منابع مشابه
Hierarchically Specified Unit Disk Graphs
We characterize the complexity of a number of basic optimization problems for unit disk graphs speciied hierarchically as in BOW83, LW87a, Le88, LW92]. Both PSPACE-hardness results and polynomial time approximations are presented for most of the problems considered. These problems include minimum vertex coloring, maximum independent set, minimum clique cover, minimum dominating set and minimum ...
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We will give distributed approximation schemes for the maximum matching problem and the minimum connected dominating set problem in unit-disk graphs. The algorithms are deterministic, run in a poly-logarithmic number of rounds in the message passing model and the approximation error can be made O(1/ log |G|) where |G| is the order of the graph and k is a positive integer.
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Unit-Disk Graphs (UDGs) are intersection graphs of equal diameter (or unit diameter w.l.o.g.) circles in the Euclidean plane. In the geometric (or disk) representation, each circle is specified by the coordinates of its center. Three equivalent graph models can be defined with vertices representing the circles [18]. In the intersection graph model, two vertices are adjacent if the corresponding...
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The minimum clique partition (MCP) problem is that of partitioning the vertex set of a given graph into a minimum number of cliques. Given n points in the plane, the corresponding unit disk graph (UDG) has these points as vertices, and edges connecting points at distance at most 1. MCP in unit disk graphs is known to be NP-hard and several constant factor approximations are known, including a r...
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Mobile ad hoc networks are frequently modeled by unit disk graphs. We consider several classical graph theoretic problems on unit disk graphs (Maximum Independent Set, Minimum Vertex Cover, and Minimum (Connected) Dominating Set), which are relevant to such networks. We propose two new notions for unit disk graphs: thickness and density. The thickness of a graph is the number of disk centers in...
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ژورنال
عنوان ژورنال: Algorithmica
سال: 2017
ISSN: 0178-4617,1432-0541
DOI: 10.1007/s00453-017-0308-2