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International Symposium on Parameterized and Exact Computation

IPEC 2013: Parameterized and Exact Computation pp 150–162Cite as

Faster Exact Algorithms for Some Terminal Set Problems

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8246))

Abstract

Many problems on graphs can be expressed in the following language: given a graph G = (V,E) and a terminal set T ⊆ V, find a minimum size set S ⊆ V which intersects all “structures” (such as cycles or paths) passing through the vertices in T. We call this class of problems as terminal set problems. In this paper we introduce a general method to obtain faster exact exponential time algorithms for many terminal set problems. More precisely, we show that

  • Node Multiway Cut can be solved in time O(1.4766n).

  • Directed Unrestricted Node Multiway Cut can be solved in time O(1.6181n).

  • There exists a deterministic algorithm for Subset Feedback Vertex Set running in time O(1.8980n) and a randomized algorithm with expected running time O(1.8826n). Furthermore, Subset Feedback Vertex on chordal graphs can be solved in time O(1.6181n).

  • Directed Subset Feedback Vertex Set can be solved in time O(1.9993n).

A key feature of our method is that, it uses the existing best polynomial time, fixed parameter tractable and exact exponential time algorithms for the non-terminal version of the same problem (i.e. when T = V), as subroutines. Therefore faster algorithms for these special cases will imply further improvements in the running times of our algorithms. Our algorithms for Node Multiway Cut, and Subset Feedback Vertex Set on chordal graphs improve the current best algorithms for these problems and answers an open question posed in [15]. Furthermore, our algorithms for Directed Unrestricted Node Multiway Cut and Directed Subset Feedback Vertex Set are the first exact algorithms improving upon the brute force O *(2n)-algorithms.

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Author information

Authors and Affiliations

  1. University of Maryland, USA

    Rajesh Chitnis

  2. University of Bergen, Norway

    Fedor V. Fomin, Daniel Lokshtanov & Saket Saurabh

  3. Institute of Mathematical Sciences, India

    Pranabendu Misra, M. S. Ramanujan & Saket Saurabh

Authors
  1. Rajesh Chitnis
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  2. Fedor V. Fomin
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  3. Daniel Lokshtanov
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  4. Pranabendu Misra
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  5. M. S. Ramanujan
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  6. Saket Saurabh
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Editor information

Editors and Affiliations

  1. Royal Holloway, University of London, Egham Hill, TW20 0EX, Egham, UK

    Gregory Gutin

  2. Institute of Information Systems, Vienna University of Technology, (184/3), Favoritenstraße 9-11, 1040, Vienna, Austria

    Stefan Szeider

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© 2013 Springer International Publishing Switzerland

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Chitnis, R., Fomin, F.V., Lokshtanov, D., Misra, P., Ramanujan, M.S., Saurabh, S. (2013). Faster Exact Algorithms for Some Terminal Set Problems. In: Gutin, G., Szeider, S. (eds) Parameterized and Exact Computation. IPEC 2013. Lecture Notes in Computer Science, vol 8246. Springer, Cham. https://doi.org/10.1007/978-3-319-03898-8_14

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  • DOI: https://doi.org/10.1007/978-3-319-03898-8_14

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-03897-1

  • Online ISBN: 978-3-319-03898-8

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