Topology recognition and leader election are fundamental tasks in distributed computing in networks. The first of them requires each node to find a labeled isomorphic copy of the network, while the result of the second one consists in a single node adopting the label 1 (leader), with all other nodes adopting the label 0 and learning a path to the leader. We consider both these problems in netwo...

A Distributed system is an application which executes a collection of protocols to coordinate the actions of multiple processes on a network, such that all components cooperate together in order to perform a single or small set of related tasks. It is very difficult for processes to cooperate with each other because of failures of any of the process during communication. The leader election is ...

In heterotic string theory compactified on T , the T-duality orbits of dyons of charge (Q,P ) are characterized by O(6, 22; R ) invariants Q, P 2 and Q · P together with a set of invariants of the discrete T-duality group O(6, 22; ZZ). We study the action of S-duality group on the discrete T-duality invariants and study its consequence for the dyon degeneracy formula. In particular we find that...

We resolve a conjecture proposed by D.E. Knuth concerning a recurrence arising in the satisfiability problem. Knuth’s recurrence resembles recurrences arising in the analysis of tries, in particular PATRICIA tries, and asymmetric leader election. We solve Knuth’s recurrence exactly and asymptotically, using analytic techniques such as the Mellin transform and analytic depoissonization.

A silent self-stabilizing asynchronous distributed algorithm, SSLE, for the leader election problem, in a connected unoriented network with unique IDs, is given. SSLE uses O(log n) space per process and stabilizes in O(n) rounds, where n is the number of processes in the network.

To establish lower bounds on the amount of replication, there is a common partition argument used to construct indistinguishable executions such that one violates some property of interest. This violation leads to the conclusion that the lower bound on process replication is of the form n > bkt/bc, where t is the maximum number of process failures in any of these executions and k, b are positiv...

Formation of scatternet using Bluetooth devices increases device tractability thereby inviting new networking applications to be designed on it. In this paper we propose Bluetooth Scatternet Formation and Routing Protocol (BSFRP). It is a distributed protocol that handles node mobility and enables multi-hop communication. BSFRP defines rules for topology discovery, scatternet formation and rout...

Among the familiar basic facts concerning unrestricted permutational wreath products (sketched in the first few paragraphs of the last section of Cossey, Kegel, and Kov~cs [2]), the Embedding Theorem has the central role. It asserts the existence of an embedding; the proof is a construction which involves arbitrarily chosen coset representatives, with the effect that the embedding constructed m...

We present a survey of formal speci cation techniques applied to the Tree Identify Protocol of the IEEE 1394 High Performance Serial Bus. Speci cations written in a variety of formalisms are compared with regard to a number of criteria including expressiveness, readability, standardisation, and level of analysis.

This paper presents a protocol for leader election in complete networks with a sense of direction. Sense of direction provides nodes the capability of distinguishing between their incident links according to a global scheme. We propose a protocol for leader election which requires O(N) messages and O(log N) time. The protocol is message optimal and the time complexity is a signiicant improvemen...