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Optimal gossiping in paths and cycles

Francis C.M. Lau, S.H. Zhang
<span title="">2003</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/usw2n4yaarcurchx7i4on2iqea" style="color: black;">Journal of Discrete Algorithms</a> </i> &nbsp;
We study the path and the cycle which are essential building blocks for more complex structures. We present tight lower bounds and algorithms which match them.  ...  In the gossiping problem, each node in a network possesses a token initially; after gossiping, every node has a copy of every other node's token. The nodes exchange their tokens by packets.  ...  Acknowledgements This work is supported in part by a Hong Kong RGC Grant (9/2002). The authors are grateful to the reviewers for their useful comments.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s1570-8667(03)00038-8">doi:10.1016/s1570-8667(03)00038-8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5da46tzrdbc5rjnaiv2guucfge">fatcat:5da46tzrdbc5rjnaiv2guucfge</a> </span>
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Better bounds for perpetual gossiping

A.D. Scott
<span title="">1997</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lx7dev2le5anbg6oarljwh7lie" style="color: black;">Discrete Applied Mathematics</a> </i> &nbsp;
Improving upon results of Liestman and Richards, we give bounds on W,(G) for the cases when G is a path, cycle or hypercube. *  ...  In the perpetual gossiping problem, introduced by Lie&man and Richards, information may be generated at any time and at any vertex of a graph G; adjacent vertices can communicate by telephone calls.  ...  As before, let C be an optimal gossiping scheme for C, with gossip window of size w = W,(C,).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0166-218x(96)00088-1">doi:10.1016/s0166-218x(96)00088-1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/uob7zmwel5h4bepixpvocemlu4">fatcat:uob7zmwel5h4bepixpvocemlu4</a> </span>
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Gossiping in chordal rings under the line model

Lali Barrière, Johanne Cohen, Margarida Mitjana
<span title="">2001</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
We p r o p o s e polynomial algorithms to derive optimal or near optimal gossip protocols in the chordal ring.  ...  Our gossip algorithms are based on the so-called 3-phase gossip method 15]. For that purpose, the Section 3 gives a decomposition of the chordal ring into disjoint cycles.  ...  Gossip Algorithm for the chordal ring C(N c) In this section, we describe a polynomial time algorithm to compute an optimal communication scheme for gossiping in any chordal ring C(N c).  ... 
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Subject Index

<span title="">2003</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/usw2n4yaarcurchx7i4on2iqea" style="color: black;">Journal of Discrete Algorithms</a> </i> &nbsp;
factorizations of strings, 357 Gossiping Optimal gossiping in paths and cycles, 461 Group communication Cooperative computing with fragmentable and mergeable groups, 211 H-PRAM Optimal broadcast  ...  graphs, 281; Optimal gossiping in paths and cycles, 461 Interval routing The compactness of adaptive routing tables, 237 Leader election Exact communication costs for consensus and leader in a  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s1570-8667(03)00075-3">doi:10.1016/s1570-8667(03)00075-3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/icg7if3uingibmjwy2mjud4rwe">fatcat:icg7if3uingibmjwy2mjud4rwe</a> </span>
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Page 6973 of Mathematical Reviews Vol. , Issue 96k [page]

<span title="">1996</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
(D-PDRB; Paderborn); Wagener, Hubert (D-PDRB; Paderborn) Gossiping in vertex-disjoint paths mode in d-dimensional grids and planar graphs.  ...  In this paper we describe new algorithms for embedding Hamiltonian cycles along with ranking and unranking algorithms with respect to them, and for embedding the set of cycles.  ... 
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Optimal Routing in Gossip Networks

Y. Shavitt, A. Shay
<span title="">2005</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/fmebo7gm4vhg7ljs3x2bbrazk4" style="color: black;">IEEE Transactions on Vehicular Technology</a> </i> &nbsp;
Our gossip network model was built based on research done in "ad-hoc networks" and "stochastic shortest path routing".  ...  Travelers then use the gossip information to recourse their path and find the shortest path to destination.  ...  We assume that under all weight distributions there are no negative cost cycles in the network and there is always a path between source and destination.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tvt.2005.851351">doi:10.1109/tvt.2005.851351</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/l5wwuia7zrce5jdck3jhseh5dm">fatcat:l5wwuia7zrce5jdck3jhseh5dm</a> </span>
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Note on optimal gossiping in some weak-connected graphs

Juraj Hromkovič, Claus-Dieter Jeschke, Burkhard Monien
<span title="">1994</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
Acknowledgment We would like to thank Mike Paterson and the unknown referees for the suggestions and comments which have helped to improve the presentation of this paper.  ...  Optimal or almost optimal gossip algorithms are designed for two-dimensional grids in [ 11, and for multidimensional grids in [4] .  ...  In this way we obtain optimal gossip algorithms for some families of graphs which have at least one bridge or at least one cycle which is edge-disjoint from all other cycles in the graph.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0304-3975(94)90049-3">doi:10.1016/0304-3975(94)90049-3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3oqbdbnaj5c2vecaxkqdz4zfgq">fatcat:3oqbdbnaj5c2vecaxkqdz4zfgq</a> </span>
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Page 3077 of Mathematical Reviews Vol. , Issue 95e [page]

