6,207 research outputs found
Spanning trees with few branch vertices
A branch vertex in a tree is a vertex of degree at least three. We prove
that, for all , every connected graph on vertices with minimum
degree at least contains a spanning tree having at most
branch vertices. Asymptotically, this is best possible and solves, in less
general form, a problem of Flandrin, Kaiser, Ku\u{z}el, Li and Ryj\'a\u{c}ek,
which was originally motivated by an optimization problem in the design of
optical networks.Comment: 20 pages, 2 figures, to appear in SIAM J. of Discrete Mat
An FPT Algorithm for Spanning Trees with Few Branch Vertices Parameterized by Modular-Width
The minimum branch vertices spanning tree problem consists in finding a spanning tree T of an input graph G having the minimum number of branch vertices, that is, vertices of degree at least three in T. This NP-hard problem has been widely studied in the literature and has many important applications in network design and optimization. Algorithmic and combinatorial aspects of the problem have been extensively studied and its fixed parameter tractability has been recently considered. In this paper we focus on modular-width and show that the problem of finding a spanning tree with the minimum number of branch vertices is FPT with respect to this parameter
A Faster Exact Algorithm for the Directed Maximum Leaf Spanning Tree Problem
Given a directed graph , the Directed Maximum Leaf Spanning Tree
problem asks to compute a directed spanning tree (i.e., an out-branching) with
as many leaves as possible. By designing a Branch-and-Reduced algorithm
combined with the Measure & Conquer technique for running time analysis, we
show that the problem can be solved in time \Oh^*(1.9043^n) using polynomial
space. Hitherto, there have been only few examples. Provided exponential space
this run time upper bound can be lowered to \Oh^*(1.8139^n)
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