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Parameterized Single-Exponential Time Polynomial Space Algorithm for Steiner Tree

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Automata, Languages, and Programming (ICALP 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9134))

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Abstract

In the Steiner tree problem, we are given as input a connected \(n\)-vertex graph with edge weights in \(\{1,2,\ldots ,W\}\), and a subset of \(k\) terminal vertices. Our task is to compute a minimum-weight tree that contains all the terminals. We give an algorithm for this problem with running time \({\mathcal O}(7.97^k\cdot n^4\cdot \log {W})\) using \({\mathcal O}(n^3\cdot \log {nW} \cdot \log k)\) space. This is the first single-exponential time, polynomial-space FPT algorithm for the weighted Steiner Tree problem.

The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreements 267959, 338077 and 306992

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Author information

Authors and Affiliations

  1. University of Bergen, Bergen, Norway

    Fedor V. Fomin, Daniel Lokshtanov, Fahad Panolan & Saket Saurabh

  2. Aalto University, Espoo, Finland

    Petteri Kaski

  3. Institute of Mathematical Sciences, Chennai, India

    Fahad Panolan & Saket Saurabh

Authors
  1. Fedor V. Fomin
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  2. Petteri Kaski
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  3. Daniel Lokshtanov
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  4. Fahad Panolan
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  5. Saket Saurabh
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Corresponding author

Correspondence to Fahad Panolan .

Editor information

Editors and Affiliations

  1. Reykjavik University, Reykjavik, Iceland

    Magnús M. Halldórsson

  2. Kyoto University, Kyoto, Japan

    Kazuo Iwama

  3. The University of Tokyo, Tokyo, Japan

    Naoki Kobayashi

  4. Technische Universiteit Eindhoven, Eindhoven, The Netherlands

    Bettina Speckmann

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Fomin, F.V., Kaski, P., Lokshtanov, D., Panolan, F., Saurabh, S. (2015). Parameterized Single-Exponential Time Polynomial Space Algorithm for Steiner Tree. In: Halldórsson, M., Iwama, K., Kobayashi, N., Speckmann, B. (eds) Automata, Languages, and Programming. ICALP 2015. Lecture Notes in Computer Science(), vol 9134. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47672-7_40

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  • DOI: https://doi.org/10.1007/978-3-662-47672-7_40

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-47671-0

  • Online ISBN: 978-3-662-47672-7

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