Improved Parameterized and Exact Algorithms for Cut Problems on Trees

Authors

Iyad Kanj, DePaul University
Guohui Lin, University of AlbertaFollow
Tian Liu, Peking UniversityFollow
Weitian Tong, Georgia Southern UniversityFollow
Ge Xia, Lafayette College
Jinhui Xu, State University of New York at Buffalo
Boting Yang, University of Regina
Fenghui Zhang, Google Kirkland
Peng Zhang, Shandong University
Binhai Zhu, Montana State University

Document Type

Article

Publication Date

11-23-2015

Publication Title

Theoretical Computer Science

DOI

10.1016/j.tcs.2015.06.010

ISSN

0304-3975

Abstract

We study the Multicut on Trees and the Generalized Multiway Cut on Trees problems. For the Multicut on Trees problem, we present a parameterized algorithm that runs in time O ∗(ρk), where ρ = √√2 + 1 < 1.554 is the positive root of the polynomial x4 − 2x2 − 1. This improves the current-best algorithm of Chen et al. that runs in time O ∗(1.619k). For the Generalized Multiway Cut on Trees problem, we show that this problem is solvable in polynomial time if the number of terminal sets is fixed; this answers an open question posed in a recent paper by Liu and Zhang. By reducing the Generalized Multiway Cut on Trees problem to the Multicut on Trees problem, our results give a parameterized algorithm that solves the Generalized Multiway Cut on Trees problem in time O ∗(ρk).

Recommended Citation

Kanj, Iyad, Guohui Lin, Tian Liu, Weitian Tong, Ge Xia, Jinhui Xu, Boting Yang, Fenghui Zhang, Peng Zhang, Binhai Zhu. 2015. "Improved Parameterized and Exact Algorithms for Cut Problems on Trees." Theoretical Computer Science, 607 (3): 455-470. doi: 10.1016/j.tcs.2015.06.010
https://digitalcommons.georgiasouthern.edu/compsci-facpubs/57