<span title="">1995</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Summary (p. 355): “We study perpetual gossip in paths, cycles, hypercubes, and complete graphs. We find optimal 1-call perpetual gossip schemes for paths of length n and for cycles of n vertices.  ...  We give nontrivial lower and upper bounds on the size of the minimum gossip window for k-call perpetual gossip in paths and cycles for larger k.  ... 
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Page 6355 of Mathematical Reviews Vol. , Issue 95j [page]

<span title="">1995</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
For those networks in which a Hamiltonian path exists (hypercubes, cube connected cycles, butterflies, shuffle 95j:90040 exchange, etc.) optimal algorithms can be obtained quite easily, but for complete  ...  A thorough study of these communi- cation modes is presented by giving optimal algorithms for broad- casting, accumulation and gossiping in most of the well-known parallel architectures.  ... 
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Page 7099 of Mathematical Reviews Vol. , Issue 97K [page]

<span title="">1997</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
The main results are (1) optimal gossip al- gorithms for paths, complete graphs and flakes in both modes; and (2) for hypercubes, cube-connected cycles, butterfly networks, etc., gossip algorithms which  ...  Since optimal broadcast and accumulation algorithms for these modes can be achieved in a straightforward way for al- most all interconnection networks used, the paper concentrates on the gossip problem  ... 
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Epidemic Broadcast Trees

Joao Leitao, Jose Pereira, Luis Rodrigues
<span title="">2007</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/vb3ehoarofgm5p24f2dqjxmp3a" style="color: black;">2007 26th IEEE International Symposium on Reliable Distributed Systems (SRDS 2007)</a> </i> &nbsp;
We use a low cost scheme to build and maintain broadcast trees embedded on a gossip-based overlay.  ...  The protocol sends the message payload preferably via tree branches but uses the remaining links of the gossip overlay for fast recovery and expedite tree healing.  ...  This is expected, as these failures may remove links that were part of the optimal paths between nodes.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/srds.2007.27">doi:10.1109/srds.2007.27</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/srds/LeitaoPR07.html">dblp:conf/srds/LeitaoPR07</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ongbfjjc7rbwfid63tk2vgi67e">fatcat:ongbfjjc7rbwfid63tk2vgi67e</a> </span>
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Page 7259 of Mathematical Reviews Vol. , Issue 2004i [page]

<span title="">2004</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Algorithms for gossiping in paths and cycles are given which achieve these bounds. A. T.  ...  [Zhang, Shu Hua'] | PRC-HK-CIS: Hong Kong Optimal gossiping in paths and cycles. (English summary) J. Discrete Algorithms 1 (2003), no. 5-6, 461—475.  ... 
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Communication in the two-way listen-in vertex-disjoint paths mode

Hans-Joachim Böckenhauer
<span title="">2001</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
In this paper we will design optimal broadcast, accumulation, and gossip algorithms for various classes of networks including paths, cycles, and hypercube-like networks.  ...  In Section 4 we will determine the exact broadcast, accumulation, and gossip complexity of complete graphs, paths, cycles, hypercubes, and hypercube-like networks.  ...  In the rest of the section we will present our main results, optimal accumulation and gossip algorithms for grids with an odd number of vertices.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0304-3975(00)00214-0">doi:10.1016/s0304-3975(00)00214-0</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hwkgqkzecvgzxkp7egay4ru2r4">fatcat:hwkgqkzecvgzxkp7egay4ru2r4</a> </span>
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Optimal algorithms for dissemination of information in generalized communication modes [chapter]

R. Feldmann, J. Hromkovic, S. Madhavapeddy, B. Monien, P. Mysliwietz
<span title="">1992</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
For those networks in which a Hamiltonian path exists (hypercubes, cube connected cycles, butterflies, shuffle exchange, etc.) optimal algorithms can be obtained quite easily, but for complete binary trees  ...  A thorough study of these communication modes will be presented by giving optimal algorithms for broadcasting, accwnulatian and gossiping in most of the well-known parallel architectures.  ...  Edge-disjoint paths mode In this section we give some results for broadcast, accumulation and gossip in edge-disjoint paths mode.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-55599-4_84">doi:10.1007/3-540-55599-4_84</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/64zeze37ivaj5d67tzedqqpysu">fatcat:64zeze37ivaj5d67tzedqqpysu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170930102612/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/8d2/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS8wMTY2MjE4eDk0OTAxNzkx.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ce/48/ce4867018557d63a2ca57382db651b5a56802b1e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-55599-4_84"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Optimal algorithms for dissemination of information in generalized communication modes

R. Feldmann, J. Hromkovič, S. Madhavapeddy, B. Monien, P. Mysliwietz
<span title="">1994</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lx7dev2le5anbg6oarljwh7lie" style="color: black;">Discrete Applied Mathematics</a> </i> &nbsp;
For those networks in which a Hamiltonian path exists (hypercubes, cube connected cycles, butterflies, shuffle exchange, etc.) optimal algorithms can be obtained quite easily, but for complete binary trees  ...  A thorough study of these communication modes will be presented by giving optimal algorithms for broadcasting, accwnulatian and gossiping in most of the well-known parallel architectures.  ...  Edge-disjoint paths mode In this section we give some results for broadcast, accumulation and gossip in edge-disjoint paths mode.  ... 
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