Approximation algorithm on multi-way maxcut partitioning

  • Jun Dong Cho
  • Salil Raje
  • Majid Sarrafzadeh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 855)


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=⌈log2k⌉, 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....


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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Jun Dong Cho
    • 1
  • Salil Raje
    • 2
  • Majid Sarrafzadeh
    • 2
  1. 1.Samsung ElectronicsBuchun Kyunggi-DoKorea
  2. 2.Northwestern UniversityEvanstonUSA

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