2-Sensor Problem

Ad-hoc networks of sensor nodes are in general semi-permanently deployed. However, the topology of such networks continuously changes over time, due to the power of some sensors wearing out to new sensors being inserted into the network, or even due to designers moving sensors around during a network re-design phase (for example, in response to a change in the requirements of the network). In this paper, we address the problem of covering a given path by a limited number of sensors — in our case to two, and show its relation to the well-studied matrix multiplication problem.

[1]  Miodrag Potkonjak,et al.  Coverage problems in wireless ad-hoc sensor networks , 2001, Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213).

[2]  Jirí Matousek,et al.  Computing Dominances in E^n , 1991, Inf. Process. Lett..

[3]  Jerzy W. Jaromczyk,et al.  An efficient algorithm for the Euclidean two-center problem , 1994, SCG '94.

[4]  Yin-Te Tsai,et al.  A near-quadratic algorithm for the alpha-connected two-center decision problem , 2002, CCCG.

[5]  Zhiming Ma,et al.  Coverage Problem of Wireless Sensor Networks , 2005, CJCDGCGT.

[6]  H. S. Wolff,et al.  iRun: Horizontal and Vertical Shape of a Region-Based Graph Compression , 2022, Sensors.

[7]  N. S. Barnett,et al.  Private communication , 1969 .

[8]  Micha Sharir.  A Near-Linear Algorithm for the Planar 2-Center Problem , 1997, Discret. Comput. Geom..

[9]  Kyung-Yong Chwa,et al.  Two-center problems for a convex polygon , 1998 .

[10]  David Eppstein,et al.  Faster construction of planar two-centers , 1997, SODA '97.

[11]  John Hershberger.  A Faster Algorithm for the Two-Center Decision Problem , 1993, Inf. Process. Lett..

[12]  Micha Sharir,et al.  Planar geometric location problems , 2005, Algorithmica.

[13]  Don Coppersmith,et al.  Matrix multiplication via arithmetic progressions , 1987, STOC.

[14]  Donald B. Johnson,et al.  Generalized Selection and Ranking: Sorted Matrices , 1984, SIAM J. Comput..

[15]  Micha Sharir,et al.  The Discrete 2-Center Problem , 1997, SCG '97.

[16]  Yu-Chee Tseng,et al.  The Coverage Problem in a Wireless Sensor Network , 2003, WSNA '03.