Faster Exact and Approximate Algorithms for k-Cut

In the k-cut problem, we are given an edge-weighted graph G and an integer k, and have to remove a set of edges with minimum total weight so that G has at least k connected components. The current best algorithms are an O(n^(2-o(1))k) randomized algorithm due to Karger and Stein, and an Õ(n^2k) dete...

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Bibliographic Details
Published in:2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS) pp. 113 - 123
Main Authors: Gupta, Anupam, Lee, Euiwoong, Li, Jason
Format: Conference Proceeding
Language:English
Published: IEEE 01.10.2018
Subjects:
Approximation algorithms
Color
Computer science
Encoding
Forestry
graph algorithms
Heuristic algorithms
minimum k-cut
parameterized algorithm
Runtime
ISSN:2575-8454
Online Access:Get full text
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Summary:In the k-cut problem, we are given an edge-weighted graph G and an integer k, and have to remove a set of edges with minimum total weight so that G has at least k connected components. The current best algorithms are an O(n^(2-o(1))k) randomized algorithm due to Karger and Stein, and an Õ(n^2k) deterministic algorithm due to Thorup. Moreover, several 2-approximation algorithms are known for the problem (due to Saran and Vazirani, Naor and Rabani, and Ravi and Sinha). It has remained an open problem to (a) improve the runtime of exact algorithms, and (b) to get better approximation algorithms. In this paper we show an O(k^O(k) n^(2Ω/3 + o(1))k)-time algorithm for k-cut. Moreover, we show an (1+ε)-approximation algorithm that runs in time O((k/ε)^O(k) n^k + O(1)), and a 1.81-approximation in fixed-parameter time O(2^O(k^2) poly(n)).
ISSN:2575-8454
DOI:10.1109/FOCS.2018.00020