TY - GEN

T1 - Approximate Distance Sensitivity Oracles in Subquadratic Space

AU - Bilò, Davide

AU - Chechik, Shiri

AU - Choudhary, Keerti

AU - Cohen, Sarel

AU - Friedrich, Tobias

AU - Krogmann, Simon

AU - Schirneck, Martin

N1 - Publisher Copyright:
© 2023 ACM.

PY - 2023/6/2

Y1 - 2023/6/2

N2 - An f-edge fault-tolerant distance sensitive oracle (f-DSO) with stretch σ ≥ 1 is a data structure that preprocesses a given undirected, unweighted graph G with n vertices and m edges, and a positive integer f. When queried with a pair of vertices s, t and a set F of at most f edges, it returns a σ-approximation of the s-t-distance in G-F. We study f-DSOs that take subquadratic space. Thorup and Zwick [JACM2015] showed that this is only possible for σ ≥ 3. We present, for any constant f ≥ 1 and α (0, 1/2), and any ϵ > 0, an f-DSO with stretch 3 + that takes O(n2-α/f+1/ϵ) · O(logn/ϵ)f+1 space and has an O(nα/ϵ2) query time. We also give an improved construction for graphs with diameter at most D. For any constant k, we devise an f-DSO with stretch 2k-1 that takes O(Df+o(1) n1+1/k) space and has O(Do(1)) query time, with a preprocessing time of O(Df+o(1) mn1/k). Chechik, Cohen, Fiat, and Kaplan [SODA 2017] presented an f-DSO with stretch 1+ and preprocessing time O(n5) · O(logn/ϵ)f, albeit with a super-quadratic space requirement. We show how to reduce their preprocessing time to O(mn2) · O(logn/ϵ)f.

AB - An f-edge fault-tolerant distance sensitive oracle (f-DSO) with stretch σ ≥ 1 is a data structure that preprocesses a given undirected, unweighted graph G with n vertices and m edges, and a positive integer f. When queried with a pair of vertices s, t and a set F of at most f edges, it returns a σ-approximation of the s-t-distance in G-F. We study f-DSOs that take subquadratic space. Thorup and Zwick [JACM2015] showed that this is only possible for σ ≥ 3. We present, for any constant f ≥ 1 and α (0, 1/2), and any ϵ > 0, an f-DSO with stretch 3 + that takes O(n2-α/f+1/ϵ) · O(logn/ϵ)f+1 space and has an O(nα/ϵ2) query time. We also give an improved construction for graphs with diameter at most D. For any constant k, we devise an f-DSO with stretch 2k-1 that takes O(Df+o(1) n1+1/k) space and has O(Do(1)) query time, with a preprocessing time of O(Df+o(1) mn1/k). Chechik, Cohen, Fiat, and Kaplan [SODA 2017] presented an f-DSO with stretch 1+ and preprocessing time O(n5) · O(logn/ϵ)f, albeit with a super-quadratic space requirement. We show how to reduce their preprocessing time to O(mn2) · O(logn/ϵ)f.

KW - approximate shortest paths

KW - distance sensitivity oracle

KW - fault-tolerant data structure

KW - subquadratic space

UR - http://www.scopus.com/inward/record.url?scp=85159813972&partnerID=8YFLogxK

U2 - 10.1145/3564246.3585251

DO - 10.1145/3564246.3585251

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AN - SCOPUS:85159813972

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 1396

EP - 1409

BT - STOC 2023 - Proceedings of the 55th Annual ACM Symposium on Theory of Computing

A2 - Saha, Barna

A2 - Servedio, Rocco A.

PB - Association for Computing Machinery

T2 - 55th Annual ACM Symposium on Theory of Computing, STOC 2023

Y2 - 20 June 2023 through 23 June 2023

ER -