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16
Experimental analysis of dynamic all pairs shortest path algorithms
 In Proceedings of the fifteenth annual ACMSIAM symposium on Discrete algorithms
, 2004
"... We present the results of an extensive computational study on dynamic algorithms for all pairs shortest path problems. We describe our implementations of the recent dynamic algorithms of King and of Demetrescu and Italiano, and compare them to the dynamic algorithm of Ramalingam and Reps and to stat ..."
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Cited by 37 (5 self)
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We present the results of an extensive computational study on dynamic algorithms for all pairs shortest path problems. We describe our implementations of the recent dynamic algorithms of King and of Demetrescu and Italiano, and compare them to the dynamic algorithm of Ramalingam and Reps and to static algorithms on random, realworld and hard instances. Our experimental data suggest that some of the dynamic algorithms and their algorithmic techniques can be really of practical value in many situations. 1
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 (10 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 and queries in optimal worstcase time. No previous fully dynamic algorithm was known for this problem. In the special case where edge weights can only be increased, we give a randomized algorithm with onesided error which supports updates faster in O(S We also show how to obtain query/update tradeo#s for this problem, by introducing two new families of algorithms. Algorithms in the first family achieve an update bound of O(n/k), and improve over the best known update bounds for k in the . Algorithms in the second family achieve an update bound of ), and are competitive with the best known update bounds (first family included) for k in the range (n/S) # Work partially supported by the IST Programme of the EU under contract n. IST199914. 186 (ALCOMFT) and by CNR, the Italian National Research Council, under contract n. 01.00690.CT26. Portions of this work have been presented at the 42nd Annual Symp. on Foundations of Computer Science (FOCS 2001) [8] and at the 29th International Colloquium on Automata, Languages, and Programming (ICALP'02) [9].
Improved Dynamic Reachability Algorithms for Directed Graphs
, 2002
"... We obtain several new dynamic algorithms for maintaining the transitive closure of a directed graph, and several other algorithms for answering reachability queries without explicitly maintaining a transitive closure matrix. Among our algorithms are: (i) A decremental algorithm for maintaining the ..."
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Cited by 30 (5 self)
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We obtain several new dynamic algorithms for maintaining the transitive closure of a directed graph, and several other algorithms for answering reachability queries without explicitly maintaining a transitive closure matrix. Among our algorithms are: (i) A decremental algorithm for maintaining the transitive closure of a directed graph, through an arbitrary sequence of edge deletions, in O(mn) total expected time, essentially the time needed for computing the transitive closure of the initial graph. Such a result was previously known only for acyclic graphs.
Speeding up dynamic shortest path algorithms
 AT&T labs Research Technical Report, TD5RJ8B, Florham Park, NJ
, 2003
"... doi 10.1287/ijoc.1070.0231 ..."
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Oracles for distances avoiding a failed node or link
 SIAM J. Comput
"... Abstract. We consider the problem of preprocessing an edgeweighted directed graph G to answer queries that ask for the length and first hop of a shortest path from any given vertex x to any given vertex y avoiding any given vertex or edge. As a natural application, this problem models routing in ne ..."
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Cited by 8 (0 self)
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Abstract. We consider the problem of preprocessing an edgeweighted directed graph G to answer queries that ask for the length and first hop of a shortest path from any given vertex x to any given vertex y avoiding any given vertex or edge. As a natural application, this problem models routing in networks subject to node or link failures. We describe a deterministic oracle with constant query time for this problem that uses O(n2 log n) space, where n is the number of vertices in G. The construction time for our oracle is O(mn2 + n3 log n). However, if one is willing to settle for Θ(n2.5) space, we can improve the preprocessing time to O(mn1.5 + n2.5 log n) while maintaining the constant query time. Our algorithms can find the shortest path avoiding a failed node or link in time proportional to the length of the path.
