Arthur L. Liestman

A survey of gossiping and broadcasting in communication networks

Gossiping and broadcasting are two problems of information dissemination described for a group of individuals connected by a communication network. In gossiping every person in the network knows a unique item of information and needs to communicate it to everyone else. In broadcasting one individual has an item of information which needs to be communicated to everyone else. We review the results that have been obtained on these and related problems.

Approximating minimum size weakly-connected dominating sets for clustering mobile ad hoc networks

We present a series of approximation algorithms for finding a smallweakly-connected dominating set (WCDS) in a given graph to be usedin clustering mobile ad hoc networks. The structure of a graph canbe simplified using WCDSs and made more succinct for routing in adhoc networks. The theoretical performance ratio of these algorithmsis O(ln Δ) compared to the minimum size WCDS, whereΔ is the maximum degree of the input graph. The first twoalgorithms are based on the centralized approximation algorithms ofGuha and Khuller cite guha-khuller-1998 for finding small connecteddominating sets (CDSs). The main contribution of this work is acompletely distributed algorithm for finding small WCDSs and theperformance of this algorithm is shown to be very close to that ofthe centralized approach. Comparisons between our work and someprevious work (CDS-based) are also given in terms of the size ofresultant dominating sets and graph connectivity degradation.

Additive graph spanners

A spanning subgraph S = (V, E′) of a connected simple graph G = (V, E) is a f(x)-spanner if for any pair of nodes u and v, dS(u, v) ≦ f(dG(u, v)), where dG and dS are the usual distance functions in graphs G and S, respectively. We are primarily interested in (t + x)-spanners, which we refer to as additive spanners. We construct low-degree additive spanners for X-trees, pyramids, and multidimensional grids. We prove, for arbitrary t > 0, that to determine whether a given graph G has an additive spanner with no more than m edges is NP-complete.

Broadcast networks of bounded degree

Broadcasting is an information dissemination process in which a message is to be sent from a single originator to all members of a network by placing calls over the communication lines of the network. Several previous papers have investigated ways to construct sparse graphs (networks) in which this process can be completed in minimum time from any originator. The graphs produced by these methods contain high degree vertices. This paper describes graphs with fixed maximum degree in which broadcasting can be completed in near minimum time.

Sparse broadcast graphs

Abstract Broadcasting is an information dissemination process in which a message is to be sent from a single originator to all members of a network by placing calls over the communication lines of the network. Several previous papers have investigated ways to construct sparse graphs (networks) on n vertices in which this process can be completed in minimum time from any originator. In this paper, we describe four techniques to construct graphs of this type and show that they produce the sparsest known graphs for several values of n . For n = 18, n = 19, n = 30 and n = 31 we also show that our new graphs are minimum broadcast graphs (i.e., that no graph with fewer edges is possible). These new graphs can be used with other techniques to improve the best known results for many larger values of n .

Broadcasting in bounded degree graphs

Broadcasting is an information dissemination process in which a message is to be sent from a single originator to all members of a network by placing calls over the communication lines of the network. Several previous papers have investigated methods to construct sparse graphs (networks) in which this process can be completed in minimum time from any originator. The graphs produced by these methods contain high degree vertices. [Liestman and Peters, SIAM Journal on Discrete Mathematics, 1 (1988), pp. 531–540 ] and [Bermond and Peyrat, Proceedings of the 19th SE Conference on Combinatorics, Graph Theory and Computing, Congressus Numerantium, 1988, pp. 283–292] began an investigation of graphs with fixed maximum degree in which broadcasting can be completed in near minimum time. This investigation is continued in this paper by giving lower bounds and constructing bounded degree graphs that allow rapid broadcasting. The constructions use ideas developed by Jerrum and Skyum [IEEE Transactions on Computers, C-...

Fault-tolerant broadcast graphs

Broadcasting refers to the process of information dissemination in a communications network whereby a message, originated by one member, is transmitted to all members of the network. By incorporating redundancy in the calling scheme, the completion of the broadcast may be guaranteed in the presence of up to k link failures. A k fault-tolerant broadcast graph represents a network configuration which admits such a scheme. This article investigates these graphs and the tradeoff between the time allowed for broadcasting and the number of edges required in the graph.

A proposal for a fault-tolerant binary hypercube architecture

A modular fault-tolerant binary hypercube architecture is proposed that uses redundant processors and is suitable for use in long-life unmaintained applications. Each module initially contains 2/sup i/ (for any >or=0) active processors and k spare processors and is constructed so that each of the spare processors can replace any of the active processors (or any of the other spares) within the module. Thus, the module can tolerate up to k processor faults. This scheme is compared to previously proposed fault-tolerant binary hypercube architectures. It is shown that the scheme can achieve the same level of reliability as other proposed schemes while using significantly fewer spares.<<ETX>>

A ZONAL ALGORITHM FOR CLUSTERING AN HOC NETWORKS

A Mobile Ad Hoc Network (MANET) is an infrastructureless wireless network that can support highly dynamic mobile units. The multi-hop feature of a MANET suggests the use of clustering to simplify routing. Graph domination can be used in defining clusters in MANETs. A variant of dominating set which is more suitable for clustering MANETs is the weakly-connected dominating set. A cluster is defined to be the set of vertices dominated by a particular vertex in the dominating set. As it is NP-complete to determine whether a given graph has a weakly-connected dominating set of a particular size, we present a zonal distributed algorithm for finding small weakly-connected dominating sets. In this new approach, we divide the graph into regions, construct a weakly-connected dominating set for each region, and make adjustments along the borders of the regions to produce a weakly-connected dominating set of the entire graph. We present experimental evidence that this zonal algorithm has similar performance to and provides better cluster connectivity than previous algorithms.

Generalizations of broadcasting and gossiping

Three generalizations of broadcasting and gossiping are considered: conference broadcasting in which broadcasting is done by conference calls, partial gossiping in which every gossip must learn at least k pieces of information, and set to set gossiping in which one subset of the members must learn all of the messages of another subset of the members.