TY - GEN
T1 - Faster exact and approximate algorithms for k-cut
AU - Gupta, Anupam
AU - Lee, Euiwoong
AU - Li, Jason
N1 - Publisher Copyright:
© 2018 IEEE.
PY - 2018/11/30
Y1 - 2018/11/30
N2 - 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) poly(n)).
AB - 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) poly(n)).
KW - Approximation algorithms
KW - Graph algorithms
KW - Minimum k-cut
KW - Parameterized algorithm
UR - http://www.scopus.com/inward/record.url?scp=85059803448&partnerID=8YFLogxK
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U2 - 10.1109/FOCS.2018.00020
DO - 10.1109/FOCS.2018.00020
M3 - Conference contribution
AN - SCOPUS:85059803448
T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
SP - 113
EP - 123
BT - Proceedings - 59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018
A2 - Thorup, Mikkel
PB - IEEE Computer Society
T2 - 59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018
Y2 - 7 October 2018 through 9 October 2018
ER -