منابع مشابه
Critical Points of Pairs of Varieties of Algebras
For a class V of algebras, denote by Conc V the class of all (∨, 0)semilattices isomorphic to the semilattice Conc A of all compact congruences of A, for some A in V. For classes V1 and V2 of algebras, we denote by crit(V1;V2) the smallest cardinality of a (∨, 0)-semilattice in Conc V1 which is not in Conc V2 if it exists, ∞ otherwise. We prove a general theorem, with categorical flavor, that i...
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We introduce a new problem that combines the well known All Pairs Shortest Paths (APSP) problem and the All Pairs Bottleneck Paths (APBP) problem to compute the shortest paths for all pairs of vertices for all possible flow amounts. We call this new problem the All Pairs Shortest Paths for All Flows (APSP-AF) problem. We firstly solve the APSP-AF problem on directed graphs with unit edge costs ...
متن کاملAll - 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...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2001
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171201005233