Planar graph decomposition and all pairs shortest paths
نویسندگان
چکیده
منابع مشابه
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...
متن کاملAll 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...
متن کاملAll Pairs Almost Shortest Paths
Let G = (V;E) be an unweighted undirected graph on n vertices. A simple argument shows that computing all distances in G with an additive one-sided error of at most 1 is as hard as Boolean matrix multiplication. Building on recent work of Aingworth, Chekuri and Motwani, we describe an ~ O(minfn3=2m1=2; n7=3g) time algorithmAPASP2 for computing all distances in G with an additive one-sided error...
متن کاملFully Dynamic All Pairs All Shortest Paths
We consider the all pairs all shortest paths (APASP) problem, which maintains all of the multiple shortest paths for every vertex pair in a directed graph G = (V,E) with a positive real weight on each edge. We present a fully dynamic algorithm for this problem in which an update supports either weight increases or weight decreases on a subset of edges incident to a vertex. Our algorithm runs in...
متن کاملAll Pairs Shortest Paths: Randomization and Replacement
We present a survey of results in the field of graph algorithms. We begin with an All Pairs Shortest Path algorithm with some constraints that runs in O(n) by Peres. We continue with a Replacement Paths algorithm by Williams and conclude with a smoothed analysis of a Single Source Shortest Paths algorithm by Banderier. Each of these problems has connections to randomization in graph algorithms.
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ژورنال
عنوان ژورنال: Journal of the ACM
سال: 1991
ISSN: 0004-5411,1557-735X
DOI: 10.1145/102782.102788