Approximation algorithms for the maximum leaf spanning tree problem on acyclic digraphs

Authors:
Nadine Schwartges;Joachim Spoerhase;Alexander Wolff
Affiliations:
Computer Science I, University of Würzburg, Germany;Computer Science I, University of Würzburg, Germany;Computer Science I, University of Würzburg, Germany
Venue:
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
Year:
2011

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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(√{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 P = NP.