Constrained Delaunay Triangulation for Ad Hoc Networks

Geometric spanners can be used for efficient routing in wireless ad hoc networks. Computation of existing spanners for ad hoc networks primarily focused on geometric properties without considering network requirements. In this paper, we propose a new spanner called constrained Delaunay triangulation (CDT) which considers both geometric properties and network requirements. The CDT is formed by introducing a small set of constraint edges into local Delaunay triangulation (LDel) to reduce the number of hops between nodes in the network graph. We have simulated the CDT using network simulator (ns-2.28) and compared with Gabriel graph (GG), relative neighborhood graph (RNG), local Delaunay triangulation (LDel), and planarized local Delaunay triangulation (PLDel). The simulation results show that the minimum number of hops from source to destination is less than other spanners. We also observed the decrease in delay, jitter, and improvement in throughput.

[1]  Ahmed Helmy,et al.  Energy-efficient forwarding strategies for geographic routing in lossy wireless sensor networks , 2004, SenSys '04.

[2]  Zygmunt J. Haas,et al.  Virtual backbone generation and maintenance in ad hoc network mobility management , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

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

[4]  Paramvir Bahl,et al.  Distributed Topology Control for Wireless Multihop Ad-hoc Networks , 2001, INFOCOM.

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

[6]  Felix Schmidt-Eisenlohr,et al.  Bug Fixes on the IEEE 802.11 DCF module of the Network Simulator ns-2.28 , 2006 .

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

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

[9]  Deborah Estrin,et al.  Temporal Properties of Low Power Wireless Links: Modeling and Implications on Multi-Hop Routing , 2005 .

[10]  Carl Gutwin,et al.  Classes of graphs which approximate the complete euclidean graph , 1992, Discret. Comput. Geom..

[11]  Xiang-Yang Li,et al.  Geometric Spanners for Wireless Ad Hoc Networks , 2003, IEEE Trans. Parallel Distributed Syst..

[12]  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.

[13]  Prosenjit Bose,et al.  Online Routing in Triangulations , 1999, SIAM J. Comput..

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

[15]  Marco Zuniga,et al.  An analysis of unreliability and asymmetry in low-power wireless links , 2007, TOSN.

[16]  David Eppstein Beta-skeletons have unbounded dilation , 2002, Comput. Geom..

[17]  Ivan Stojmenovic,et al.  Partial Delaunay triangulation and degree limited localized Bluetooth scatternet formation , 2004, IEEE Transactions on Parallel and Distributed Systems.

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

[19]  Theodore S. Rappaport,et al.  Wireless communications - principles and practice , 1996 .

[20]  L. Paul Chew,et al.  Constrained Delaunay triangulations , 1987, SCG '87.

[21]  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).

[22]  Fabian Kuhn,et al.  Ad-hoc networks beyond unit disk graphs , 2003, DIALM-POMC '03.

[23]  Xiang-Yang Li,et al.  Power efficient and sparse spanner for wireless ad hoc networks , 2001, Proceedings Tenth International Conference on Computer Communications and Networks (Cat. No.01EX495).

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

[25]  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).

[26]  Leonidas J. Guibas,et al.  Geometric spanners for routing in mobile networks , 2001, IEEE Journal on Selected Areas in Communications.

[27]  Jie Wu,et al.  A Dominating-Set-Based Routing Scheme in Ad Hoc Wireless Networks , 2001, Telecommun. Syst..

[28]  Xiang-Yang Li,et al.  Localized Delaunay Triangulation with Application in Ad Hoc Wireless Networks , 2003, IEEE Trans. Parallel Distributed Syst..

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

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

[31]  Jie Wu,et al.  Domination and its applications in ad hoc wireless networks with unidirectional links , 2000, Proceedings 2000 International Conference on Parallel Processing.