Improved Work Span Tradeoff for Single Source Reachability and Approximate Shortest Paths

Cao, Nairen; Fineman, Jeremy T.; Russell, Katina

doi:10.1145/3350755.3400222

Cited by 5 publications

(7 citation statements)

References 4 publications

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“…We will Overview of CFR Algorithms. [2,3]. The algorithms from CFR are based on two prior algorithms for parallel reachability by Fineman [7] and Jambulapati et al (JLS) [10].…”

Section: Stepmentioning

confidence: 99%

“…Next we give an overview of their hopset algorithm [2]. The work span tradeoff algorithm [3] works similarly.…”

Section: Stepmentioning

confidence: 99%

“…For = ( 1/4 ), the CFR [2] algorithm can be used to achieve the desired bound. For = ( 1/4 ), we use the CFR algorithm that has a work span tradeoff [3]. Section 3.2 gives the specific parameter settings.…”

Section: Stepmentioning

confidence: 99%

“…One of the steps in their framework involves computing shortest paths to a carefully selected subset of the vertices by simulating a parallel algorithm for SSSP in CONGEST. We achieve our improved bound by replacing the algorithm used in this step, instead adapting the parallel algorithm of Cao et al (CFR) [2,3] to the CONGEST model.…”

Section: Introductionmentioning

confidence: 99%

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Brief Announcement

Cao

Fineman

Russell

2021

Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing

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“…We will Overview of CFR Algorithms. [2,3]. The algorithms from CFR are based on two prior algorithms for parallel reachability by Fineman [7] and Jambulapati et al (JLS) [10].…”

Section: Stepmentioning

confidence: 99%

“…Next we give an overview of their hopset algorithm [2]. The work span tradeoff algorithm [3] works similarly.…”

Section: Stepmentioning

confidence: 99%

Section: Stepmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Brief Announcement

Cao

Fineman

Russell

2021

Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing

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“…Hopsets also suffer from the √ n barrier on the number of hops achievable with a linear shortcut set. Cao, Fineman and Russell [CFR20a,CFR20b,CFR21] presented the first nearly work-efficient parallel algorithms with O(m) work and span of n 1/2+o (1) . At the heart of their solution lies a computation of (β, ) hopsets with hopbound β = n 1/2+o (1) with O(n) edges (i.e., almost the same tradeoff as that of the folklore algorithm).…”

Section: Approximate Directed Hopsetsmentioning

confidence: 99%

New Diameter-Reducing Shortcuts and Directed Hopsets: Breaking the $\sqrt{n}$ Barrier

Kogan

Parter

2021

Preprint

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For an n-vertex digraph G = (V, E), a shortcut set is a (small) subset of edges H taken from the transitive closure of G that, when added to G guarantees that the diameter of G ∪ H is small. Shortcut sets, introduced by Thorup in 1993, have a wide range of applications in algorithm design, especially in the context of parallel, distributed and dynamic computation on directed graphs. A folklore result in this context shows that every n-vertex digraph admits a shortcut set of linear size (i.e., of O(n) edges) that reduces the diameter to 1 O( √ n). Despite extensive research over the years, the question of whether one can reduce the diameter to o(We provide the first improved diameter-sparsity tradeoff for this problem, breaking the √ n diameter barrier. Specifically, we show an O(n ω )-time randomized algorithm 2 for computing a linear shortcut set that reduces the diameter of the digraph to O(n 1/3 ). This narrows the gap w.r.t the current diameter lower bound of Ω(n 1/6 ) by [Huang and Pettie, SWAT '18]. Moreover, we show that a diameter of O(n 1/2 ) can in fact be achieved with a sublinear number of O(n 3/4 ) shortcut edges. Formally, letting S(n, D) be the bound on the size of the shortcut set required in order to reduce the diameter of any n-vertex digraph to at most D, our algorithms yield:We also extend our algorithms to provide improved (β, ) hopsets for n-vertex weighted directed graphs.* This project is funded by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 949083).1 The notation O(•) hides poly-logarithmic terms in n.2 Where ω is the optimal matrix multiplication constant.

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