Surrounding Nodes in Coordinate-Free Networks

Consider a network of nodes in the plane whose locations are unknown but which establish communication links based on proximity. We solve the following problems: given a node in the network, (1) determine if a given cycle surrounds the node; and (2) find some cycle that surrounds the node. The only localization capabilities assumed are unique IDs with binary proximity measure, and, in some cases, cyclic orientation of neighbors. We give complete algorithms for finding and verifying surrounding cycles when cyclic orientation data is available. We also provide an efficient but non-complete algorithm in the case where angular data is not available.

[1]  Jie Gao,et al.  Localization and routing in sensor networks by local angle information , 2005, MobiHoc '05.

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

[3]  Gaurav S. Sukhatme,et al.  A Unifying Framework for Tunable Topology Control in Sensor Networks , 2005 .

[4]  Vin de Silva,et al.  Coverage in sensor networks via persistent homology , 2007 .

[5]  Sándor P. Fekete,et al.  Deterministic boundary recognition and topology extraction for large sensor networks , 2005, SODA '06.

[6]  Leonidas J. Guibas,et al.  Locating and bypassing routing holes in sensor networks , 2004, IEEE INFOCOM 2004.

[7]  Roger Wattenhofer,et al.  Unit disk graph approximation , 2004, DIALM-POMC '04.

[8]  A. Jadbabaie.  On geographic routing without location information , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[9]  Leonidas J. Guibas,et al.  GLIDER: gradient landmark-based distributed routing for sensor networks , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[10]  Bonaventure Intercontinental,et al.  ON DECISION AND CONTROL , 1985 .

[11]  B. Dundas,et al.  DIFFERENTIAL TOPOLOGY , 2002 .

[12]  Abubakr Muhammad,et al.  Blind Swarms for Coverage in 2-D , 2005, Robotics: Science and Systems.

[13]  Vin de Silva,et al.  Coordinate-free Coverage in Sensor Networks with Controlled Boundaries via Homology , 2006, Int. J. Robotics Res..