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Minimum Bisection

1999; Feige, Krauthgamer

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Encyclopedia of Algorithms

Keywords and Synonyms

Graph bisection          

Problem Definition

Overview

Minimum bisection is a basic representative of a family of discrete optimization problems dealing with partitioning the vertices of an input graph. Typically, one wishes to minimize the number of edges going across between the different pieces, while keeping some control on the partition, say by restricting the number of pieces and/or their size. (This description corresponds to an edge-cut of the graph; other variants correspond to a vertex-cut with similar restrictions.) In the minimum bisection problem, the goal is to partition the vertices of an input graph into two equal-size sets, such that the number of edges connecting the two sets is as small as possible.

In a seminal paper in 1988, Leighton and Rao [14] devised for Minimum-Bisection a logarithmic-factor bicriteria approximation algorithm.Footnote 1Their algorithm has found numerous applications, but the question of finding a true approximation with a similar...

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Notes

  1. 1.

    A bicriteria approximation algorithm partitions the vertices into two sets each containing at most 2/3 of the vertices, and its value, i. e. the number of edges connecting the two sets, is compared against that of the best partition into equal-size sets.

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Author information

Authors and Affiliations

  1. Weizmann Institute of Science, Rehovot, Israel

    Robert Krauthgamer

  2. IBM Almaden Research Center, San Jose, CA, USA

    Robert Krauthgamer

Authors
  1. Robert Krauthgamer
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer ScienceMcCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL, 60208, USA

    Ming-Yang Kao Professor of Computer Science

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© 2008 Springer-Verlag

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Krauthgamer, R. (2008). Minimum Bisection. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_231

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