640 research outputs found
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)
Cooperating Distributed Grammar Systems of Finite Index Working in Hybrid Modes
We study cooperating distributed grammar systems working in hybrid modes in
connection with the finite index restriction in two different ways: firstly, we
investigate cooperating distributed grammar systems working in hybrid modes
which characterize programmed grammars with the finite index restriction;
looking at the number of components of such systems, we obtain surprisingly
rich lattice structures for the inclusion relations between the corresponding
language families. Secondly, we impose the finite index restriction on
cooperating distributed grammar systems working in hybrid modes themselves,
which leads us to new characterizations of programmed grammars of finite index.Comment: In Proceedings AFL 2014, arXiv:1405.527
Vertex and edge covers with clustering properties: complexity and algorithms
We consider the concepts of a t-total vertex cover and a t-total edge cover (t≥1), which generalise the notions of a vertex cover and an edge cover, respectively. A t-total vertex (respectively edge) cover of a connected graph G is a vertex (edge) cover S of G such that each connected component of the subgraph of G induced by S has at least t vertices (edges). These definitions are motivated by combining the concepts of clustering and covering in graphs. Moreover they yield a spectrum of parameters that essentially range from a vertex cover to a connected vertex cover (in the vertex case) and from an edge cover to a spanning tree (in the edge case). For various values of t, we present NP-completeness and approximability results (both upper and lower bounds) and FTP algorithms for problems concerned with finding the minimum size of a t-total vertex cover, t-total edge cover and connected vertex cover, in particular improving on a previous FTP algorithm for the latter problem
minimum dominating set of queens: A trivial programming exercise?
Abstractminimum dominating set of queens is one of the typical programming exercises of a first year’s computer science course. However, little work has been published on the complexity of this problem. We analyse here several algorithms and show that advanced algorithmic techniques may dramatically speed up solving this problem
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