Faster parallel algorithm for approximate shortest path
Faster parallel algorithm for approximate shortest path
复制标题
近似最短路径的更快并行算法
DOI：
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复制
发表时间：
2019
期刊：
影响因子：
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通讯作者：
Jason Li
中科院分区：
文献类型：
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作者：
Jason Li
我们介绍了第一个M polygog（n）工作，在计算（1+є） - 加权，无向图上的最短路径（1+є）模型中的Polyg（n）时间算法。 jacm'00]可以实现O（M 1+є0）工作和多数时间（N）时间。连续优化，研究了与密切相关的最小翻译问题的最短路径问题。 ℓ1-插入，并建立循环算法，该算法在三个问题上循环并减少每个循环的图形大小。更快的平行算法，用于themimate tangemantm的themagimigation算法，尤其是在先前的最佳M 1+O（1）工作算法的Sherman [Soda'17]的最小翻译算法。除了算法和组合学中的几个主题定理外，几乎完全独立。
We present the first m polylog(n) work, polylog(n) time algorithm in the PRAM model that computes (1+є)-approximate single-source shortest paths on weighted, undirected graphs. This improves upon the breakthrough result of Cohen [JACM’00] that achieves O(m 1+є0 ) work and polylog(n) time. While most previous approaches, including Cohen’s, leveraged the power of hopsets, our algorithm builds upon the recent developments in continuous optimization, studying the shortest path problem from the lens of the closely-related minimum transshipment problem. To obtain our algorithm, we demonstrate a series of near-linear work, polylogarithmic-time reductions between the problems of approximate shortest path, approximate transshipment, and ℓ1-embeddings, and establish a recursive algorithm that cycles through the three problems and reduces the graph size on each cycle. As a consequence, we also obtain faster parallel algorithms for approximate transshipment and ℓ1-embeddings with polylogarithmic distortion. The minimum transshipment algorithm in particular improves upon the previous best m 1+o(1) work sequential algorithm of Sherman [SODA’17]. To improve readability, the paper is almost entirely self-contained, save for several staple theorems in algorithms and combinatorics.
通过低跳模拟器并行近似无向最短路径
DOI：
10.1145/3357713.3384321
发表时间：
2020
期刊：
Symposium on Theory of Computing (STOC
影响因子：
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作者：
Andoni, Alexandr;Stein, Clifford;Zhong, Peilin
通讯作者：
Zhong, Peilin
次线性加法扳手下界的层次结构
DOI：
10.1137/1.9781611974782.36
发表时间：
2017
期刊：
SODA 2017
影响因子：
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作者：
Abboud, Amir;Bodwin, Greg;Pettie, Seth
通讯作者：
Pettie, Seth