A shortest-path algorithm finds a path containing the minimal cost between two vertices in a
graph. A plethora of shortest-path algorithms is studied in the literature that span across …

We present an improved oracle for the distance sensitivity problem. The goal is to
preprocess a directed graph G=(V, E) with non-negative edge weights to answer queries of …

Shortest paths in directed planar graphs with negative lengths Page 1 30 Shortest Paths in
Directed Planar Graphs with Negative Lengths: A Linear-Space O(nlog 2 n)-Time Algorithm …

Spontaneous failure is an unavoidable aspect of all networks, particularly those with a
physical basis such as communications networks or road networks. Whether due to …

Shortest paths computation is one of the most fundamental problems in computer science.
An important variant of the problem is when edges can fail, and one needs to compute …

A distance sensitivity oracle is a data structure which, given two nodes s and t in a directed
edge-weighted graph G and an edge e, returns the shortest length of an st path not …

A distance sensitivity oracle of an n-vertex graph G=(V, E) is a data structure that can report
shortest paths when edges of the graph fail. A query (u∈ V, v∈ V, S⊆ E) to this oracle …

Abstract Let G=(V, E) be a directed graph with positive edge weights, let s, t be two specified
vertices in this graph, and let π (s, t) be the shortest path between them. In the replacement …

This paper considers a natural fault-tolerant shortest paths problem: for some constant
integer f, given a directed weighted graph with no negative cycles and two fixed vertices s …

In this work we derandomize two central results in graph algorithms, replacement paths and
distance sensitivity oracles (DSOs) matching in both cases the running time of the …