On Construction of Quality Fault-Tolerant Virtual Backbone in Wireless Networks

In this paper, we study the problem of computing quality fault-tolerant virtual backbone in homogeneous wireless network, which is defined as the k-connected m-dominating set problem in a unit disk graph. This problem is NP-hard, and thus many efforts have been made to find a constant factor approximation algorithm for it, but never succeeded so far with arbitrary k ≥ 3 and m ≥ 1 pair. We propose a new strategy for computing a smaller-size 3-connected m-dominating set in a unit disk graph with any m ≥ 1. We show the approximation ratio of our algorithm is constant and its running time is polynomial. We also conduct a simulation to examine the average performance of our algorithm. Our result implies that while there exists a constant factor approximation algorithm for the k-connected m-dominating set problem with arbitrary k ≤ 3 and m ≥ 1 pair, the k-connected m-dominating set problem is still open with k > 3.

[1]  Reinhard Diestel,et al.  Graph Theory , 1997 .

[2]  Ding-Zhu Du,et al.  On the construction of 2-connected virtual backbone in wireless networks , 2009, IEEE Transactions on Wireless Communications.

[3]  Vaduvur Bharghavan,et al.  Enhancing ad hoc routing with dynamic virtual infrastructures , 2001, Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213).

[4]  Weili Wu,et al.  A Better Theoretical Bound to Approximate Connected Dominating Set in Unit Disk Graph , 2008, WASA.

[5]  Ding-Zhu Du,et al.  Connected Dominating Sets in Wireless Networks with Different Transmission Ranges , 2007, IEEE Transactions on Mobile Computing.

[6]  Samir Khuller,et al.  Approximation Algorithms for Connected Dominating Sets , 1996, Algorithmica.

[7]  Donghyun Kim,et al.  Constructing Connected Dominating Sets with Bounded Diameters inWireless Networks , 2007, International Conference on Wireless Algorithms, Systems and Applications (WASA 2007).

[8]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[9]  Jie Wu,et al.  On constructing k-connected k-dominating set in wireless networks , 2005, 19th IEEE International Parallel and Distributed Processing Symposium.

[10]  Ning Zhang,et al.  Trade-off scheme for fault tolerant connected dominating sets on size and diameter , 2008, FOWANC '08.

[11]  Weili Wu,et al.  Construction of fault-tolerant virtual backbones in wireless networks , 2011 .

[12]  Weili Wu,et al.  Minimum connected dominating sets and maximal independent sets in unit disk graphs , 2006, Theor. Comput. Sci..

[13]  Donghyun Kim,et al.  Constructing weakly connected dominating set for secure clustering in distributed sensor network , 2010, Journal of Combinatorial Optimization.

[14]  Donghyun Kim,et al.  Construction of Minimum Connected Dominating Set in 3-Dimensional Wireless Network , 2008, WASA.

[15]  Donghyun Kim,et al.  Constructing Minimum Connected Dominating Sets with Bounded Diameters in Wireless Networks , 2009, IEEE Transactions on Parallel and Distributed Systems.

[16]  Panos M. Pardalos,et al.  Connected Dominating Set in Wireless Networks , 2013 .

[17]  Ivan Stojmenovic,et al.  On calculating power-aware connected dominating sets for efficient routing in ad hoc wireless networks , 2002, J. Commun. Networks.

[18]  Yingshu Li,et al.  Construction algorithms for k-connected m-dominating sets in wireless sensor networks , 2008, MobiHoc '08.

[19]  Ning Zhang,et al.  On approximation algorithms of k-connected m-dominating sets in disk graphs , 2007, Theor. Comput. Sci..

[20]  Yiwei Wu and Yingshu Li,et al.  Connected Dominating Sets , 2009 .

[21]  Weili Wu,et al.  A greedy approximation for minimum connected dominating sets , 2004, Theor. Comput. Sci..

[22]  Yingshu Li,et al.  Constructing k-Connected m-Dominating Sets in Wireless Sensor Networks , 2007, MILCOM 2007 - IEEE Military Communications Conference.

[23]  Charles J. Colbourn,et al.  Unit disk graphs , 1991, Discret. Math..

[24]  Weiping Shang,et al.  On minimum m-connected k-dominating set problem in unit disc graphs , 2008, J. Comb. Optim..

[25]  Yu-Chee Tseng,et al.  The Broadcast Storm Problem in a Mobile Ad Hoc Network , 1999, Wirel. Networks.

[26]  Peng-Jun Wan,et al.  Distributed Construction of Connected Dominating Set in Wireless Ad Hoc Networks , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[27]  Ding-Zhu Du,et al.  Localized Construction of Connected Dominating Set in Wireless Networks , 2004 .

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

[29]  Deying Li,et al.  Minimum Power Strongly Connected Dominating Sets in Wireless Networks , 2008, ICWN.

[30]  Minming Li,et al.  Tighter Approximation Bounds for Minimum CDS in Wireless Ad Hoc Networks , 2009, ISAAC.

[31]  Michael Segal,et al.  A simple improved distributed algorithm for minimum CDS in unit disk graphs , 2005, WiMob'2005), IEEE International Conference on Wireless And Mobile Computing, Networking And Communications, 2005..

[32]  Shiow-Fen Hwang,et al.  A study of recent research trends and experimental guidelines in mobile ad-hoc network , 2005, 19th International Conference on Advanced Information Networking and Applications (AINA'05) Volume 1 (AINA papers).

[33]  Donghyun Kim,et al.  Recyclable Connected Dominating Set for Large Scale Dynamic Wireless Networks , 2008, WASA.

[34]  Donghyun Kim,et al.  A Better Approximation Algorithm for Computing Connected Dominating Sets in Unit Ball Graphs , 2010, IEEE Transactions on Mobile Computing.

[35]  Deying Li,et al.  A polynomial‐time approximation scheme for the minimum‐connected dominating set in ad hoc wireless networks , 2003, Networks.

[36]  David S. Johnson,et al.  Approximation algorithms for combinatorial problems , 1973, STOC.

[37]  Arunabha Sen,et al.  Broadcast scheduling algorithms for radio networks , 1995, Proceedings of MILCOM '95.

[38]  Ian F. Akyildiz,et al.  Sensor Networks , 2002, Encyclopedia of GIS.

[39]  K. Menger.  Zur allgemeinen Kurventheorie , 1927 .

[40]  Jens Vygen,et al.  The Book Review Column1 , 2020, SIGACT News.

[41]  Raheem A. Beyah,et al.  On the construction of k-connected m-dominating sets in wireless networks , 2012, J. Comb. Optim..