Abstract
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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Hofmeister, T., Lefmann, H. (1996). A combinatorial design approach to MAXCUT. In: Puech, C., Reischuk, R. (eds) STACS 96. STACS 1996. Lecture Notes in Computer Science, vol 1046. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60922-9_36
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DOI: https://doi.org/10.1007/3-540-60922-9_36
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