TY - GEN

T1 - A linear-size logarithmic stretch path-reporting distance oracle for general graphs

AU - Elkin, Michael

AU - Pettie, Seth

N1 - Funding Information:
This research was financially supported by the Tribology and Surface Engineering Program, the National Science Foundation through Grant CMS-9501877.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - In a seminal paper [27] for any n-vertex undirected graph G=(V E) and a parameter k 1, 2,. Thorup and Zwick constructed a distance oracle of size 0 (kn1+1/k) which upon a query (u, v) constructs a path H between u and v of length δ (u, v) such that dG (n, v) ≤δ (u, v) ≤ (2k-1)dG (u, v). 'l'he query time of the oracle from [27] is O (k) (in addition to the length of the returned path), and it was subsequently improved to 0 (1) [29, 11]. A major drawback of the oracle of [27] is that its space is ω (n.·log vi). Mendel and Naor [18] devised an oracle with space O (n1+1/k) and stretch O (k), but their oracle can only report distance estimates and not actual paths. In this paper we devise a path-reporting distance oracle with size O (n1+1/k), stretch O (k) and query time O (nε), for an arbitrarily small ε > 0. In particular, for k=logn our oracle provides logarithmic stretch using linear size. Another variant of our oracle has linear size, polylogarithmic stretch, and query time O (1og log vi). For unweighted graphs we devise a distance oracle with multiplicative stretch O (1), additive stretch O (β (k)), for a function β, space O (n1+1/kk · β), and query time O (n), for an arbitrarily small constant ε> o T he tradeoff between multiplicative stretch and size in these oracles is far below Erdôs's girth conjecture threshold (which is stretch 2k-1 and size O (n1+1/kk)).

AB - In a seminal paper [27] for any n-vertex undirected graph G=(V E) and a parameter k 1, 2,. Thorup and Zwick constructed a distance oracle of size 0 (kn1+1/k) which upon a query (u, v) constructs a path H between u and v of length δ (u, v) such that dG (n, v) ≤δ (u, v) ≤ (2k-1)dG (u, v). 'l'he query time of the oracle from [27] is O (k) (in addition to the length of the returned path), and it was subsequently improved to 0 (1) [29, 11]. A major drawback of the oracle of [27] is that its space is ω (n.·log vi). Mendel and Naor [18] devised an oracle with space O (n1+1/k) and stretch O (k), but their oracle can only report distance estimates and not actual paths. In this paper we devise a path-reporting distance oracle with size O (n1+1/k), stretch O (k) and query time O (nε), for an arbitrarily small ε > 0. In particular, for k=logn our oracle provides logarithmic stretch using linear size. Another variant of our oracle has linear size, polylogarithmic stretch, and query time O (1og log vi). For unweighted graphs we devise a distance oracle with multiplicative stretch O (1), additive stretch O (β (k)), for a function β, space O (n1+1/kk · β), and query time O (n), for an arbitrarily small constant ε> o T he tradeoff between multiplicative stretch and size in these oracles is far below Erdôs's girth conjecture threshold (which is stretch 2k-1 and size O (n1+1/kk)).

UR - http://www.scopus.com/inward/record.url?scp=84938273214&partnerID=8YFLogxK

U2 - 10.1137/1.9781611973730.55

DO - 10.1137/1.9781611973730.55

M3 - Conference contribution

AN - SCOPUS:84938273214

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 805

EP - 821

BT - Proceedings of the 26th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015

PB - Association for Computing Machinery

T2 - 26th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015

Y2 - 4 January 2015 through 6 January 2015

ER -