Broadcast networks of bounded degree
SIAM Journal on Discrete Mathematics
On the number of rounds necessary to disseminate information
SPAA '89 Proceedings of the first annual ACM symposium on Parallel algorithms and architectures
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
SIAM Journal on Computing
Broadcasting in bounded degree graphs
SIAM Journal on Discrete Mathematics
Fast information sharing in a complete network
Discrete Applied Mathematics
Methods and problems of communication in usual networks
Proceedings of the international workshop on Broadcasting and gossiping 1990
Broadcasting in butterfly and deBruijn networks
Proceedings of the international workshop on Broadcasting and gossiping 1990
Traffic-light scheduling on the grid
Proceedings of the international workshop on Broadcasting and gossiping 1990
Proceedings of the international workshop on Broadcasting and gossiping 1990
Gossiping in vertex-disjoint paths mode in d-dimensional grids and planar graphs
Information and Computation
Optimal algorithms for broadcast and gossip in the edge-disjoint path modes
Information and Computation
Broadcasting and gossiping on de Bruijn, shuffle-exchange and similar networks
Discrete Applied Mathematics - Special issue: network communications broadcasting and gossiping
On the Optimality of General Lower Bounds for Broadcasting and Gossiping
SIAM Journal on Discrete Mathematics
Network Communication in Edge-Colored Graphs: Gossiping
IEEE Transactions on Parallel and Distributed Systems
Lower Bounds on Broadcasting Time of de Bruijn Networks
Euro-Par '96 Proceedings of the Second International Euro-Par Conference on Parallel Processing - Volume I
Effective Systolic Algorithms for Gossiping in Cycles and Two-Dimensional Grids (Extended Abstract)
FCT '95 Proceedings of the 10th International Symposium on Fundamentals of Computation Theory
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Gossiping is an extensively investigated information dissemination process in which each processor has a distinct item of information and has to collect all the items possessed by the other processors. In this paper we provide an innovative and general lower bound technique relying on the novel notion of delay digraph of a gossiping protocol and on the use of matrix norm methods. Such a technique is very powerful and allows the determination of new and significantly improved lower bounds in many cases. In fact, we derive the first general lower bound on the gossiping time of systolic protocols, i.e., constituted by a periodic repetition of simple communication steps. In particular, given any network of n processors and any systolic period s, in the directed and the undirected half-duplex cases every s-systolic gossip protocol takes at least log(n)/log(1/@l)-O(loglog(n)) time steps, where @l is the unique solution between 0 and 1 of @l.p"@?"s"/"2"@?(@l).p"@?"s"/"2"@?(@l)=1, with p"i(@l)=1+@l^2+...+@l^2^i^-^2 for any integer i0. We then provide improved lower bounds in the directed and half-duplex cases for many well-known network topologies, such as Butterfly, de Bruijn, and Kautz graphs. All the results are extended also to the full-duplex case. Our technique is very general, as for s-~ it allows the determination of improved results even for non-systolic protocols. In fact, for general networks, as a simple corollary it yields a lower bound only an O(loglog(n)) additive factor far from the general one independently proved in [Proc. 1st ACM Symposium on Parallel Algorithms and Architectures (SPAA), 1989, p. 318; Topics in Combinatorics and Graph Theory (1990) 451; SIAM Journal on Computing 21(1) (1992) 111; Discrete Applied Mathematics 42 (1993) 75] for all graphs and any (non-systolic) gossip protocol. Moreover, for specific networks, it significantly improves with respect to the previously known results, even in the full-duplex case. Correspondingly, better lower bounds on the gossiping time of non-systolic protocols are determined in the directed, half-duplex and full-duplex cases for Butterfly, de Bruijn, and Kautz graphs. Even if in this paper we give only a limited number of examples, our technique has wide applicability and gives a general framework that often allows to get improved lower bounds on the gossiping time of systolic and non-systolic protocols in the directed, half-duplex and full-duplex cases.