Google Research

Beating Approximation Factor 2 for Minimum k-way Cut in Planar and Minor-free Graphs

Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), SIAM (2019), pp. 1055-1068

Abstract

The k-cut problem asks, given a connected graph G and a positive integer k, to find a minimum-weight set of edges whose removal splits G into k connected components. We give the first polynomial-time algorithm with approximation factor 2−ε (with constant ε>0) for the k-cut problem in planar and minor-free graphs. Applying more complex techniques, we further improve our method and give a polynomial-time approximation scheme for the k-cut problem in both planar and minor-free graphs. Despite persistent effort, to the best of our knowledge, this is the first improvement for the k-cut problem over standard approximation factor of 2 in any major class of graphs.

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