Branch and bound algorithm for vertex bisection minimization problem

Pallavi Jain, Gur Saran, Kamal Srivastava

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

6 Scopus citations

Abstract

Vertex Bisection Minimization problem (VBMP) consists of partitioning the vertex set V of a graph G = (V, E) into two sets B and B′ where |B| = ⎿|V|/2⏌ such that its vertex width (VW) is minimized. Vertex width is defined as the number of vertices in B which are adjacent to at least one vertex in B′. It is an NP-complete problem in general but polynomially solvable for trees and hypercubes. VBMP has applications in fault tolerance and is related to the complexity of sending messages to processors in interconnection networks via vertex disjoint paths. In this paper, we propose a branch and bound algorithm for VBMP which uses a greedy heuristic to determine upper bound for the vertex width. We have devised a strategy to obtain lower bounds on the vertex width of partial solutions. A tree pruning procedure which reduces the size of search tree is also incorporated into the algorithm. This algorithm has been experimented on selected benchmark graphs. Results indicate that except for five of the selected graphs, the algorithm is able to, run through the search tree very fast.

Original languageEnglish
Title of host publicationAdvanced Computing and Communication Technologies - Proceedings of the 9th ICACCT, 2015
EditorsH.A. Nagarajaram, Ramesh K. Choudhary, Jyotsna Kumar Mandal, Nitin Auluck
PublisherSpringer Verlag
Pages17-23
Number of pages7
ISBN (Print)9789811010217
DOIs
StatePublished - 1 Jan 2016
Externally publishedYes
Event9th International Conference on Advanced Computing and Communication Technologies, ICACCT 2015 - New Delhi, India
Duration: 28 Nov 201529 Nov 2015

Publication series

NameAdvances in Intelligent Systems and Computing
Volume452
ISSN (Print)2194-5357

Conference

Conference9th International Conference on Advanced Computing and Communication Technologies, ICACCT 2015
Country/TerritoryIndia
CityNew Delhi
Period28/11/1529/11/15

Keywords

  • Branch and bound
  • Graph layout
  • NP-complete
  • Vertex bisection
  • Vertex width

ASJC Scopus subject areas

  • Control and Systems Engineering
  • General Computer Science

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