Sphere Packings, Lattices and Groups

NC-Approximation Schemes for NP- and PSPACE-Hard Problems for Geometric Graphs

A connected dominating set in a graph is a subset of vertices such that every vertex is either in the subset or adjacent to a vertex in the subset and the subgraph induced by the subset is connected. A minimum-connected dominating set is such a vertex subset with minimum cardinality. An application in ad hoc wireless networks requires the study of the minimum-connected dominating set in unit-disk graphs. In this paper, we design a (1 + 1/s)-approximation for the minimum-connected dominating set in unit-disk graphs, running in time nO((s log s)2). © 2003 Wiley Periodicals, Inc.

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A Polynomial-Time Approximation Scheme for the Minimum-Connected Dominating Set in Ad Hoc Wireless Networks

A number of studies have shown the abundance of unused spectrum in the TV bands. This is in stark contrast to the overcrowding of wireless devices in the ISM bands. A recent trend to alleviate this disparity is the design of Cognitive Radios, which constantly sense the spectrum and opportunistically utilize unused frequencies in the TV bands. In this paper, we introduce the concept of a time-spectrum block to model spectrum reservation, and use it to present a theoretical formalization of the spectrum allocation problem in cognitive radio networks. We present a centralized and a distributed protocol for spectrum allocation and show that these protocols are close to optimal in most scenarios. We have implemented the distributed protocol in QualNet and show that our analysis closely matches the simulation results.

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Allocating dynamic time-spectrum blocks in cognitive radio networks

3 Centralized CDS Construction 335 3.1 Guha and Khuller’s Algorithm . . . . . . . . . . . . . . . . . . . . . 336 3.2 Ruan’s Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 3.3 Cheng’s Greedy Algorithm . . . . . . . . . . . . . . . . . . . . . . . . 340 3.4 Min’s Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341 3.5 Butenko’s Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 341

/pdf/connected-dominating-set-in-sensor-networks-and-manets-n5bp2dbz8n.pdf

Connected Dominating Set in Sensor Networks and MANETs

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 competitive ratio of 6 for unit disk graphs. Our heuristics do not need a geometric representation of unit disk graphs. Geometric representations are used only in establishing the performance guarantees of the heuristics. Several of our approximation algorithms can be extended to intersection graphs of circles of arbitrary radii in the plane, intersection graphs of regular polygons, and to intersection graphs of higher dimensional regular objects.

H. Breu

Papers

Simple heuristics for unit disk graphs

Geometry based heuristics for unit disk graphs.