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Directed Steiner Tree with Branching Constraint

  • Dimitri Watel
  • Marc-Antoine Weisser
  • Cédric Bentz
  • Dominique Barth
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8591)

Abstract

Given a directed weighted graph G, a root r and k terminals, the k-Directed Steiner Tree problem is to find a minimum cost tree rooted at r and spanning all terminals. If this problem has several applications in multicast routing in packet switching networks, the modeling is not adapted anymore in networks based upon the circuit switching principle in which some nodes, called non diffusing nodes, are not able to duplicate packets. We define a more general problem, named Directed Steiner Tree with Limited number of Diffusing nodes (DSTLD), able to model the multicast in a network containing at most d diffusing nodes. We show that DSTLD is XP with respect to d, and use this result to build a \(\lceil \frac{k-1}{d} \rceil\)-approximation XP in d for DST. Finally, we prove that, under the assumption that NP \(\not\subseteq\) DTIME[n O(loglogn)], there is no polynomial approximation algorithm for DSTLD with ratio \(1+(\frac{1}{e} - \varepsilon) \cdot \frac{k}{d-1}\) for every constant ε > 0.

Keywords

Directed Steiner Tree Approximation Diffusing node 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Dimitri Watel
    • 1
    • 3
  • Marc-Antoine Weisser
    • 1
  • Cédric Bentz
    • 2
  • Dominique Barth
    • 3
  1. 1.SUPELEC System Sciences, Computer Science DPT.Gif Sur YvetteFrance
  2. 2.CEDRIC-CNAM 292Paris Cédex 03France
  3. 3.University of VersaillesVersaillesFrance

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