Algebraic gossip: a network coding approach to optimal multiple rumor mongering
The problem of simultaneously disseminating k messages in a large network of n nodes, in a decentralized and distributed manner, where nodes only have knowledge about their own contents, is studied. In every discrete time-step, each node selects a communication partner randomly, uniformly among all...
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| Veröffentlicht in: | IEEE transactions on information theory 2006-06, Vol.52 (6), p.2486-2507 |
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| container_title | IEEE transactions on information theory |
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| creator | Deb, S. Medard, M. Choute, C. |
| description | The problem of simultaneously disseminating k messages in a large network of n nodes, in a decentralized and distributed manner, where nodes only have knowledge about their own contents, is studied. In every discrete time-step, each node selects a communication partner randomly, uniformly among all nodes and only one message can be transmitted. The goal is to disseminate rapidly, with high probability, all messages to all nodes. It is shown that a random linear coding (RLC) based protocol disseminates all messages to all nodes in time ck+/spl Oscr/(/spl radic/kln(k)ln(n)), where c |
| doi_str_mv | 10.1109/TIT.2006.874532 |
| format | Article |
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In every discrete time-step, each node selects a communication partner randomly, uniformly among all nodes and only one message can be transmitted. The goal is to disseminate rapidly, with high probability, all messages to all nodes. It is shown that a random linear coding (RLC) based protocol disseminates all messages to all nodes in time ck+/spl Oscr/(/spl radic/kln(k)ln(n)), where c<3.46 using pull-based dissemination and c<5.96 using push-based dissemination. Simulations suggest that c<2 might be a tighter bound. Thus, if k/spl Gt/(ln(n))/sup 3/, the time for simultaneous dissemination RLC is asymptotically at most ck, versus the /spl Omega/(klog/sub 2/(n)) time of sequential dissemination. Furthermore, when k/spl Gt/(ln(n))/sup 3/, the dissemination time is order optimal. When k/spl Lt/(ln(n))/sup 2/, RLC reduces dissemination time by a factor of /spl Omega/(/spl radic/k/lnk) over sequential dissemination. The overhead of the RLC protocol is negligible for messages of reasonable size. A store-and-forward mechanism without coding is also considered. It is shown that this approach performs no better than a sequential approach when k=/spl prop/n. Owing to the distributed nature of the system, the proof requires analysis of an appropriate time-varying Bernoulli process.</description><identifier>ISSN: 0018-9448</identifier><identifier>ISSN: 1063-6692</identifier><identifier>EISSN: 1557-9654</identifier><identifier>EISSN: 1558-2566</identifier><identifier>DOI: 10.1109/TIT.2006.874532</identifier><identifier>CODEN: IETTAW</identifier><language>eng</language><publisher>New York: IEEE</publisher><subject>Algebra ; Asymptotic properties ; Centralized control ; Coding ; Communication system control ; Communications networks ; Data communications ; Data transmission ; Decentralized ; Distributed algorithms ; Distributed computing ; Electrical equipment industry ; Gossip algorithms ; Laboratories ; message dissemination ; Messages ; Network coding ; Networks ; Optimization ; Protocols ; Simulation ; Time measurement ; Time varying systems</subject><ispartof>IEEE transactions on information theory, 2006-06, Vol.52 (6), p.2486-2507</ispartof><rights>Copyright Institute of Electrical and Electronics Engineers, Inc. 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In every discrete time-step, each node selects a communication partner randomly, uniformly among all nodes and only one message can be transmitted. The goal is to disseminate rapidly, with high probability, all messages to all nodes. It is shown that a random linear coding (RLC) based protocol disseminates all messages to all nodes in time ck+/spl Oscr/(/spl radic/kln(k)ln(n)), where c<3.46 using pull-based dissemination and c<5.96 using push-based dissemination. Simulations suggest that c<2 might be a tighter bound. Thus, if k/spl Gt/(ln(n))/sup 3/, the time for simultaneous dissemination RLC is asymptotically at most ck, versus the /spl Omega/(klog/sub 2/(n)) time of sequential dissemination. Furthermore, when k/spl Gt/(ln(n))/sup 3/, the dissemination time is order optimal. When k/spl Lt/(ln(n))/sup 2/, RLC reduces dissemination time by a factor of /spl Omega/(/spl radic/k/lnk) over sequential dissemination. The overhead of the RLC protocol is negligible for messages of reasonable size. A store-and-forward mechanism without coding is also considered. It is shown that this approach performs no better than a sequential approach when k=/spl prop/n. Owing to the distributed nature of the system, the proof requires analysis of an appropriate time-varying Bernoulli process.