Geometric spanners for routing in mobile networks

We propose a new routing graph, the restricted Delaunay graph (RDG), for mobile ad hoc networks. Combined with a node clustering algorithm, the RDG can be used as an underlying graph for geographic routing protocols. This graph has the following attractive properties: 1) it is planar; 2) between any two graph nodes there exists a path whose length, whether measured in terms of topological or Euclidean distance, is only a constant times the minimum length possible; and 3) the graph can be maintained efficiently in a distributed manner when the nodes move around. Furthermore, each node only needs constant time to make routing decisions. We show by simulation that the RDG outperforms previously proposed routing graphs in the context of the Greedy perimeter stateless routing (GPSR) protocol. Finally, we investigate theoretical bounds on the quality of paths discovered using GPSR.

[1]  Jie Gao,et al.  Well-separated pair decomposition for the unit-disk graph metric and its applications , 2003, STOC '03.

[2]  John Hershberger.  Smooth kinetic maintenance of clusters , 2003, SCG '03.

[3]  Xiang-Yang Li,et al.  Distributed construction of a planar spanner and routing for ad hoc wireless networks , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[4]  Roger Wattenhofer,et al.  Asymptotically optimal geometric mobile ad-hoc routing , 2002, DIALM '02.

[5]  Xiang-Yang Li,et al.  Geometric spanners for wireless ad hoc networks , 2002, Proceedings 22nd International Conference on Distributed Computing Systems.

[6]  David G. Kirkpatrick,et al.  On the Spanning Ratio of Gabriel Graphs and beta-skeletons , 2002, LATIN.

[7]  L. Devroye,et al.  ON THE SPANNING RATIO OF GABRIEL GRAPHS AND β-SKELETONS , 2002 .

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

[9]  Leonidas J. Guibas,et al.  Discrete mobile centers , 2001, SCG '01.

[10]  Li Li,et al.  Distributed topology control for power efficient operation in multihop wireless ad hoc networks , 2001, Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213).

[11]  Rahul Jain,et al.  Geographical routing using partial information for wireless ad hoc networks , 2001, IEEE Wirel. Commun..

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

[13]  David R. Karger,et al.  A scalable location service for geographic ad hoc routing , 2000, MobiCom '00.

[14]  Ravi Prakash,et al.  Max-min d-cluster formation in wireless ad hoc networks , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[15]  Brad Karp,et al.  Greedy Perimeter Stateless Routing for Wireless Networks , 2000 .

[16]  David Eppstein,et al.  Spanning Trees and Spanners , 2000, Handbook of Computational Geometry.

[17]  J. Y. Wu,et al.  On calculating connected dominating set for efficient routing in ad hoc wireless networks , 1999, DIALM '99.

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

[19]  Elizabeth M. Belding-Royer,et al.  A review of current routing protocols for ad hoc mobile wireless networks , 1999, IEEE Wirel. Commun..

[20]  Charles E. Perkins,et al.  Ad-hoc on-demand distance vector routing , 1999, Proceedings WMCSA'99. Second IEEE Workshop on Mobile Computing Systems and Applications.

[21]  Imrich Chlamtac,et al.  A distance routing effect algorithm for mobility (DREAM) , 1998, MobiCom '98.

[22]  Nitin H. Vaidya,et al.  Location-aided routing (LAR) in mobile ad hoc networks , 1998, MobiCom '98.

[23]  Teresa H. Meng,et al.  Minimum energy mobile wireless networks , 1998, ICC '98. 1998 IEEE International Conference on Communications. Conference Record. Affiliated with SUPERCOMM'98 (Cat. No.98CH36220).

[24]  Vaduvur Bharghavan,et al.  Routing in ad-hoc networks using minimum connected dominating sets , 1997, Proceedings of ICC'97 - International Conference on Communications.

[25]  M. S. Corson,et al.  A highly adaptive distributed routing algorithm for mobile wireless networks , 1997, Proceedings of INFOCOM '97.

[26]  C C. Chiang,et al.  Routing in Clustered Multihop, Mobile Wireless Networks With Fading Channel , 1997 .

[27]  Mario Gerla,et al.  Multicluster, mobile, multimedia radio network , 1995, Wirel. Networks.

[28]  Carl Gutwin,et al.  The Delauney Triangulation Closely Approximates the Complete Euclidean Graph , 1989, WADS.

[29]  David P. Dobkin,et al.  Delaunay graphs are almost as good as complete graphs , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[30]  A. Ephremides,et al.  A design concept for reliable mobile radio networks with frequency hopping signaling , 1987, Proceedings of the IEEE.

[31]  Paul Chew,et al.  There is a planar graph almost as good as the complete graph , 1986, SCG '86.

[32]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .