All-pairs shortest paths in O ( n 2 ) time with high probability
نویسندگان
چکیده
منابع مشابه
All - Pairs Shortest Paths in O ( n 2 ) Time with High Probability
We present an all-pairs shortest path algorithm whose running time on a complete directed graph on n vertices whose edge weights are chosen independently and uniformly at random from [0, 1] is O(n2), in expectation and with high probability. This resolves a long-standing open problem. The algorithm is a variant of the dynamic all-pairs shortest paths algorithm of Demetrescu and Italiano [2006]....
متن کاملAll-Pairs Shortest Paths in O(n) time with high probability
We present an all-pairs shortest path algorithm whose running time on a complete directed graph on n vertices whose edge weights are chosen independently and uniformly at random from [0, 1] is O(n), in expectation and with high probability. This resolves a long standing open problem. The algorithm is a variant of the dynamic all-pairs shortest paths algorithm of Demetrescu and Italiano. The ana...
متن کاملAll-Pairs Nearly 2-Approximate Shortest-Paths in O(n polylog n) Time
Let G(V, E) be an unweighted undirected graph on |V | = n vertices. Let δ(u, v) denote the shortest distance between vertices u, v ∈ V . An algorithm is said to compute all-pairs t-approximate shortestpaths/distances, for some t ≥ 1, if for each pair of vertices u, v ∈ V , the path/distance reported by the algorithm is not longer/greater than t · δ(u, v). This paper presents two randomized algo...
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Given a simple connected unweighted undirected graph G = (V (G), E(G)) with |V (G)| = n and |E(G)| = m, we present a new algorithm for the all−pairs shortest−path (APSP) problem. The running time of our algorithm is in O(n log n). This bound is an improvement over previous best known O(n) time bound of Raimund Seidel (1995) for general graphs. The algorithm presented does not rely on fast matri...
متن کاملAll-Pairs Nearly 2-Approximate Shortest-Paths in O(n2 polylog n) Time
Let G = (V,E) be an unweighted undirected graph on |V | = n vertices and |E| = m edges. Let δ(u, v) denote the distance between vertices u, v ∈ V . An algorithm is said to compute all-pairs t-approximate shortest-paths/distances, for some t ≥ 1, if for each pair of vertices u, v ∈ V , the path/distance reported by the algorithm is not longer/greater than t · δ(u, v). This paper presents two ext...
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ژورنال
عنوان ژورنال: Journal of the ACM
سال: 2013
ISSN: 0004-5411,1557-735X
DOI: 10.1145/2508028.2505988