Distance Oracles for Unweighted Graphs: Breaking the Quadratic Barrier with Constant Additive Error
Distance Oracles for Unweighted Graphs: Breaking the Quadratic Barrier with Constant Additive Error
复制标题
未加权图的距离预言：打破具有恒定加性误差的二次障碍
DOI：
10.1007/978-3-540-70575-8_50
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
Jayant Upadhyay
中科院分区：
文献类型：
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作者：
Surender Baswana;Akshay Gaur;Sandeep Sen;Jayant Upadhyay
Thorup和Zwick在第二篇论文中[ACM，52（1），2005年，2005年，第1-24页]表明，可以在designa数据结构的亚地带时间中预处理加权的无向图onnvertices，该数据结构仅占据次级次级空间，并且但是，对于任何一对顶点，可以在恒定时间内回答距离查询。目前，最著名的算法[4,3]在这些算法中实现了这些算法的预期o（n2）预处理时间。在实现此目标时，引入（小）恒定的添加误差。其中斜差误差变为2·Wmax（u，v） - sherewmax（u，v）是顶点u，v之间最短路径中的最简短的edge。
Thorup and Zwick, in the seminal paper [Journal of ACM, 52(1),2005, pp 1-24], showed that a weighted undirected graph onnvertices can be preprocessed in subcubic time to designa data structure which occupies only subquadratic space, and yet,for any pair of vertices, can answer distance query approximatelyin constant time. The data structure is termed as approximatedistance oracle. Subsequently, there has been improvement in theirpreprocessing time, and presently the best known algorithms [4,3]achieve expected O(n2) preprocessingtime for these oracles. For a class of graphs, these algorithmsindeed run in θ(n2) time. Inthis paper, we are able to break this quadratic barrier at theexpense of introducing a (small) constant additive error forunweighted graphs. In achieving this goal, we have been able topreserve the optimal size-stretch trade offs of the oracles. One ofour algorithms can be extended to weighted graphs, where theadditive error becomes 2·wmax(u,v) - herewmax(u,v) is the heaviestedge in the shortest path between vertices u,v.