Randomized distributed shortest paths algorithms
Randomized distributed shortest paths algorithms
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随机分布式最短路径算法
DOI：
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发表时间：
1989
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通讯作者：
B. Awerbuch
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文献类型：
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作者：
B. Awerbuch
本文涉及在异步通信网络中找到最短路径的分布式算法。 <Italic> e </italic> + <italic> v </italic>•<italic> d </italic>）通信。 /italic> <supscrpt> 1+ε</supscrpt>）和<italic> o </Tailic>（<italic> e </tatic> <supscrpt> <supscrpt> 1+ε</supscrpt>）消息，用于任何ε > 0。（这里，<italic> v </italic>是节点的数量，<italic> e </italic>是边数，<italic> d </italic>是直径。）这构成了一个主要步骤要实现＆ohgr的下限;（<italic> e </italic>）通信和＆ohgr;（<italic> d </italic>）时间。
对于一般（加权）最短路径问题，先前已知的最短路径算法<Italic> o </italic>（<italic> k </italic> </italic>·<italic> v </italic> v </italic> <supscrpt> <supscrpt> 2 </supscrpt </supscrpt </supscrpt >）消息和<italic> o </italic>（<Italic> v </italic>·log <Subcrpt> <Italic> k </italic> </itscrpt> </subscrpt> <italic> v </italic> v </italic>）时间算法需要<Italic> o </italic>（<italic> e </italic> <supscrpt> 1 +ε</supscrpt>·log <italic> w </italic> w </italic>）消息和<italic> o </italic> o </italic> o </italic> （<italic> v </italic> <supscrpt> 1 +ε</supscrpt>·log <italic> w </italic>）时间。
我们的结果使得可以改善其他基本网络问题（例如领导者选举）的明显解决方案。
This paper is concerned with distributed algorithm for finding shortest paths in an asynchronous communication network. For the problem of Breadth First Search, the best previously known algorithms required either &THgr;(<italic>V</italic>) time, or &THgr; (<italic>E</italic> + <italic>V</italic> · <italic>D</italic>) communication. We present new algorithm, which requires <italic>O</italic>(<italic>D</italic><supscrpt>1+ε</supscrpt>) time, and <italic>O</italic>(<italic>E</italic><supscrpt>1+ε</supscrpt>) messages, for any ε > 0. (Here, <italic>V</italic> is number of nodes, <italic>E</italic> is number of edges and <italic>D</italic> is the diameter.) This constitutes a major step towards achieving the lower bounds, which are &OHgr;(<italic>E</italic>) communication and &OHgr;(<italic>D</italic>) time.
For the general (weighted) shortest paths problem, previously known shortest-paths algorithms required <italic>O</italic>(<italic>k</italic> · <italic>V</italic><supscrpt>2</supscrpt>) messages and <italic>O</italic>(<italic>V</italic> · log<subscrpt><italic>k</italic></subscrpt> <italic>V</italic>) time. Our algorithm requires <italic>O</italic>(<italic>E</italic><supscrpt>1 + ε</supscrpt> · log <italic>W</italic>) messages and <italic>O</italic> (<italic>V</italic><supscrpt>1 + ε</supscrpt> · log <italic>W</italic>) time.
Our results enable to improve significantly solutions for other basic network problems (e.g. leader election).