Results 1  10
of
650
AllPairs Shortest Paths in O(n 2 ) time with high probability
"... Abstract We present an allpairs 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 2 ), in expectation and with high probability. This resolves a long standing open problem. Th ..."
Abstract
 Add to MetaCart
Abstract We present an allpairs 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 2 ), in expectation and with high probability. This resolves a long standing open problem
On the AllPairs ShortestPath Algorithm Of Moffat and Takaoka
, 1997
"... We review how to solve the allpairs shortestpath problem in a nonnegatively Ž 2 weighted digraph with n vertices in expected time On log n.. This bound is shown to hold with high probability for a wide class of probability distributions on nonnegatively weighted digraphs. We also prove that, for ..."
Abstract

Cited by 14 (4 self)
 Add to MetaCart
We review how to solve the allpairs shortestpath problem in a nonnegatively Ž 2 weighted digraph with n vertices in expected time On log n.. This bound is shown to hold with high probability for a wide class of probability distributions on nonnegatively weighted digraphs. We also prove that
Finding the Hidden Path: Time Bounds for AllPairs Shortest Paths
, 1993
"... We investigate the allpairs shortest paths problem in weighted graphs. We present an algorithmthe Hidden Paths Algorithmthat finds these paths in time O(m* n+n² log n), where m is the number of edges participating in shortest paths. Our algorithm is a practical substitute for Dijkstra&ap ..."
Abstract

Cited by 75 (0 self)
 Add to MetaCart
's algorithm. We argue that m* is likely to be small in practice, since m* = O(n log n) with high probability for many probability distributions on edge weights. We also prove an Ω(mn) lower bound on the running time of any pathcomparison based algorithm for the allpairs shortest paths problem. Path
Fibonacci Heaps and Their Uses in Improved Network optimization algorithms
, 1987
"... In this paper we develop a new data structure for implementing heaps (priority queues). Our structure, Fibonacci heaps (abbreviated Fheaps), extends the binomial queues proposed by Vuillemin and studied further by Brown. Fheaps support arbitrary deletion from an nitem heap in qlogn) amortized tim ..."
Abstract

Cited by 739 (18 self)
 Add to MetaCart
in the problem graph: ( 1) O(n log n + m) for the singlesource shortest path problem with nonnegative edge lengths, improved from O(m logfmh+2)n); (2) O(n*log n + nm) for the allpairs shortest path problem, improved from O(nm lo&,,,+2,n); (3) O(n*logn + nm) for the assignment problem (weighted bipartite
AllPairs Shortest Paths and the Essential Subgraph
, 1995
"... The essential subgraph H of a weighted graph or digraph G contains an edge (v, w) if that edge is uniquely the leastcost path between its vertices. Let s denote the number of edges of H. This paper presents an algorithm for solving allpairs shortest paths on G that requires O(ns + n 2 log n) wor ..."
Abstract

Cited by 16 (2 self)
 Add to MetaCart
The essential subgraph H of a weighted graph or digraph G contains an edge (v, w) if that edge is uniquely the leastcost path between its vertices. Let s denote the number of edges of H. This paper presents an algorithm for solving allpairs shortest paths on G that requires O(ns + n 2 log n
More algorithms for allpairs shortest paths in weighted graphs
 In Proceedings of 39th Annual ACM Symposium on Theory of Computing
, 2007
"... In the first part of the paper, we reexamine the allpairs shortest paths (APSP) problem and present a new algorithm with running time O(n 3 log 3 log n / log 2 n), which improves all known algorithms for general realweighted dense graphs. In the second part of the paper, we use fast matrix multipl ..."
Abstract

Cited by 75 (3 self)
 Add to MetaCart
In the first part of the paper, we reexamine the allpairs shortest paths (APSP) problem and present a new algorithm with running time O(n 3 log 3 log n / log 2 n), which improves all known algorithms for general realweighted dense graphs. In the second part of the paper, we use fast matrix
Average update times for fullydynamic allpairs shortest paths
 Proceedings of the 19th International Symposium on Algorithms and Computation (ISAAC 2008), Gold Coast, Australia, 2008, LNCS 5369
"... Abstract We study the fullydynamic all pairs shortest path problem for graphs with arbitrary nonnegative edge weights. It is known for digraphs that an update of the distance matrix costs Õ(n2.75) 1 worstcase time [Thorup, STOC ’05] and Õ(n2) amortized time [Demetrescu and Italiano, J.ACM ’04] wh ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
Abstract We study the fullydynamic all pairs shortest path problem for graphs with arbitrary nonnegative edge weights. It is known for digraphs that an update of the distance matrix costs Õ(n2.75) 1 worstcase time [Thorup, STOC ’05] and Õ(n2) amortized time [Demetrescu and Italiano, J.ACM ’04
Fully Dynamic Algorithms for Maintaining AllPairs Shortest Paths and Transitive Closure in Digraphs
 IN PROC. 40TH IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS’99
, 1999
"... This paper presents the first fully dynamic algorithms for maintaining allpairs shortest paths in digraphs with positive integer weights less than b. For approximate shortest paths with an error factor of (2 + ffl), for any positive constant ffl, the amortized update time is O(n 2 log 2 n= log ..."
Abstract

Cited by 77 (0 self)
 Add to MetaCart
This paper presents the first fully dynamic algorithms for maintaining allpairs shortest paths in digraphs with positive integer weights less than b. For approximate shortest paths with an error factor of (2 + ffl), for any positive constant ffl, the amortized update time is O(n 2 log 2 n
Decremental AllPairs ALL Shortest Paths and Betweenness Centrality
"... Abstract. We consider the all pairs all shortest paths (APASP) problem, which maintains the shortest path dag rooted at every vertex in a directed graph G = (V, E) with positive edge weights. For this problem we present a decremental algorithm (that supports the deletion of a vertex, or weight incr ..."
Abstract
 Add to MetaCart
increases on edges incident to a vertex). Our algorithm runs in amortized O(ν * 2 · log n) time per update, where n = V , and ν * bounds the number of edges that lie on shortest paths through any given vertex. Our APASP algorithm can be used for the decremental computation of betweenness centrality (BC
Discounted deterministic Markov decision processes and discounted allpairs shortest paths
 ACM Transcations on Algorithms
"... We present two new algorithms for finding optimal strategies for discounted, infinitehorizon, Deterministic Markov Decision Processes (DMDP). The first one is an adaptation of an algorithm of Young, Tarjan and Orlin for finding minimum mean weight cycles. It runs in O(mn + n 2 log n) time, where n ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
in many situations. Both algorithms improve on a recent O(mn 2)time algorithm of Andersson and Vorobyov. We also present a randomized Õ(m1/2 n 2)time algorithm for finding Discounted AllPairs Shortest Paths (DAPSP), improving several previous algorithms. 1
Results 1  10
of
650