Quasipolynomial Multicut-mimicking Networks and Kernels for Multiway Cut Problems
Article No.: 15, Pages 1 - 19
Abstract
We show the existence of an exact mimicking network of kO(log k) edges for minimum multicuts over a set of terminals in an undirected graph, where k is the total capacity of the terminals, i.e., the sum of the degrees of the terminal vertices. Furthermore, using the best available approximation algorithm for Small Set Expansion, we show that a mimicking network of kO(log3 k) edges can be computed in randomized polynomial time. As a consequence, we show quasipolynomial kernels for several problems, including Edge Multiway Cut, Group Feedback Edge Set for an arbitrary group, and Edge Multicut parameterized by the solution size and the number of cut requests. The result combines the matroid-based irrelevant edge approach used in the kernel for s-Multiway Cut with a recursive decomposition and sparsification of the graph along sparse cuts. This is the first progress on the kernelization of Multiway Cut problems since the kernel for s-Multiway Cut for constant value of s (Kratsch and Wahlström, FOCS 2012).
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- Quasipolynomial Multicut-mimicking Networks and Kernels for Multiway Cut Problems
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Publication History
Published: 04 March 2022
Accepted: 01 November 2021
Revised: 01 November 2021
Received: 01 February 2021
Published in TALG Volume 18, Issue 2
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