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Minimum Bisection

  • Reference work entry
  • First Online:
Encyclopedia of Algorithms

  • 725 Accesses

Years and Authors of Summarized Original Work

  • 1999; Feige, Krauthgamer

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-Bisectiona logarithmic-factor bicriteria approximation algorithm. (A bicriteria approximation algorithm partitions the vertices into two sets each...

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Recommended Reading

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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 Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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© 2016 Springer Science+Business Media New York

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Krauthgamer, R. (2016). Minimum Bisection. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_231

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