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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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...
متن کاملBalanced Line Separators of Unit Disk Graphs
We prove a geometric version of the graph separator theorem for the unit disk intersection graph: for any set of n unit disks in the plane there exists a line ` such that ` intersects at most O( √ (m+ n) logn) disks and each of the halfplanes determined by ` contains at most 2n/3 unit disks from the set, where m is the number of intersecting pairs of disks. We also show that an axis-parallel li...
متن کاملGeometry based heuristics for unit disk graphs
Unit disk graphs are intersection graphs of circles of unit radius in the plane. We present simple and provably good heuristics for a number of classical NP-hard optimization problems on unit disk graphs. The problems considered include maximum independent set, minimum vertex cover, minimum coloring and minimum dominating set. We also present an on-line coloring heuristic which achieves a compe...
متن کاملImproper colouring of (random) unit disk graphs
For any graph G, the k-improper chromatic number χ(G) is the smallest number of colours used in a colouring of G such that each colour class induces a subgraph of maximum degree k. We investigate the ratio of the kimproper chromatic number to the clique number for unit disk graphs and random unit disk graphs to extend results of McDiarmid and Reed (1999); McDiarmid (2003) (where they considered...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1990
ISSN: 0012-365X
DOI: 10.1016/0012-365x(90)90358-o