

LA - eng

KW - Semidefinite programming; Sparsest Cut; combinatorics; semidefinite programming; sparsest cut

UR - http://eudml.org/doc/276365

ER -

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