Convergence to Equilibrium in Local Interaction Games

In many applications of wireless ad hoc and sensor networks, position-awareness is of great importance. Often, as in the case of geometric routing, it is sufficient to have virtual coordinates, rather than real coordinates. In this paper, we address the problem of obtaining virtual coordinates based on connectivity information. In particular, we propose the first approximation algorithm for this problem and discuss implementational aspects.

[1]  Roger Wattenhofer,et al.  Analyzing connectivity-based multi-hop ad-hoc positioning , 2004 .

[2]  Santosh S. Vempala Random projection: a new approach to VLSI layout , 1998, Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280).

[3]  Uriel Feige,et al.  Approximating the Bandwidth via Volume Respecting Embeddings , 2000, J. Comput. Syst. Sci..

[4]  Mihai Badoiu,et al.  Approximation algorithm for embedding metrics into a two-dimensional space , 2003, SODA '03.

[5]  Moni Naor,et al.  Know thy neighbor's neighbor: the power of lookahead in randomized P2P networks , 2004, STOC '04.

[6]  Brad Karp,et al.  GPSR: greedy perimeter stateless routing for wireless networks , 2000, MobiCom '00.

[7]  Yan Zhang,et al.  Geometric ad-hoc routing: of theory and practice , 2003, PODC '03.

[8]  Yinyu Ye,et al.  Semidefinite programming for ad hoc wireless sensor network localization , 2004, Third International Symposium on Information Processing in Sensor Networks, 2004. IPSN 2004.

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

[10]  Jan M. Rabaey,et al.  Robust Positioning Algorithms for Distributed Ad-Hoc Wireless Sensor Networks , 2002, USENIX Annual Technical Conference, General Track.

[11]  Mani B. Srivastava,et al.  Dynamic fine-grained localization in Ad-Hoc networks of sensors , 2001, MobiCom '01.

[12]  Santosh S. Vempala,et al.  Semi-definite relaxations for minimum bandwidth and other vertex-ordering problems , 2000, Theor. Comput. Sci..

[13]  B. Hofmann-Wellenhof,et al.  Global Positioning System , 1992 .

[14]  Robert Tappan Morris,et al.  Practical, distributed network coordinates , 2004, Comput. Commun. Rev..

[15]  Ivan Stojmenovic,et al.  Routing with Guaranteed Delivery in Ad Hoc Wireless Networks , 1999, DIALM '99.

[16]  Hui Zhang,et al.  Predicting Internet network distance with coordinates-based approaches , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[17]  B. R. Badrinath,et al.  Error characteristics of ad hoc positioning systems (aps) , 2004, MobiHoc '04.

[18]  Scott Shenker,et al.  Geographic routing without location information , 2003, MobiCom '03.

[19]  Ying Zhang,et al.  Localization from mere connectivity , 2003, MobiHoc '03.

[20]  Joseph Naor,et al.  Divide-and-conquer approximation algorithms via spreading metrics , 1995, Proceedings of IEEE 36th Annual Foundations of Computer Science.

[21]  Radhika Nagpal,et al.  Organizing a Global Coordinate System from Local Information on an Ad Hoc Sensor Network , 2003, IPSN.

[22]  B. R. Badrinath,et al.  Ad hoc positioning system (APS) , 2001, GLOBECOM'01. IEEE Global Telecommunications Conference (Cat. No.01CH37270).

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

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

[25]  L. Lovász,et al.  Geometric Algorithms and Combinatorial Optimization , 1981 .

[26]  Santosh S. Vempala,et al.  The Random Projection Method , 2005, DIMACS Series in Discrete Mathematics and Theoretical Computer Science.

[27]  Tian He,et al.  Range-free localization schemes in large scale sensor network , 2003, MobiCom 2003.

[28]  L. El Ghaoui,et al.  Convex position estimation in wireless 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).