Gossiping in Vertex-Disjoint Path Mode in Interconnection Networks

The communication modes (one-way and two-way mode) used for disseminating information among processors of interconnection networks via vertex-disjoint paths in one communication step are investigated. The complexity of communication algorithms is measured by the number of communication steps (rounds). Since optimal broadcast and accumulation algorithms for these modes can be achieved in a straightforward way for almost all interconnection networks used, the paper concentrates on the gossip problem. The main results are listed below: 1. Optimal gossip algorithms for paths, complete graphs and flakes in both modes. 2. For hypercubes, cube-connected cycles, butterfly networks, etc., gossip algorithms which are only about O(log2 log2n) rounds slower than the optimal gossip algorithms on complete graphs are designed. Furthermore, it is shown that at least Ω(log2 log2 log2n) rounds more than needed by the optimal gossip algorithm on the complete graph are necessary for every “well-structured” gossip algorithm on networks with “small” degree.

[1]  F. Leighton,et al.  Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes , 1991 .

[2]  Frank Harary,et al.  The communication problem on graphs and digraphs , 1974 .

[3]  Pierre Fraigniaud,et al.  Methods and problems of communication in usual networks , 1994, Discret. Appl. Math..

[4]  Burkhard Monien,et al.  Embedding one interconnection network in another , 1990 .

[5]  Arthur M. Farley.  Minimum-time line broadcast networks , 1980, Networks.

[6]  Rainer Feldmann,et al.  The Cube-Connected Cycles Network Is a Subgraph of the Butterfly Network , 1992, Parallel Process. Lett..

[7]  David W. Krumme,et al.  Gossiping in Minimal Time , 1992, SIAM J. Comput..

[8]  P. Slater,et al.  Gossips and telegraphs , 1979 .

[9]  Rainer Bodendiek,et al.  Topics In Combinatorics and Graph Theory , 1992 .

[10]  Juraj Hromkovic,et al.  Optimal algorithms for dissemination of information in generalized communication modes , 1994, Discret. Appl. Math..

[11]  Arthur L. Liestman,et al.  A survey of gossiping and broadcasting in communication networks , 1988, Networks.

[12]  Juraj Hromkovic,et al.  Optimal Algorithms for Dissemination of Information in Some Interconnection Networks (Extended Abstract) , 1990, MFCS.

[13]  Walter Knödel,et al.  New gossips and telephones , 1975, Discret. Math..

[14]  Peter Winkler,et al.  Fast Information Sharing in a Complete Network , 1993, Discret. Appl. Math..

[15]  Ralf Klasing,et al.  Broadcasting in Butterfly and deBruijn Networks , 1992, Discret. Appl. Math..

[16]  Rainer Feldmann,et al.  The Shuffle Exchange Network has a Hamiltonian Path , 1992, MFCS.

[17]  Juraj Hromkovic,et al.  Optimal Algorithms for Disemination of Information in Generalized Communication Modes , 1992, PARLE.

[18]  Shimon Even,et al.  On the number of rounds necessary to disseminate information , 1989, SPAA '89.

[19]  R. Labahn,et al.  Quick Gossiping by Multi-Telegraphs , 1990 .