Finding non-dominated bicriteria shortest pairs of disjoint simple paths

Finding non-dominated bicriteria shortest pairs of disjoint simple paths

k-Pairs Non-Crossing Shortest Paths in a Simple Polygon

This paper presents a simple O(n + k) time algorithm to compute the set of k non-crossing shortest paths between k source-destination pairs of points on the boundary of a simple polygon of n vertices. Paths are allowed to overlap but are not allowed to cross in the plane. A byproduct of this result is an O(n) time algorithm to compute a balanced geodesic triangulation which is easy to implement...

Finding k Simple Shortest Paths and Cycles

We present algorithms and hardness results for several problems related to finding multiple simple shortest paths in a graph. Our main result is a new algorithm for finding k simple shortest paths for all pairs of vertices in a weighted directed graph G = (V,E). For k = 2 our algorithm runs in O(mn + n logn) time where m and n are the number of edges and vertices in G. Our approach is based on ...

All - Pairs Shortest Paths ÆÆÆ

In the previous chapter, we saw algorithms to find the shortest path from a source vertex s to a target vertex t in a directed graph. As it turns out, the best algorithms for this problem actually find the shortest path from s to every possible target (or from every possible source to t) by constructing a shortest path tree. The shortest path tree specifies two pieces of information for each no...

All Pairs Shortest Paths Algorithms

Given a communication network or a road network one of the most natural algorithmic question is how to determine the shortest path from one point to another. In this paper we deal with one of the most fundamental problems of Graph Theory, the All Pairs Shortest Path (APSP) problem. We study three algorithms namely The FloydWarshall algorithm, APSP via Matrix Multiplication and the Johnson’s alg...