NDLI: The vertex separator problem: algorithms and computations

Content Provider	Springer Nature Link
Author	Souza, Cid de Balas, Egon
Copyright Year	2005
Abstract	This is a companion paper to our polyhedral study [1] of the Vertex Separator (VS) Problem. Given an undirected graph G, the VS problem consists in identifying a minimum-weight vertex set whose removal disconnects G, subject to bounds on the size of the resulting components. In this paper, we describe versions of a branch-and-cut algorithm based on the results of that polyhedral study. It uses two families of cuts, symmetric and asymmetric, for which we develop polynomial-time greedy separation routines. A heuristic to generate feasible separators is also used. A computational experiment on several data sets from the literature compares the performance of three versions of our algorithm to that of the commercial MIP solver XPRESS. This experiment throws a sharp light on the role of cut density, known to software developers but never before documented in the literature. It convincingly shows that the practical usefulness of cuts in integer programming depends not only on their strength, but also on their sparsity: everything else being equal, the smaller the cut support, the better. The power of the inequalities proposed here is well illustrated by the computational tests on dense graphs. This is in accordance with the previous observation, since the support of these cuts tends to decrease with graph density.
Starting Page	609
Ending Page	631
Page Count	23
File Format	PDF
ISSN	00255610
Journal	Mathematical Programming
Volume Number	103
Issue Number	3
e-ISSN	14364646
Language	English
Publisher	Springer-Verlag
Publisher Date	2005-03-14
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mathematics of Computing Numerical Analysis Combinatorics Calculus of Variations and Optimal Control Optimization Mathematical and Computational Physics Mathematical Methods in Physics Numerical and Computational Methods Operation Research/Decision Theory
Content Type	Text
Resource Type	Article
Subject	Mathematics Software

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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