Approximate Distance Sensitivity Oracles in Subquadratic Space

Bilò, Davide; Chechik, Shiri; Choudhary, Keerti; Cohen, Sarel; Friedrich, Tobias; Krogmann, Simon; Schirneck, Martin

doi:10.1145/3564246.3585251

Cited by 3 publications

(4 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let st ⋄ e be a candidate departing path, then we can find it using the algorithm given in Section 5. 6.…”

Section: Querying For a Candidate Departing Pathmentioning

confidence: 99%

“…Gupta and Singh [5] designed an SDO (1) with O(n n) space and O(1) query time. Recently Bilò et al [6] built the SDO(1) (described in [5]) in O(m n + n 2 ) time. Many different aspects of distance oracles have been studied in literature [3,[7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we will focus on building SDO (1). Due to Bilò et al [6], the time to build SDO (1) is O(m n+n 2 ). Chechik and Cohen [13] showed that, the first term in this running time is a conditional lower bound for SSRP problem.…”

Section: Introductionmentioning

confidence: 99%

“…However it is not clear if the second term is necessary. In this paper, we build an SDO (1) in O(m n) time -this preprocessing algorithm has a better runtime (for sparse graphs) than [6] , which is state of the art for this problem till now. Using our SDO(1) data structure, we are able to reduce the runtime of the algorithm solving SSRP problem too.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Near Optimal Algorithm for Fault Tolerant Distance Oracle and Single Source Replacement Path problem

Dey,

Gupta

2023

Preprint

View full text Add to dashboard Cite

In a graph G with fixed source s, we design a distance oracle that can answer the following query: QU(s,t,e) -- find the length of the shortest path from the source s to any destination vertex t while avoiding any edge e. We design a deterministic algorithm that builds such an oracle in $\Tilde{O}(m\sqrt n)$ time\footnote{$\Tilde{O}$ hides poly$\log n$ factor} \footnote{A preliminary version of this article appeared in the Proceedings of 30th Annual European Symposium on Algorithms (ESA 2022), 5-9 September 2022, Potsdam, Germany \cite{DeyGupta} }. Our oracle uses $\Tilde{O}(n\sqrt n)$ space and can answer queries in $\Tilde{O}(1)$ time. Our oracle is an improvement of the work of Bil\'{o} et al. (ESA 2021) in the preprocessing time, which constructs the first deterministic oracle for this problem in $\Tilde{O}(m\sqrt n+n^2)$ time. Using our distance oracle, we also solve the single source replacement path problem (SSRP problem).Chechik and Cohen (SODA 2019) designed a randomised combinatorial algorithm to solve the $\SSR$ problem. The running time of their algorithm is $\Tilde{O}(m\sqrt n + |R|)$ time, where R is the output set of the SSRP problem in G. Our SSRP algorithm is optimal (upto polylogarithmic factor) as there is a conditional lower bound of $\Omega(m\sqrt n)$ for any combinatorial algorithm that solves this problem.

show abstract

“…Let st ⋄ e be a candidate departing path, then we can find it using the algorithm given in Section 5. 6.…”

Section: Querying For a Candidate Departing Pathmentioning

confidence: 99%