Linear and quadratic programming approaches for the general graph partitioning problem

Neng Fan, Panos M. Pardalos

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

The graph partitioning problem is to partition the vertex set of a graph into a number of nonempty subsets so that the total weight of edges connecting distinct subsets is minimized. Previous research requires the input of cardinalities of subsets or the number of subsets for equipartition. In this paper, the problem is formulated as a zero-one quadratic programming problem without the input of cardinalities. We also present three equivalent zero-one linear integer programming reformulations. Because of its importance in data biclustering, the bipartite graph partitioning is also studied. Several new methods to determine the number of subsets and the cardinalities are presented for practical applications. In addition, hierarchy partitioning and partitioning of bipartite graphs without reordering one vertex set, are studied.

Original languageEnglish (US)
Pages (from-to)57-71
Number of pages15
JournalJournal of Global Optimization
Volume48
Issue number1
DOIs
StatePublished - Sep 2010
Externally publishedYes

Fingerprint

Graph Partitioning
Quadratic programming
Integer programming
Quadratic Programming
Linear programming
Subset
Cardinality
Bipartite Graph
Partitioning
Biclustering
Equipartition
Reordering
Integer Linear Programming
Zero
Vertex of a graph
Reformulation
Partition
Graph
Distinct
Graph in graph theory

Keywords

  • Bipartite graph partitioning
  • Graph partitioning
  • Linear programming
  • Quadratic programming

ASJC Scopus subject areas

  • Computer Science Applications
  • Control and Optimization
  • Applied Mathematics
  • Management Science and Operations Research

Cite this

Linear and quadratic programming approaches for the general graph partitioning problem. / Fan, Neng; Pardalos, Panos M.

In: Journal of Global Optimization, Vol. 48, No. 1, 09.2010, p. 57-71.

Research output: Contribution to journalArticle

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