Self-stabilizing master-slave token circulation and efficient size-computation in a unidirectional ring of arbitrary size

Self-stabilizing algorithms represent an extension of distributed algorithms in which nodes of the network have neither coordination, synchronization, nor initialization. We consider the model where there is one designated master node and all other nodes are anonymous and have constant space. Recently, Lee et al. obtained such an algorithm for determining the size of a unidirectional ring. We provide a new algorithm that converges much quicker. This algorithm exploits a token-circulation idea due to Afek and Brown. Disregarding the time for stabilization, our algorithm computes the size of the ring at the master node in O(n log n) time compared to O(n3) steps used in the algorithm by Lee et al. using the same computing paradigm. It seems likely that one should be able to obtain master-slave algorithms for other problems in networks.

[1]  Mohamed G. Gouda,et al.  The alternator , 2007, Distributed Computing.

[2]  David E. Culler,et al.  System architecture directions for networked sensors , 2000, SIGP.

[3]  Gerard Tel,et al.  Introduction to Distributed Algorithms: Contents , 2000 .

[4]  Jonathan W. Hui,et al.  T 2 : A Second Generation OS For Embedded Sensor Networks , 2005 .

[5]  Janos Simon,et al.  Deterministic, Constant Space, Self-Stabilizing Leader Election on Uniform Rings , 1995, WDAG.

[6]  Shing-Tsaan Huang,et al.  A space-efficient self-stabilizing algorithm for measuring the size of ring networks , 2005, Inf. Process. Lett..

[7]  Dhiraj K. Pradhan,et al.  A cluster-based approach for routing in dynamic networks , 1997, CCRV.

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

[9]  Yehuda Afek,et al.  Self-stabilization over unreliable communication media , 2005, Distributed Computing.

[10]  Geoffrey Brown,et al.  Self-Stabilization of the Alternating-Bit Protocol , 1989, The Sixteenth Conference of Electrical and Electronics Engineers in Israel,.

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

[12]  Mohamed F. Younis,et al.  Energy-aware routing in cluster-based sensor networks , 2002, Proceedings. 10th IEEE International Symposium on Modeling, Analysis and Simulation of Computer and Telecommunications Systems.

[13]  Shlomi Dolev,et al.  Memory requirements for silent stabilization , 1999, Acta Informatica.