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)


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.


Steiner Tree Recursive Call Steiner Tree Problem Polynomial Space Terminal Vertex 
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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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