Solving planar k-terminal cut in O(nc√k) time

Authors:
Philip N. Klein;Dániel Marx
Affiliations:
Computer Science Department, Brown University, Providence, RI;Computer and Automation Research Institute, Hungarian Academy of Sciences (MTA SZTAKI), Budapest, Hungary
Venue:
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Year:
2012

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Abstract

The problem Planark-Terminal Cut is as follows: given an undirected planar graph with edge-costs and with k vertices designated as terminals, find a minimum-cost set of edges whose removal pairwise separates the terminals. It was known that the complexity of this problem is O(n2k−4logn). We show that there is a constant c such that the complexity is $O(n^{c\sqrt{k}})$. This matches a recent lower bound of Marx showing that the $c\sqrt{k}$ term in the exponent is best possible up to the constant c (assuming the Exponential Time Hypothesis).