Branch and bound algorithm for vertex bisection minimization problem

Pallavi Jain; Gur Saran; Kamal Srivastava

doi:10.1007/978-981-10-1023-1_2

Branch and bound algorithm for vertex bisection minimization problem

Pallavi Jain, Gur Saran, Kamal Srivastava

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

8 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 language	English
Title of host publication	Advanced Computing and Communication Technologies - Proceedings of the 9th ICACCT, 2015
Editors	H.A. Nagarajaram, Ramesh K. Choudhary, Jyotsna Kumar Mandal, Nitin Auluck
Publisher	Springer Verlag
Pages	17-23
Number of pages	7
ISBN (Print)	9789811010217
DOIs	https://doi.org/10.1007/978-981-10-1023-1_2
State	Published - 1 Jan 2016
Externally published	Yes
Event	9th International Conference on Advanced Computing and Communication Technologies, ICACCT 2015 - New Delhi, India Duration: 28 Nov 2015 → 29 Nov 2015

Publication series

Name	Advances in Intelligent Systems and Computing
Volume	452
ISSN (Print)	2194-5357

Conference

Conference	9th International Conference on Advanced Computing and Communication Technologies, ICACCT 2015
Country/Territory	India
City	New Delhi
Period	28/11/15 → 29/11/15

Keywords

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

ASJC Scopus subject areas

Control and Systems Engineering
General Computer Science

Access to Document

10.1007/978-981-10-1023-1_2

Cite this

Jain, P., Saran, G., & Srivastava, K. (2016). Branch and bound algorithm for vertex bisection minimization problem. In H. A. Nagarajaram, R. K. Choudhary, J. K. Mandal, & N. Auluck (Eds.), Advanced Computing and Communication Technologies - Proceedings of the 9th ICACCT, 2015 (pp. 17-23). (Advances in Intelligent Systems and Computing; Vol. 452). Springer Verlag. https://doi.org/10.1007/978-981-10-1023-1_2

Jain, Pallavi ; Saran, Gur ; Srivastava, Kamal. / Branch and bound algorithm for vertex bisection minimization problem. Advanced Computing and Communication Technologies - Proceedings of the 9th ICACCT, 2015. editor / H.A. Nagarajaram ; Ramesh K. Choudhary ; Jyotsna Kumar Mandal ; Nitin Auluck. Springer Verlag, 2016. pp. 17-23 (Advances in Intelligent Systems and Computing).

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title = "Branch and bound algorithm for vertex bisection minimization problem",

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.",

keywords = "Branch and bound, Graph layout, NP-complete, Vertex bisection, Vertex width",

author = "Pallavi Jain and Gur Saran and Kamal Srivastava",

note = "Publisher Copyright: {\textcopyright} Springer Science+Business Media Singapore 2016.; 9th International Conference on Advanced Computing and Communication Technologies, ICACCT 2015 ; Conference date: 28-11-2015 Through 29-11-2015",

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Jain, P, Saran, G & Srivastava, K 2016, Branch and bound algorithm for vertex bisection minimization problem. in HA Nagarajaram, RK Choudhary, JK Mandal & N Auluck (eds), Advanced Computing and Communication Technologies - Proceedings of the 9th ICACCT, 2015. Advances in Intelligent Systems and Computing, vol. 452, Springer Verlag, pp. 17-23, 9th International Conference on Advanced Computing and Communication Technologies, ICACCT 2015, New Delhi, India, 28/11/15. https://doi.org/10.1007/978-981-10-1023-1_2

Branch and bound algorithm for vertex bisection minimization problem. / Jain, Pallavi; Saran, Gur; Srivastava, Kamal.
Advanced Computing and Communication Technologies - Proceedings of the 9th ICACCT, 2015. ed. / H.A. Nagarajaram; Ramesh K. Choudhary; Jyotsna Kumar Mandal; Nitin Auluck. Springer Verlag, 2016. p. 17-23 (Advances in Intelligent Systems and Computing; Vol. 452).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Saran, Gur

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N2 - 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.

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ER -

Branch and bound algorithm for vertex bisection minimization problem

Abstract

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Keywords

ASJC Scopus subject areas

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