Paper Info
Title
A Multilevel Bilinear Programming Algorithm For the Vertex Separator Problem.
Abstract
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. The Vertex Separator Problem was formulated in the paper 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. We develop a method for improving upon a given vertex separator by applying a Mountain Climbing Algorithm to the bilinear program using an incidence vector for the separator as a starting guess. Sufficient conditions are developed under which the algorithm can improve upon the starting guess after at most two iterations. The refinement algorithm is augmented with a perturbation technique to enable escapes from local optima and is embedded in a multilevel framework for solving large scale instances of the problem. The multilevel algorithm is shown through computational experiments to perform particularly well on communication and collaboration networks.
Year
DOI
Venue
2014
https://doi.org/10.1007/s10589-017-9945-2
Computational Optimization and Applications
Keywords
Field
DocType
Vertex separator,Continuous formulation,Graph partitioning,Multilevel,Weighted edge contractions,Multilevel algorithm,90C35,90C27,90C20,90C06
Discrete mathematics,Combinatorics,Vertex (geometry),Vertex (graph theory),Algorithm,Reachability,Vertex separator,Vertex cover,Bilinear program,Mathematics,Feedback vertex set,Bilinear interpolation
Journal
Volume
Issue
ISSN
abs/1410.4885
1
0926-6003
Citations 
PageRank 
References 
4
0.41
19
Authors
3
Name
Order
Citations
PageRank
William W. Hager11603214.67
James T. Hungerford2111.57
Ilya Safro322625.29