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]  Baruch Awerbuch,et al.  Optimal distributed algorithms for minimum weight spanning tree, counting, leader election, and related problems , 1987, STOC.

[3]  Mario Gerla,et al.  On demand multicast routing with unidirectional links , 2005, IEEE Wireless Communications and Networking Conference, 2005.

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

[5]  Bing-Hong Liu,et al.  Virtual-Coordinate-Based Delivery-Guaranteed Routing Protocol in Wireless Sensor Networks , 2008, IEEE/ACM Transactions on Networking.

[6]  Ivan Stojmenovic,et al.  Position Based Routing Algorithms for Ad Hoc Networks: A Taxonomy , 2004 .

[7]  David Peleg,et al.  Localized spanner construction for ad hoc networks with variable transmission range , 2008, TOSN.

[8]  J. J. Garcia-Luna-Aceves,et al.  Channel access scheduling in Ad Hoc networks with unidirectional links , 2001, DIALM '01.

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

[10]  B. Ripley,et al.  Introduction to the Theory of Coverage Processes. , 1989 .

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

[12]  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.

[13]  Michael Segal,et al.  Energy efficient communication in ad hoc networks from user's and designer's perspective , 2005, MOCO.

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

[15]  Andrea E. F. Clementi,et al.  Some Recent Theoretical Advances and Open Questions on Energy Consumption in Ad-Hoc Wireless Networks , 2001 .

[16]  Gruia Calinescu,et al.  Network Lifetime and Power Assignment in ad hoc Wireless Networks , 2003, ESA.

[17]  J. Seaman.  Introduction to the theory of coverage processes , 1990 .

[18]  Mikkel Thorup,et al.  Approximate distance oracles , 2001, JACM.

[19]  Kay Römer,et al.  The design space of wireless sensor networks , 2004, IEEE Wireless Communications.

[20]  Daniel Mossé,et al.  Providing a bidirectional abstraction for unidirectional ad hoc networks , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[21]  Andrea E. F. Clementi,et al.  Hardness Results for the Power Range Assignmet Problem in Packet Radio Networks , 1999, RANDOM-APPROX.

[22]  Leandros Tassiulas,et al.  Energy conserving routing 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).

[23]  Hanan Shpungin.  Energy efficient online routing in wireless ad hoc networks , 2011, 2011 8th Annual IEEE Communications Society Conference on Sensor, Mesh and Ad Hoc Communications and Networks.

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

[25]  W. Rabiner,et al.  Design considerations for distributed microsensor systems , 1999, Proceedings of the IEEE 1999 Custom Integrated Circuits Conference (Cat. No.99CH36327).

[26]  Madhav V. Marathe,et al.  Algorithmic Aspects of Topology Control Problems for Ad Hoc Networks , 2002, MobiHoc '02.

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

[28]  Yuanyuan Zhang,et al.  Reliable Key Establishment Scheme Exploiting Unidirectional Links in Wireless Sensor Networks , 2008, 2008 IEEE/IFIP International Conference on Embedded and Ubiquitous Computing.

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

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

[31]  Dimitri P. Bertsekas,et al.  Data Networks , 1986 .

[32]  Hanan Shpungin,et al.  Improved Multi-criteria Spanners for Ad-Hoc Networks Under Energy and Distance Metrics , 2010, INFOCOM.

[33]  Wen-Tsuen Chen,et al.  The strongly connecting problem on multihop packet radio networks , 1989, IEEE Trans. Commun..

[34]  S. Rao Kosaraju,et al.  Faster algorithms for some geometric graph problems in higher dimensions , 1993, SODA '93.

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

[36]  Krishna M. Sivalingam,et al.  Power optimization in routing protocols for wireless and mobile networks , 2002 .

[37]  Errol L. Lloyd.  On triangulations of a set of points in the plane , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

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

[39]  Katia Obraczka,et al.  Energy-efficient collision-free medium access control for wireless sensor networks , 2003, SenSys '03.

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

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

[42]  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).

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

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

[45]  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).

[46]  Edith Cohen.  Fast Algorithms for Constructing t-Spanners and Paths with Stretch t , 1998, SIAM J. Comput..

[47]  Leonidas J. Guibas,et al.  Geometric spanners for routing in mobile networks , 2005 .

[48]  Joseph P. Macker,et al.  Mobile ad hoc networking and the IETF , 1999, MOCO.

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

[50]  Giri Narasimhan,et al.  Geometric spanner networks , 2007 .

[51]  Christian Schindelhauer,et al.  Geometric spanners with applications in wireless networks , 2007, Comput. Geom..

[52]  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.

[53]  Paul J.M. Havinga,et al.  A Lightweight Medium Access Protocol (LMAC) for Wireless Sensor Networks: Reducing Preamble Transmissions and Transceiver State Switches , 2004 .

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

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

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

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

[58]  Matthew J. Katz,et al.  Minimum power energy spanners in wireless ad hoc networks , 2010, 2010 Proceedings IEEE INFOCOM.

[59]  Joseph P. Macker,et al.  Mobile ad hoc networking and the IETF , 2006, MOCO.

[60]  Hanan Shpungin,et al.  Novel algorithms for the network lifetime problem in wireless settings , 2008, Wirel. Networks.

[61]  Roger Wattenhofer,et al.  Topology control meets SINR: the scheduling complexity of arbitrary topologies , 2006, MobiHoc '06.

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

[63]  Giri Narasimhan,et al.  New sparseness results on graph spanners , 1992, SCG '92.