Bounded-hop strong connectivity for flocking swarms

In this paper we consider a set of n mobile wireless nodes, which have no information about each other. The only information a single node holds is its current location and future mobility plan. We develop a two-phase distributed self-stabilizing scheme for producing a bounded hop-diameter communication graph. The first phase is dedicated to the construction of an underlying topology for the dissemination of data needed for the second phase. In the second phase the required topology is constructed by means of an asymmetric power assignment under two modes — static and dynamic. The former aims to provide a steady topology for some time interval, while the latter uses the constant node locations changes to produce a constantly changing topology, which succeeds to preserve the required property of the bounded hop-diameter. For the static mode we provide an O(λ,λ2)-bicriteria approximation algorithm so that given a parameter 1 ≤ λ ≤ n −1, we construct a power assignment which induces a static h-bounded hop communication graph, h = n/λ+logλ, with a cost of at most λ times the optimum and network lifetime of at least 1/λ2 times the optimum. For the dynamic mode, given a parameter 1 ≤ h ≤ n −1 we construct an optimal power assignment (in terms of network lifetime) which induces a dynamic h-bounded hop communication graph.

[1]  Afonso Ferreira,et al.  The Minimum Range Assignment Problem on Linear Radio Networks , 2002, Algorithmica.

[2]  Leonidas J. Guibas,et al.  Data structures for mobile data , 1997, SODA '97.

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

[4]  Andrea E. F. Clementi,et al.  Efficient Algorithms for Low-Energy Bounded-Hop Broadcast in Ad-Hoc Wireless Networks , 2004, STACS.

[5]  Leonidas J. Guibas,et al.  Deformable spanners and applications. , 2006, Computational geometry : theory and applications.

[6]  Peter Sanders,et al.  Energy Optimal Routing in Radio Networks Using Geometric Data Structures , 2002, ICALP.

[7]  Bettina Speckmann.  Kinetic Data Structures , 2008, Encyclopedia of Algorithms.

[8]  Andrea E. F. Clementi,et al.  The Power Range Assignment Problem in Radio Networks on the Plane , 2000, STACS.

[9]  Gruia Calinescu,et al.  Bounded-hops power assignment in ad-hoc wireless networks , 2004, 2004 IEEE Wireless Communications and Networking Conference (IEEE Cat. No.04TH8733).

[10]  Reuven Cohen,et al.  Topology Maintenance in Asynchronous Sensor Networks , 2008, 2008 5th Annual IEEE Communications Society Conference on Sensor, Mesh and Ad Hoc Communications and Networks.

[11]  Leonidas J. Guibas,et al.  Kinetic Data Structures , 2004, Handbook of Data Structures and Applications.

[12]  Budhaditya Deb,et al.  A topology discovery algorithm for sensor networks with applications to network management , 2001 .

[13]  Ranveer Chandra,et al.  Adaptive Topology Discovery in Hybrid Wireless Networks , 2002 .

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

[15]  Stefan Funke,et al.  Bounded-Hop Energy-Efficient Broadcast in Low-Dimensional Metrics Via Coresets , 2007, STACS.

[16]  Romit Roy Choudhury,et al.  A distributed mechanism for topology discovery in ad hoc wireless networks using mobile agents , 2000, MobiHoc.

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

[18]  Shlomi Dolev,et al.  Self Stabilization , 2004, J. Aerosp. Comput. Inf. Commun..

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

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

[21]  Michael Segal,et al.  Approximation Algorithms for the Mobile Piercing Set Problem with Applications to Clustering in Ad-Hoc Networks , 2001 .

[22]  Michael Segal,et al.  Dynamic Coverage in Ad-Hoc Sensor Networks , 2005, Mob. Networks Appl..

[23]  Andrea E. F. Clementi,et al.  On the Power Assignment Problem in Radio Networks , 2004, Mob. Networks Appl..

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

[25]  Christian Scheideler,et al.  Constant density spanners for wireless ad-hoc networks , 2005, SPAA '05.

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

[27]  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).

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

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

[30]  M. Segal,et al.  Low-Energy Fault-Tolerant Bounded-Hop Broadcast in Wireless Networks , 2009, IEEE/ACM Transactions on Networking.