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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Schwartges, N., Spoerhase, J., Wolff, A. (2012). Approximation Algorithms for the Maximum Leaf Spanning Tree Problem on Acyclic Digraphs. In: Solis-Oba, R., Persiano, G. (eds) Approximation and Online Algorithms. WAOA 2011. Lecture Notes in Computer Science, vol 7164. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29116-6_7
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DOI: https://doi.org/10.1007/978-3-642-29116-6_7
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