Improved Multi-criteria Spanners for Ad-Hoc Networks Under Energy and Distance Metrics

This paper studies the problem of topology control in random wireless ad-hoc networks through power assignment for n nodes uniformly distributed in a unit square. In particular, we are interested in asymmetric power assignments so that the induced communication graph has a good distance and energy stretch simultaneously, with additional optimization objectives: both minimizing the total energy consumption, interference level, hop-diameter, and maximizing the network lifetime. We present several power assignments with varying construction time complexity. The probability of our results converges to one as the number of network nodes, n, increases. To the best of our knowledge, these are the first results for spanner construction in wireless ad-hoc networks with provable bounds for both, energy and distance, metrics simultaneously.

[1]  Xiang-Yang Li,et al.  Minimum power assignment in wireless ad hoc networks with spanner property , 2004, 2004 Workshop on High Performance Switching and Routing, 2004. HPSR..

[2]  Chunming Qiao,et al.  A Constant Approximation Algorithm for Interference Aware Broadcast in Wireless Networks , 2007, IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications.

[3]  Roger Wattenhofer,et al.  Does topology control reduce interference? , 2004, MobiHoc '04.

[4]  M. Segal,et al.  Near Optimal Multicriteria Spanner Constructions in Wireless Ad-Hoc Networks , 2009, IEEE INFOCOM 2009.

[5]  Joachim Gudmundsson,et al.  On Spanners of Geometric Graphs , 2009, Int. J. Found. Comput. Sci..

[6]  Pravin M. Vaidya,et al.  A sparse graph almost as good as the complete graph on points inK dimensions , 1991, Discret. Comput. Geom..

[7]  Ram Ramanathan,et al.  Topology control of multihop wireless networks using transmit power adjustment , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[8]  Andrzej Pelc,et al.  Power consumption in packet radio networks , 2000, Theor. Comput. Sci..

[9]  Madhav V. Marathe,et al.  Algorithmic Aspects of Topology Control Problems for Ad Hoc Networks , 2005, Mob. Networks Appl..

[10]  Mikkel Thorup,et al.  Approximate distance oracles , 2005, J. ACM.

[11]  Madhav V. Marathe,et al.  Bi-Criteria Approximation Algorithms for Power-Efficient and Low-Interference Topology Control in Unreliable Ad Hoc Networks , 2009, IEEE INFOCOM 2009.

[12]  Kaveh Pahlavan,et al.  Wireless Information Networks , 1995 .

[13]  Rolf Klein,et al.  Computing Geometric Minimum-Dilation Graphs Is NP-Hard , 2006, Graph Drawing.

[14]  Hanan Shpungin,et al.  Fault-tolerant power assignment and backbone in wireless networks , 2006, Fourth Annual IEEE International Conference on Pervasive Computing and Communications Workshops (PERCOMW'06).

[15]  David Peleg,et al.  Distributed Computing: A Locality-Sensitive Approach , 1987 .

[16]  David P. Dobkin,et al.  On sparse spanners of weighted graphs , 1993, Discret. Comput. Geom..

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

[18]  Honghai Zhang,et al.  Asymptotic Critical Total Power for $k$ -Connectivity of Wireless Networks , 2008, IEEE/ACM Transactions on Networking.

[19]  Xiang-Yang Li,et al.  Low-Interference Topology Control for Wireless Ad Hoc Networks , 2005, Ad Hoc Sens. Wirel. Networks.

[20]  Tomas Johansson,et al.  Reducing interference in ad hoc networks through topology control , 2005, DIALM-POMC '05.

[21]  Martin Raab,et al.  "Balls into Bins" - A Simple and Tight Analysis , 1998, RANDOM.

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

[23]  Hanan Shpungin,et al.  Power efficient resilience and lifetime in wireless ad-hoc networks , 2008, FOWANC '08.

[24]  Otfried Cheong,et al.  Computing a minimum-dilation spanning tree is NP-hard , 2008, Comput. Geom..

[25]  Srdjan Krco.  Health Care Sensor Networks - Architecture and Protocols , 2005, Ad Hoc Sens. Wirel. Networks.

[26]  Jeffrey S. Salowe.  Constructing multidimensional spanner graphs , 1991, Int. J. Comput. Geom. Appl..

[27]  Giri Narasimhan,et al.  New sparseness results on graph spanners , 1995, Int. J. Comput. Geom. Appl..

[28]  Dániel Marx,et al.  Computing Geometric Minimum-Dilation Graphs is NP-Hard , 2010, Int. J. Comput. Geom. Appl..

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