Simple heuristics and PTASs for intersection graphs in wireless ad hoc networks

In wireless ad hoc networks, each wireless device has a transmission range, which is usually modeled as a disk centered at this node. A wireless node can send message directly to all nodes lying inside this disk. We present several intersection graphs to model the wireless networks. Then we present some simple heuristics and/or PTASs to approximate the maximum independent set, the minimum vertex cover and the minimum graph coloring in these graph models.

[1]  W. Thurston,et al.  Three-Dimensional Geometry and Topology, Volume 1 , 1997, The Mathematical Gazette.

[2]  David G. Kirkpatrick,et al.  Unit disk graph recognition is NP-hard , 1998, Comput. Geom..

[3]  Dorit S. Hochbaum,et al.  Efficient bounds for the stable set, vertex cover and set packing problems , 1983, Discret. Appl. Math..

[4]  Harry B. Hunt,et al.  Simple heuristics for unit disk graphs , 1995, Networks.

[5]  F. McMorris,et al.  Topics in Intersection Graph Theory , 1987 .

[6]  R. Möhring.  Algorithmic graph theory and perfect graphs , 1986 .

[7]  F. Roberts.  Graph Theory and Its Applications to Problems of Society , 1987 .

[8]  Wolfgang Maass,et al.  Approximation schemes for covering and packing problems in image processing and VLSI , 1985, JACM.

[9]  G. Szekeres,et al.  An inequality for the chromatic number of a graph , 1968 .

[10]  A. Gräf,et al.  On Coloring Unit Disk Graphs , 1998, Algorithmica.

[11]  Klaus Jansen,et al.  Polynomial-time approximation schemes for geometric graphs , 2001, SODA '01.

[12]  J. Mark Keil,et al.  An optimal algorithm for finding dominating cycles in circular-arc graphs , 1992, Discret. Appl. Math..

[13]  Harry B. Hunt,et al.  NC-Approximation Schemes for NP- and PSPACE-Hard Problems for Geometric Graphs , 1998, J. Algorithms.

[14]  W. Thurston,et al.  Three-Dimensional Geometry and Topology, Volume 1 , 1997, The Mathematical Gazette.

[15]  Charles J. Colbourn,et al.  Unit disk graphs , 1991, Discret. Math..