A combinatorial design approach to MAXCUT

  • Thomas Hofmeister
  • Hanno Lefmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1046)


The k-MAXCUT problem for undirected graphs G=(V, E) consists of finding a partition
such that the number of edges with endpoints in two different sets Vi is maximized. We offer a new approach to this problem by showing that the combinatorial notion of block designs can be used to algorithmically obtain partitions which achieve lower bounds for which until now only existence proofs were known.

In the case of k=2, we show that already known approaches can be improved by giving a simpler linear time algorithm which also yields better bounds. In particular, we give a linear time algorithm which achieves a bound of Edwards [11] which was previously proved by intricate methods.

For general k and graphs with m edges, we are able to compute partitions of size m · (k}-1)/k · (1+1/Δ) if the maximum degree Δ of G is odd. The algorithms can also be applied to weighted graphs.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Thomas Hofmeister
    • 1
  • Hanno Lefmann
    • 1
  1. 1.Lehrstuhl Informatik IIUniversität DortmundDortmundGermany

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