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All Pairs Lightest Shortest Paths
 In Proceedings of the 31th Annual ACM Symposium on Theory of Computing
, 1999
"... Two vertices in a weighted directed graph may be connected by many shortest paths. Although all these paths are shortest in terms of weight, the number of edges on them may vary substantially. This leads us to consider the All Pairs Lightest Shortest Paths (APLSP) problem. A solution to this problem ..."
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Cited by 8 (5 self)
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to this problem is a representation of shortest paths between all of pairs of vertices in the graph such that each of these shortest paths uses a minimal, or a close to minimal, number of edges. We present the following algorithms for obtaining exact or approximate solutions to the APLSP problem: ffl An ~ O(n 2
Dynamic approximate allpairs shortest paths: Breaking the O(mn) barrier and derandomization
 In Proc. FOCS
, 2013
"... We study dynamic (1 + )approximation algorithms for the allpairs shortest paths problem in unweighted undirected nnode medge graphs under edge deletions. The fastest algorithm for this problem is a randomized algorithm with a total update time of Õ(mn) and constant query time by Roditty and Zwi ..."
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Cited by 2 (1 self)
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We study dynamic (1 + )approximation algorithms for the allpairs shortest paths problem in unweighted undirected nnode medge graphs under edge deletions. The fastest algorithm for this problem is a randomized algorithm with a total update time of Õ(mn) and constant query time by Roditty
AN OPTIMAL PARALLEL ALGORITHM FOR SOLVING ALLPAIRS SHORTEST PATHS PROBLEM ON CIRCULARARC GRAPHS
"... Abstract. The shortestpaths problem is a fundamental problem in graph theory and finds diverse applications in various fields. This is why shortest path algorithms have been designed more thoroughly than any other algorithm in graph theory. A large number of optimization problems are mathematicall ..."
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Cited by 1 (0 self)
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. This paper presents an O(n2) time sequential algorithm and an O(n2/p + log n) time parallel algorithm on EREW PRAM model for solving all pairs shortest paths problem on circulararc graphs, where p and n represent respectively the number of processors and the number of vertices of the circulararc graph.
On dynamic shortest paths problems
, 2004
"... We obtain the following results related to dynamic versions of the shortestpaths problem: (i) Reductions that show that the incremental and decremental singlesource shortestpaths problems, for weighted directed or undirected graphs, are, in a strong sense, at least as hard as the static allpairs ..."
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Cited by 41 (2 self)
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shortestpaths problem. We also obtain slightly weaker results for the corresponding unweighted problems. (ii) A randomized fullydynamic algorithm for the allpairs shortestpaths problem in directed unweighted graphs with an amortized update time of ~O(mpn) and a worst case query time is O(n3/4). (iii) A
THE SHORTESTPATH PROBLEM FOR GRAPHS WITH RANDOM ARCLENGTHS
, 1985
"... We consider the problem of finding the shortest distance between all pairs of vertices in a complete digraph on n vertices, whose arclengths are nonnegative random variables. We describe an algorithm which solves this problem in O(n(m + n log n)) expected time, where m is the expected number of ar ..."
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Cited by 102 (5 self)
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; for this case, we describe an algorithm which runs in O(n 2log n) expected time. In our treatment of the shortestpath problem we consider the following problem in combinatorial probability theory. A town contains n people, one of whom knows a rumour. At the first stage he tells someone chosen randomly from
Combining All Pairs Shortest Paths and All Pairs Bottleneck Paths Problems?
"... Abstract. 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 ..."
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for All Flows (APSPAF) problem. We firstly solve the APSPAF problem on directed graphs with unit edge costs and real edge capacities in Õ( tn(ω+9)/4) = Õ( tn2.843) time, where n is the number of vertices, t is the number of distinct edge capacities (flow amounts) and O(nω) < O(n2.373) is the time
All Pairs Shortest Paths in Undirected Graphs with Integer Weights
 In IEEE Symposium on Foundations of Computer Science
, 1999
"... We show that the All Pairs Shortest Paths (APSP) problem for undirected graphs with integer edge weights taken from the range f1; 2; : : : ; Mg can be solved using only a logarithmic number of distance products of matrices with elements in the range f1; 2; : : : ; Mg. As a result, we get an algorith ..."
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Cited by 56 (7 self)
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algorithm of Galil and Margalit. 1. Introduction The All Pairs Shortest Paths (APSP) problem is one of the most fundamental algorithmic graph problems. The APSP problem for directed or undirected graphs with real weights can be solved using classical methods, in O(mn + n 2 log n) time (Dijkstra [4
All pairs shortest paths on a hypercube multiprocessor
, 1987
"... this paper, we consider parallel solutions to the all pairs problem only. As with other studies, our development considers finding only the length of the shortest paths. We are interested in solving the all pairs problems on an MIMD hypercube in which each processor has local memory. Specifically, o ..."
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Cited by 20 (1 self)
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this paper, we consider parallel solutions to the all pairs problem only. As with other studies, our development considers finding only the length of the shortest paths. We are interested in solving the all pairs problems on an MIMD hypercube in which each processor has local memory. Specifically
Fully Dynamic All Pairs Shortest Paths with Real Edge Weights
 In IEEE Symposium on Foundations of Computer Science
, 2001
"... We present the first fully dynamic algorithm for maintaining all pairs shortest paths in directed graphs with realvalued edge weights. Given a dynamic directed graph G such that each edge can assume at most S di#erent real values, we show how to support updates in O(n amortized time and que ..."
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Cited by 36 (9 self)
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We present the first fully dynamic algorithm for maintaining all pairs shortest paths in directed graphs with realvalued edge weights. Given a dynamic directed graph G such that each edge can assume at most S di#erent real values, we show how to support updates in O(n amortized time
Efficient Parallel Algorithms for Computing All Pair Shortest Paths in Directed Graphs
, 1997
"... . We present parallel algorithms for computing all pair shortest paths in directed graphs. Our algorithm has time complexity O( f (n)/p + I (n) log n) on the PRAM using p processors, where I (n) is log n on the EREW PRAM, log log n on the CCRW PRAM, f (n) is o(n 3 ). On the randomized CRCW PRAM we a ..."
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Cited by 25 (0 self)
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. We present parallel algorithms for computing all pair shortest paths in directed graphs. Our algorithm has time complexity O( f (n)/p + I (n) log n) on the PRAM using p processors, where I (n) is log n on the EREW PRAM, log log n on the CCRW PRAM, f (n) is o(n 3 ). On the randomized CRCW PRAM we
Results 21  30
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650