Algorithmica

, Volume 61, Issue 4, pp 882–897 | Cite as

A New Algorithm for Finding Trees with Many Leaves

  • Joachim Kneis
  • Alexander Langer
  • Peter Rossmanith
Article

Abstract

We present an algorithm that finds out-trees and out-branchings with at least k leaves in directed graphs. These problems are known as Directed Maximum Leaf Out-Tree and Directed Maximum Leaf Out-Branching, respectively, and—in the case of undirected graphs—as Maximum Leaf Spanning Tree. The run time of our algorithm is O(4knm) on directed graphs and O(poly(n)+4kk2) on undirected graphs. This improves over the previously fastest algorithms for these problems with run times of 2O(klog k)poly(n) and O(poly(n)+6.75kpoly(k)) respectively.

Keywords

Graph algorithms Algorithms 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Joachim Kneis
    • 1
  • Alexander Langer
    • 1
  • Peter Rossmanith
    • 1
  1. 1.Theoretical Computer Science, Dept. of Computer ScienceRWTH Aachen UniversityAachenGermany

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