Improved parameterized and exact algorithms for cut problems on trees
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...
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| Published in: | Theoretical computer science Vol. 607; pp. 455 - 470 |
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| Main Authors: | , , , , , , , , , |
| Format: | Journal Article |
| Language: | English |
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01.11.2015
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| ISSN: | 0304-3975, 1879-2294 |
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| 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). |
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| AbstractList | 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 , where is the positive root of the polynomial . This improves the current-best algorithm of Chen et al. that runs in time . 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 . 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). |
| Author | Tong, Weitian Zhang, Peng Lin, Guohui Kanj, Iyad Liu, Tian Xu, Jinhui Zhang, Fenghui Zhu, Binhai Xia, Ge Yang, Boting |
| Author_xml | – sequence: 1 givenname: Iyad surname: Kanj fullname: Kanj, Iyad email: ikanj@cs.depaul.edu organization: School of Computing, DePaul University, 243 S. Wabash Avenue, Chicago, IL 60604, USA – sequence: 2 givenname: Guohui surname: Lin fullname: Lin, Guohui email: guohui@ualberta.ca organization: Department of Computing Science, University of Alberta, Edmonton, Alberta T6G 2E8, Canada – sequence: 3 givenname: Tian surname: Liu fullname: Liu, Tian email: lt@pku.edu.cn organization: Key Laboratory of High Confidence Software Technologies, Ministry of Education, Institute of Software, School of Electronic Engineering and Computer Science, Peking University, Beijing 100871, China – sequence: 4 givenname: Weitian surname: Tong fullname: Tong, Weitian email: weitian@ualberta.ca organization: Department of Computing Science, University of Alberta, Edmonton, Alberta T6G 2E8, Canada – sequence: 5 givenname: Ge surname: Xia fullname: Xia, Ge email: xiag@lafayette.edu organization: Department of Computer Science, Lafayette College, 506 Acopian Engineering Center, Easton, PA 18042, USA – sequence: 6 givenname: Jinhui surname: Xu fullname: Xu, Jinhui email: jinhui@buffalo.edu organization: Department of Computer Science and Engineering, State University of New York at Buffalo (SUNY Buffalo), 338 Davis Hall, Buffalo, NY 14260, USA – sequence: 7 givenname: Boting surname: Yang fullname: Yang, Boting email: boting@cs.uregina.ca organization: Department of Computer Science, University of Regina, Regina, Saskatchewan S4S 0A2, Canada – sequence: 8 givenname: Fenghui surname: Zhang fullname: Zhang, Fenghui email: fhzhang@gmail.com organization: Google Kirkland, 747 6th Street South, Kirkland, WA 98033, USA – sequence: 9 givenname: Peng orcidid: 0000-0001-7265-0983 surname: Zhang fullname: Zhang, Peng email: algzhang@sdu.edu.cn organization: School of Computer Science and Technology, Shandong University, China – sequence: 10 givenname: Binhai surname: Zhu fullname: Zhu, Binhai email: bhz@cs.montana.edu organization: Department of Computer Science, Montana State University, Bozeman, MT 59717, USA |
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| Keywords | Tree Multiway cut Multicut Parameterized algorithm Exact algorithm |
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| Title | Improved parameterized and exact algorithms for cut problems on trees |
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