The Complexity of Multiterminal Cuts
SIAM Journal on Computing
The planar multiterminal cut problem
Discrete Applied Mathematics
Which problems have strongly exponential complexity?
Journal of Computer and System Sciences
Strong computational lower bounds via parameterized complexity
Journal of Computer and System Sciences
On the Optimality of Planar and Geometric Approximation Schemes
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Parameterized Complexity
FPT suspects and tough customers: open problems of downey and fellows
The Multivariate Algorithmic Revolution and Beyond
A polynomial-time algorithm for planar multicuts with few source-sink pairs
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
An o *(1.84 k) parameterized algorithm for the multiterminal cut problem
FCT'13 Proceedings of the 19th international conference on Fundamentals of Computation Theory
An O*(1.84k) parameterized algorithm for the multiterminal cut problem
Information Processing Letters
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Given a planar graph with k terminal vertices, the Planar Multiway Cut problem asks for a minimum set of edges whose removal pairwise separates the terminals from each other. A classical algorithm of Dahlhaus et al. [2] solves the problem in time nO(k), which was very recently improved to $2^{O(k)}\cdot n^{O(\sqrt{k})}$ time by Klein and Marx [6]. Here we show the optimality of the latter algorithm: assuming the Exponential Time Hypothesis (ETH), there is no $f(k)\cdot n^{o(\sqrt{k})}$ time algorithm for Planar Multiway Cut. It also follows that the problem is W[1]-hard, answering an open question of Downey and Fellows [3].