Computer Science > Data Structures and Algorithms
[Submitted on 17 Oct 2014 (v1), last revised 17 Jul 2016 (this version, v2)]
Title:A Multilevel Bilinear Programming Algorithm For the Vertex Separator Problem
View PDFAbstract:The Vertex Separator Problem for a graph is to find the smallest collection of vertices whose removal breaks the graph into two disconnected subsets that satisfy specified size constraints. In the paper https://doi.org/10.1016/j.ejor.2014.05.042, the Vertex Separator Problem was formulated as a continuous (non-concave/non-convex) bilinear quadratic program. In this paper, we develop a more general continuous bilinear program which incorporates vertex weights, and which applies to the coarse graphs that are generated in a multilevel compression of the original Vertex Separator Problem. A Mountain Climbing Algorithm is used to find a stationary point of the continuous bilinear quadratic program, while second-order optimality conditions and perturbation techniques are used to escape from either a stationary point or a local maximizer. The algorithms for solving the continuous bilinear program are employed during the solution and refinement phases in a multilevel scheme. Computational results and comparisons demonstrate the advantage of the proposed algorithm.
Submission history
From: Ilya Safro [view email][v1] Fri, 17 Oct 2014 23:07:50 UTC (43 KB)
[v2] Sun, 17 Jul 2016 20:21:07 UTC (64 KB)
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