</description><subject>Algebra</subject><subject>Asymptotic properties</subject><subject>Centralized control</subject><subject>Coding</subject><subject>Communication system control</subject><subject>Communications networks</subject><subject>Data communications</subject><subject>Data transmission</subject><subject>Decentralized</subject><subject>Distributed algorithms</subject><subject>Distributed computing</subject><subject>Electrical equipment industry</subject><subject>Gossip algorithms</subject><subject>Laboratories</subject><subject>message dissemination</subject><subject>Messages</subject><subject>Network coding</subject><subject>Networks</subject><subject>Optimization</subject><subject>Protocols</subject><subject>Simulation</subject><subject>Time measurement</subject><subject>Time varying systems</subject><issn>0018-9448</issn><issn>1063-6692</issn><issn>1557-9654</issn><issn>1558-2566</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2006</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNp90c9LwzAUB_AgCs7p2YOX4EG8dL6kSdp4G-KPwcDL7iHJ3ma1bWraIv73ZkwQPOwUAp_3SL5fQi4ZzBgDfbdarGYcQM3KQsicH5EJk7LItJLimEwAWJlpIcpTctb37-kqJOMT8jqvt-iirTzdhr6vuntqaYvDV4gf1Id11W6p7boYrH-jQ6ChG6rG1rQZ66HqaqRxbEKkTWi3GBM-JycbW_d48XtOyerpcfXwki1fnxcP82XmBYchc545VXKBa1cUFiC3DB3zyKUvBKDWubaIjpdOOii8VKVfS8HWTvGN2Kh8Sm72a9PLPkfsB9NUvce6ti2GsTe8BA4CZIK3ByHLlUw5cSgSvf5H38MY2_QLw3mRA1dMH0JMS82Ygh262yMfU6YRN6aLKbX4bRiYXVkmlWV2ZZl9WWniaj9RIeKfVnkpBeQ__SKPJg</recordid><startdate>200606</startdate><enddate>200606</enddate><creator>Deb, S.</creator><creator>Medard, M.</creator><creator>Choute, C.</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>F28</scope><scope>FR3</scope></search><sort><creationdate>200606</creationdate><title>Algebraic gossip: a network coding approach to optimal multiple rumor mongering</title><author>Deb, S. ; Medard, M. ; Choute, C.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c420t-bc1b6824edb77a003a1eb1ce25c740e9939aeeb28b5b07c568cd541db62f4f63</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2006</creationdate><topic>Algebra</topic><topic>Asymptotic properties</topic><topic>Centralized control</topic><topic>Coding</topic><topic>Communication system control</topic><topic>Communications networks</topic><topic>Data communications</topic><topic>Data transmission</topic><topic>Decentralized</topic><topic>Distributed algorithms</topic><topic>Distributed computing</topic><topic>Electrical equipment industry</topic><topic>Gossip algorithms</topic><topic>Laboratories</topic><topic>message dissemination</topic><topic>Messages</topic><topic>Network coding</topic><topic>Networks</topic><topic>Optimization</topic><topic>Protocols</topic><topic>Simulation</topic><topic>Time measurement</topic><topic>Time varying systems</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Deb, S.</creatorcontrib><creatorcontrib>Medard, M.</creatorcontrib><creatorcontrib>Choute, C.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><jtitle>IEEE transactions on information theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Deb, S.</au><au>Medard, M.</au><au>Choute, C.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Algebraic gossip: a network coding approach to optimal multiple rumor mongering</atitle><jtitle>IEEE transactions on information theory</jtitle><stitle>TIT</stitle><date>2006-06</date><risdate>2006</risdate><volume>52</volume><issue>6</issue><spage>2486</spage><epage>2507</epage><pages>2486-2507</pages><issn>0018-9448</issn><issn>1063-6692</issn><eissn>1557-9654</eissn><eissn>1558-2566</eissn><coden>IETTAW</coden><abstract>The problem of simultaneously disseminating k messages in a large network of n nodes, in a decentralized and distributed manner, where nodes only have knowledge about their own contents, is studied. In every discrete time-step, each node selects a communication partner randomly, uniformly among all nodes and only one message can be transmitted. The goal is to disseminate rapidly, with high probability, all messages to all nodes. It is shown that a random linear coding (RLC) based protocol disseminates all messages to all nodes in time ck+/spl Oscr/(/spl radic/kln(k)ln(n)), where c<3.46 using pull-based dissemination and c<5.96 using push-based dissemination. Simulations suggest that c<2 might be a tighter bound. Thus, if k/spl Gt/(ln(n))/sup 3/, the time for simultaneous dissemination RLC is asymptotically at most ck, versus the /spl Omega/(klog/sub 2/(n)) time of sequential dissemination. Furthermore, when k/spl Gt/(ln(n))/sup 3/, the dissemination time is order optimal. When k/spl Lt/(ln(n))/sup 2/, RLC reduces dissemination time by a factor of /spl Omega/(/spl radic/k/lnk) over sequential dissemination. The overhead of the RLC protocol is negligible for messages of reasonable size. A store-and-forward mechanism without coding is also considered. It is shown that this approach performs no better than a sequential approach when k=/spl prop/n. Owing to the distributed nature of the system, the proof requires analysis of an appropriate time-varying Bernoulli process.</abstract><cop>New York</cop><pub>IEEE</pub><doi>10.1109/TIT.2006.874532</doi><tpages>22</tpages><oa>free_for_read</oa></addata></record> |
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| source | IEEE Electronic Library (IEL) |
| subjects | Algebra Asymptotic properties Centralized control Coding Communication system control Communications networks Data communications Data transmission Decentralized Distributed algorithms Distributed computing Electrical equipment industry Gossip algorithms Laboratories message dissemination Messages Network coding Networks Optimization Protocols Simulation Time measurement Time varying systems |
| title | Algebraic gossip: a network coding approach to optimal multiple rumor mongering |
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