Improved Bounds and New TradeOffs for Dynamic All Pairs Shortest Paths
"... Let G be a directed graph with n vertices, subject to dynamic updates, and such that each edge weight can assume at most S different arbitrary real values throughout the sequence of updates. We present a new algorithm for maintaining all pairs shortest paths in G in O(S n) amortized time p ..."
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Cited by 7 (3 self)
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Let G be a directed graph with n vertices, subject to dynamic updates, and such that each edge weight can assume at most S different arbitrary real values throughout the sequence of updates. We present a new algorithm for maintaining all pairs shortest paths in G in O(S n) amortized time per update and in O(1) worstcase time per distance query. This improves over previous bounds. We also show how to obtain query/update tradeoffs for this problem, by introducing two new families of algorithms. Algorithms in the first family achieve an update bound of e O(S \Delta k \Delta n and a query bound of e O(n=k), and improve over the best known update bounds for k in the range (n=S) . Algorithms in the second family achieve an update e O e O(n ), and are competitive with the best known update bounds (first family included) for k in the range (n=S) k ! .
Dynamic shortest paths and transitive closure: algorithmic techniques and data structures
 J. Discr. Algor
, 2006
"... In this paper, we survey fully dynamic algorithms for path problems on general directed graphs. In particular, we consider two fundamental problems: dynamic transitive closure and dynamic shortest paths. Although research on these problems spans over more than three decades, in the last couple of ye ..."
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Cited by 7 (1 self)
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In this paper, we survey fully dynamic algorithms for path problems on general directed graphs. In particular, we consider two fundamental problems: dynamic transitive closure and dynamic shortest paths. Although research on these problems spans over more than three decades, in the last couple of years many novel algorithmic techniques have been proposed. In this survey, we will make a special effort to abstract some combinatorial and algebraic properties, and some common datastructural tools that are at the base of those techniques. This will help us try to present some of the newest results in a unifying framework so that they can be better understood and deployed also by nonspecialists.
Improved Algorithms for Maintaining Transitive Closure and Allpairs Shortest Paths in Digraphs under edge deletions
, 2001
"... We present improved algorithms for maintaining transitive closure and allpairs shortest paths in a digraph under deletion of edges. For the problem of transitive closure, the previous best known algorithms achieving O(1) query time require O(min(m; n =m)) amortized update time, thus establish an up ..."
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Cited by 3 (0 self)
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We present improved algorithms for maintaining transitive closure and allpairs shortest paths in a digraph under deletion of edges. For the problem of transitive closure, the previous best known algorithms achieving O(1) query time require O(min(m; n =m)) amortized update time, thus establish an upper bound of O(n ) on update time per edgedeletion where m and n denote the number of edges and vertices respectively in the given graph. We present an algorithm that achieves O(1) query time for answering a query and O(n log log n) update time per edgedeletion, thus improving the upper bound to O(n 3 log n).
Oracles for Distances Avoiding a Node or Link Failure
, 2002
"... We consider the problem of preprocessing an edgeweighted directed graph G to answer queries that ask for the shortest distance from any given node x to any other node y avoiding an arbitrary failed node or link. We describe an oracle (i.e, a simple data structure) for such queries that can be store ..."
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Cited by 2 (0 self)
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We consider the problem of preprocessing an edgeweighted directed graph G to answer queries that ask for the shortest distance from any given node x to any other node y avoiding an arbitrary failed node or link. We describe an oracle (i.e, a simple data structure) for such queries that can be stored in O(n² log n) space, and which allows queries to be answered in O(1) time, where n is the number of nodes in G. We also show that if we are willing to use Θ(n 2.5) space, we can reduce the preprocessing time by a factor of √ n while maintaining the constant query time. We can also keep track of the shortest path avoiding any failed node or link by maintaining for each node the outgoing edge that should be used to get on such a path.
C.: An experimental study of algorithms for fully dynamic transitive closure
 J. Exp. Algorithmics
, 2008
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