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European Symposium on Algorithms

ESA 1994: Algorithms — ESA '94 pp 148–158Cite as

Approximation algorithm on multi-way maxcut partitioning

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 855))

Abstract

Given arbitrary positive weights associated with edges, the maximum cut problem is to find a cut of the maximum cardinality (or weight in general) that partitions the graph G into X and ¯X. Our maxcut approximation algorithm runs in O(e+n) sequential time yielding a node-balanced maxcut with size at least ⌊(e+e/n)/2⌋, improving the time complexity of O(e log e) known before. Employing a height-balanced binary decomposition, an O(e+n log k) time algorithm is devised for the maxcut k-coloring problem which always finds a k-partition of vertices such that the number of bad edges (or “defected” edges with the same color on two of its end-points) does not exceed ⌈(e/k)(n−1)/n)h⌉, where h=⌈log2 k⌉, thus improving both the time complexity O(enk) and the bound ⌋e/k⌋ known before. The bound on maxcut k-coloring is also extended to find an approximation bound for the maximum k-covering problem. The relative simplicity of the algorithms and their computational economy are both keys to their practical applications. The proposed algorithms have a number of applications, for example, in VLSI design....

This work has been supported in part by the National Science Foundation under Grant MIP-9207267.

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Author information

Authors and Affiliations

  1. Samsung Electronics, Buchun Kyunggi-Do, Korea

    Jun Dong Cho

  2. Northwestern University, 60208, Evanston, IL, USA

    Salil Raje & Majid Sarrafzadeh

Authors
  1. Jun Dong Cho
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  2. Salil Raje
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  3. Majid Sarrafzadeh
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Jan van Leeuwen

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© 1994 Springer-Verlag Berlin Heidelberg

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Cho, J.D., Raje, S., Sarrafzadeh, M. (1994). Approximation algorithm on multi-way maxcut partitioning. In: van Leeuwen, J. (eds) Algorithms — ESA '94. ESA 1994. Lecture Notes in Computer Science, vol 855. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0049405

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  • DOI: https://doi.org/10.1007/BFb0049405

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58434-6

  • Online ISBN: 978-3-540-48794-4

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