New algorithms and hardness for incremental single-source shortest paths in directed graphs
New algorithms and hardness for incremental single-source shortest paths in directed graphs
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有向图中增量单源最短路径的新算法和硬度
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
Nicole Wein
中科院分区：
文献类型：
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作者：
M. Gutenberg;V. V. Williams;Nicole Wein
在动态单源最短路径（SSSP）问题中，我们给出了图形g =（v，e），但要受边缘插入和删除和源顶点s∈V，目标是维持距离d（s ，t）对于所有t∈V。细粒度的复杂性为确切的部分动态SSSP提供了强的下限，并且近似于完全动态的SSSP [ESA'04，focs'14，stoc'15]。有效的部分动态（1+є） - Approximate SSSP算法[STOC'14，ICALP'15，SODA'14，focs'14，Stoc'16，Soda'17，Soda'17，Icalp'17，Ialicp'17，Icalp'19，Icalp'19，Stoc'19，Soda，Soda，Soda，Soda，Soda '20，尽管有很多文献，但对于（1+є） - 敏感的动态SSSP，其表现不佳，但其性能比经典的ES-Tree [Jacm'81]首先，我们在加权的有向图中提出了一个确定性的数据结构，并具有总更新时间（n 2 logw/єo（1））最小的算法在图表中的最大重量也比Henzinger等人[stoc'14，iCalp'15]改进了最佳的已知动态随机算法，我们提供了有条件的下限。 ，给定多项式预处理时间。具有O（M 2-є）预处理时间的部分动态SSSP算法需要摊销更新或查询时间m 1-O（1），这基本上是最佳的。 '14]仅用于“组合”算法，而我们的新下限并没有限制这种限制。
In the dynamic Single-Source Shortest Paths (SSSP) problem, we are given a graph G=(V,E) subject to edge insertions and deletions and a source vertex s∈ V, and the goal is to maintain the distance d(s,t) for all t∈ V. Fine-grained complexity has provided strong lower bounds for exact partially dynamic SSSP and approximate fully dynamic SSSP [ESA’04, FOCS’14, STOC’15]. Thus much focus has been directed towards finding efficient partially dynamic (1+є)-approximate SSSP algorithms [STOC’14, ICALP’15, SODA’14, FOCS’14, STOC’16, SODA’17, ICALP’17, ICALP’19, STOC’19, SODA’20, SODA’20]. Despite this rich literature, for directed graphs there are no known deterministic algorithms for (1+є)-approximate dynamic SSSP that perform better than the classic ES-tree [JACM’81]. We present the first such algorithm. We present a deterministic data structure for incremental SSSP in weighted directed graphs with total update time Õ(n 2 logW/є O(1)) which is near-optimal for very dense graphs; here W is the ratio of the largest weight in the graph to the smallest. Our algorithm also improves over the best known partially dynamic randomized algorithm for directed SSSP by Henzinger et al. [STOC’14, ICALP’15] if m=ω(n 1.1). Complementing our algorithm, we provide improved conditional lower bounds. Henzinger et al. [STOC’15] showed that under the OMv Hypothesis, the partially dynamic exact s-t Shortest Path problem in undirected graphs requires amortized update or query time m 1/2−o(1), given polynomial preprocessing time. Under a new hypothesis about finding Cliques, we improve the update and query lower bound for algorithms with polynomial preprocessing time to m 0.626−o(1). Further, under the k-Cycle hypothesis, we show that any partially dynamic SSSP algorithm with O(m 2−є) preprocessing time requires amortized update or query time m 1−o(1), which is essentially optimal. All previous conditional lower bounds that come close to our bound [ESA’04,FOCS’14] only held for “combinatorial” algorithms, while our new lower bound does not make such restrictions.
更好的距离保持器和附加扳手
影响因子：
1.3
作者：
Bodwin, Greg;Williams, Virginia Vassilevska
通讯作者：
Williams, Virginia Vassilevska
稀疏图中最短循环和路径的严格硬度
DOI：
10.1137/1.9781611975031.91
发表时间：
2018
期刊：
Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms
影响因子：
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作者：
Lincoln, A.;Vassilevska Williams, V.;Williams, R.
通讯作者：
Williams, R.
用于平衡切割的确定性算法及其在动态连接、流等方面的应用
DOI：
10.1109/focs46700.2020.00111
发表时间：
2020
期刊：
2020
影响因子：
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作者：
Chuzhoy, Julia;Gao, Yu;Li, Jason;Nanongkai, Danupon;Peng, Richard;Saranurak, Thatchaphol
通讯作者：
Saranurak, Thatchaphol