An Amortized Search Tree Analysis for k-Leaf Spanning Tree

  • Authors:
  • Daniel Raible;Henning Fernau

  • Affiliations:
  • FB 4--Abteilung Informatik, Univ.Trier, Trier, Germany 54286;FB 4--Abteilung Informatik, Univ.Trier, Trier, Germany 54286

  • Venue:
  • SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
  • Year:
  • 2009

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Abstract

The problem of finding a spanning tree in an undirected graph with a maximum number of leaves is known to be $\mathcal{NP}$-hard. We present an algorithm which finds a spanning tree with at least k leaves in time O *(3.4575 k ) which improves the currently best algorithm. The estimation of the running time is done by using a non-standard measure. The present paper is one of the few examples that employ the Measure & Conquer paradigm of algorithm analysis, developed within the field of Exact Exponential-Time Algorithmics, within the area of Parameterized Algorithmics.