Near optimal algorithms for the single source replacement paths problem

Shiri Chechik; Sarel Cohen

doi:10.1137/1.9781611975482.126

Near optimal algorithms for the single source replacement paths problem

Shiri Chechik, Sarel Cohen

Tel Aviv University

Research output: Contribution to conference › Paper › peer-review

Abstract

The Single Source Replacement Paths (SSRP) problem is as follows; Given a graph G = (V, E), a source vertex s and a shortest paths tree T_s rooted in s, output for every vertex t ∈ V and for every edge e in T_s the length of the shortest path from s to t avoiding e. We present near optimal upper bounds, by providing Õ(mn + n²) time randomized combinatorial algorithm ¹ for unweighted undirected graphs, and matching conditional lower bounds for the SSRP problem.

Original language	English
Pages	2090-2109
Number of pages	20
DOIs	https://doi.org/10.1137/1.9781611975482.126
State	Published - 2019
Event	30th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019 - San Diego, United States Duration: 6 Jan 2019 → 9 Jan 2019

Conference

Conference	30th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019
Country/Territory	United States
City	San Diego
Period	6/01/19 → 9/01/19

All Science Journal Classification (ASJC) codes

Software
General Mathematics

Access to Document

10.1137/1.9781611975482.126

Cite this

@conference{f6bbe15d591040959ce6ae38183aeb63,

title = "Near optimal algorithms for the single source replacement paths problem",

abstract = "The Single Source Replacement Paths (SSRP) problem is as follows; Given a graph G = (V, E), a source vertex s and a shortest paths tree Ts rooted in s, output for every vertex t ∈ V and for every edge e in Ts the length of the shortest path from s to t avoiding e. We present near optimal upper bounds, by providing {\~O}(mn + n2) time randomized combinatorial algorithm 1 for unweighted undirected graphs, and matching conditional lower bounds for the SSRP problem.",

author = "Shiri Chechik and Sarel Cohen",

note = "Publisher Copyright: Copyright {\textcopyright} 2019 by SIAM.; 30th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019 ; Conference date: 06-01-2019 Through 09-01-2019",

year = "2019",

doi = "10.1137/1.9781611975482.126",

language = "الإنجليزيّة",

pages = "2090--2109",

}

TY - CONF

T1 - Near optimal algorithms for the single source replacement paths problem

AU - Chechik, Shiri

AU - Cohen, Sarel

PY - 2019

Y1 - 2019

N2 - The Single Source Replacement Paths (SSRP) problem is as follows; Given a graph G = (V, E), a source vertex s and a shortest paths tree Ts rooted in s, output for every vertex t ∈ V and for every edge e in Ts the length of the shortest path from s to t avoiding e. We present near optimal upper bounds, by providing Õ(mn + n2) time randomized combinatorial algorithm 1 for unweighted undirected graphs, and matching conditional lower bounds for the SSRP problem.

AB - The Single Source Replacement Paths (SSRP) problem is as follows; Given a graph G = (V, E), a source vertex s and a shortest paths tree Ts rooted in s, output for every vertex t ∈ V and for every edge e in Ts the length of the shortest path from s to t avoiding e. We present near optimal upper bounds, by providing Õ(mn + n2) time randomized combinatorial algorithm 1 for unweighted undirected graphs, and matching conditional lower bounds for the SSRP problem.

UR - http://www.scopus.com/inward/record.url?scp=85066934410&partnerID=8YFLogxK

U2 - 10.1137/1.9781611975482.126

DO - 10.1137/1.9781611975482.126

M3 - محاضرة

SP - 2090

EP - 2109

T2 - 30th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019

Y2 - 6 January 2019 through 9 January 2019

ER -

Near optimal algorithms for the single source replacement paths problem

Abstract

Conference

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this