@inproceedings{3d2c472db14943d381bed64c9a10d504,

title = "Simplifying and unifying replacement paths algorithms in weighted directed graphs",

abstract = "In the replacement paths (RP) problem we are given a graph G and a shortest path P between two nodes s and t 1. The goal is to find for every edge e ∈ P, a shortest path from s to t that avoids e. The first result of this paper is a simple reduction from the RP problem to the problem of computing shortest cycles for all nodes on a shortest path. Using this simple reduction we unify and extremely simplify two state of the art solutions for two different well-studied variants of the RP problem. In the first variant (algebraic) we show that by using at most n queries to the Yuster-Zwick distance oracle [FOCS 2005], one can solve the the RP problem for a given directed graph with integer edge weights in the range [−M, M] in {\~O} (Mnω) time 2 3 . This improves the running time of the state of the art algorithm of Vassilevska Williams [SODA 2011] by a factor of log6 n. In the second variant (planar) we show that by using the algorithm of Klein for the multiple-source shortest paths problem (MSSP) [SODA 2005] one can solve the RP problem for directed planar graph with non negative edge weights in O (n log n) time. This matches the state of the art algorithm of Wulff-Nilsen [SODA 2010], but with arguably much simpler algorithm and analysis.",

keywords = "Distance oracle, Fault tolerance, Planar graph",

author = "Shiri Chechik and Moran Nechushtan",

note = "Publisher Copyright: {\textcopyright} Shiri Chechik and Moran Nechushtan; licensed under Creative Commons License CC-BY 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020).; 47th International Colloquium on Automata, Languages, and Programming, ICALP 2020 ; Conference date: 08-07-2020 Through 11-07-2020",

year = "2020",

month = jun,

day = "1",

doi = "10.4230/LIPIcs.ICALP.2020.29",

language = "אנגלית",

series = "Leibniz International Proceedings in Informatics, LIPIcs",

publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",

editor = "Artur Czumaj and Anuj Dawar and Emanuela Merelli",

booktitle = "47th International Colloquium on Automata, Languages, and Programming, ICALP 2020",

}