An Amortized Search Tree Analysis for k-Leaf Spanning Tree

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.

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