Compact and low delay routing labeling scheme for Unit Disk Graphs

Compact and Low Delay Routing Labeling Scheme for Unit Disk Graphs

In this paper, we propose a new compact and low delay routing labeling scheme for Unit Disk Graphs (UDGs) which often model wireless ad hoc networks. We show that one can assign each vertex of an n-vertex UDG G a compact O(log n)-bit label such that, given the label of a source vertex and the label of a destination, it is possible to compute efficiently, based solely on these two labels, a neig...

Improved Compact Routing Scheme for Chordal Graphs

Compact Labeling Scheme for Ancestor Queries

We consider the following problem. Given a rooted tree T , label the nodes of T in the most compact way such that given the labels of two nodes u and v one can determine in constant time, by looking only at the labels, if u is ancestor of v. The best known labeling scheme is rather straightforward and uses labels of length at most 2 log2 n bits each, where n is the number of nodes in the tree. ...

Approximation Algorithms for Unit Disk Graphs

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...

Geometry 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...