Approximation Algorithms for the Maximum Leaf Spanning Tree Problem on Acyclic Digraphs

  • Nadine Schwartges
  • Joachim Spoerhase
  • Alexander Wolff
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7164)

Abstract

We consider the problem Maximum Leaf Spanning Tree (MLST) on digraphs, which is defined as follows. Given a digraph G, find a directed spanning tree of G that maximizes the number of leaves. MLST is NP-hard. Existing approximation algorithms for MLST have ratios of \(O(\sqrt{\rm OPT})\) and 92.

We focus on the special case of acyclic digraphs and propose two linear-time approximation algorithms; one with ratio 4 that uses a result of Daligault and Thomassé and one with ratio 2 based on a 3-approximation algorithm of Lu and Ravi for the undirected version of the problem. We complement these positive results by observing that MLST is MaxSNP-hard on acyclic digraphs. Hence, this special case does not admit a PTAS (unless \({\cal P}=\cal NP\)).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Nadine Schwartges
    • 1
  • Joachim Spoerhase
    • 1
  • Alexander Wolff
    • 1
  1. 1.Computer Science IUniversity of WürzburgGermany

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