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Parameterized Single-Exponential Time Polynomial Space Algorithm for Steiner Tree

  • Fedor V. Fomin
  • Petteri Kaski
  • Daniel Lokshtanov
  • Fahad Panolan
  • Saket Saurabh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9134)

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.

Keywords

Steiner Tree Recursive Call Steiner Tree Problem Polynomial Space Terminal Vertex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Fedor V. Fomin
    • 1
  • Petteri Kaski
    • 2
  • Daniel Lokshtanov
    • 1
  • Fahad Panolan
    • 1
    • 3
  • Saket Saurabh
    • 1
    • 3
  1. 1.University of BergenBergenNorway
  2. 2.Aalto UniversityEspooFinland
  3. 3.Institute of Mathematical SciencesChennaiIndia

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