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12
Lifelong Planning A*
, 2005
"... Heuristic search methods promise to find shortest paths for pathplanning problems faster than uninformed search methods. Incremental search methods, on the other hand, promise to find shortest paths for series of similar pathplanning problems faster than is possible by solving each pathplanning p ..."
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Cited by 57 (3 self)
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Heuristic search methods promise to find shortest paths for pathplanning problems faster than uninformed search methods. Incremental search methods, on the other hand, promise to find shortest paths for series of similar pathplanning problems faster than is possible by solving each pathplanning problem from scratch. In this article, we develop Lifelong Planning A * (LPA*), an incremental version of A * that combines ideas from the artificial intelligence and the algorithms literature. It repeatedly finds shortest paths from a given start vertex to a given goal vertex while the edge costs of a graph change or vertices are added or deleted. Its first search is the same as that of a version of A * that breaks ties in favor of vertices with smaller gvalues but many of the subsequent searches are potentially faster because it reuses those parts of the previous search tree that are identical to the new one. We present analytical results that demonstrate its similarity to A * and experimental results that demonstrate its potential advantage in two different domains if the pathplanning problems change only slightly and the changes are close to the goal.
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 51 (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
A Dynamic Algorithm for Topologically Sorting Directed Acyclic Graphs
, 2004
"... We consider how to maintain the topological order of a directed acyclic graph (DAG) in the presence of edge insertions and deletions. We present a new algorithm and, although this has marginally inferior time complexity compared with the best previously known result, we find that its simplicity lead ..."
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Cited by 18 (1 self)
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We consider how to maintain the topological order of a directed acyclic graph (DAG) in the presence of edge insertions and deletions. We present a new algorithm and, although this has marginally inferior time complexity compared with the best previously known result, we find that its simplicity leads to better performance in practice. In addition, we provide an empirical comparison against three alternatives over a large number of random DAG's. The results show our algorithm is the best for sparse graphs and, surprisingly, that an alternative with poor theoretical complexity performs marginally better on dense 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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Implementations and Experimental Studies of Dynamic Graph Algorithms
, 2002
"... Dynamic graph algorithms have been extensively studied in the last two decades due to their wide applicability in many contexts. Recently, several implementations and experimental studies have been conducted investigating the practical merits of fundamental techniques and algorithms. In most cases, ..."
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Cited by 13 (3 self)
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Dynamic graph algorithms have been extensively studied in the last two decades due to their wide applicability in many contexts. Recently, several implementations and experimental studies have been conducted investigating the practical merits of fundamental techniques and algorithms. In most cases, these algorithms required sophisticated engineering and finetuning to be turned into efficient implementations. In this paper, we survey several implementations along with their experimental studies for dynamic problems on undirected and directed graphs. The former case includes dynamic connectivity, dynamic minimum spanning trees, and the sparsification technique. The latter case includes dynamic transitive closure and dynamic shortest paths. We also discuss the design and implementation of a software library for dynamic graph algorithms.
An Experimental Study of Dynamic Algorithms for Transitive Closure
 ACM JOURNAL OF EXPERIMENTAL ALGORITHMICS
, 2000
"... We perform an extensive experimental study of several dynamic algorithms for transitive closure. In particular, we implemented algorithms given by Italiano, Yellin, Cicerone et al., and two recent randomized algorithms by Henzinger and King. We propose a netuned version of Italiano's algori ..."
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Cited by 9 (2 self)
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We perform an extensive experimental study of several dynamic algorithms for transitive closure. In particular, we implemented algorithms given by Italiano, Yellin, Cicerone et al., and two recent randomized algorithms by Henzinger and King. We propose a netuned version of Italiano's algorithms as well as a new variant of them, both of which were always faster than any of the other implementations of the dynamic algorithms. We also considered simpleminded algorithms that were easy to implement and likely to be fast in practice. We tested and compared the above implementations on random inputs, on nonrandom inputs that are worstcase inputs for the dynamic algorithms, and on an input motivated by a realworld graph.
Shortest path tree computation in dynamic graphs
 IEEE Trans. Computers
, 2009
"... Let G = (V,E,w) be a simple digraph, in which all edge weights are nonnegative real numbers. Let G ′ be obtained from G by an application of a set of edge weight updates to G. Let s ∈ V, and let Ts and T ′s be Shortest Path Trees (SPTs) rooted at s in G and G′, respectively. The Dynamic Shortest Pa ..."
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Cited by 8 (0 self)
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Let G = (V,E,w) be a simple digraph, in which all edge weights are nonnegative real numbers. Let G ′ be obtained from G by an application of a set of edge weight updates to G. Let s ∈ V, and let Ts and T ′s be Shortest Path Trees (SPTs) rooted at s in G and G′, respectively. The Dynamic Shortest Path (DSP) problem is to compute T ′s from Ts. Existing work on this problem either focuses on a single edge weight change, or for multiple edge weight changes, some of them are incorrect or are not optimized. We correct and extend a few stateoftheart dynamic SPT algorithms to handle multiple edge weight updates. We prove that these algorithms are correct. Dynamic algorithms may not outperform static algorithms all the time. To evaluate the proposed dynamic algorithms, we compare them with the wellknown static Dijkstra’s algorithm. Extensive experiments are conducted with both reallife and artificial data sets. The experimental results suggest the most appropriate algorithms to be used under different circumstances.
Online Algorithms for Topological Order and Strongly Connected Components
, 2003
"... We consider how to maintain the topological order of a directed acyclic graph (DAG) in the presence of edge insertions and deletions. We present a new algorithm and obtain a marginally improved complexity result over the previously known O(#log#). In addition, we provide an empirical compari ..."
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Cited by 7 (0 self)
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We consider how to maintain the topological order of a directed acyclic graph (DAG) in the presence of edge insertions and deletions. We present a new algorithm and obtain a marginally improved complexity result over the previously known O(#log#). In addition, we provide an empirical comparison against three existing solutions using random DAG's. The results show our algorithm to out perform the others on sparse graphs. Finally, we show how the algorithm can be extended to identify strongly connected components online.
SHORTEST PATHS AVOIDING FORBIDDEN SUBPATHS
, 2009
"... In this paper we study a variant of the shortest path problem in graphs: given a weighted graph G and vertices s and t, and given a set X of forbidden paths in G, find a shortest st path P such that no path in X is a subpath of P. Path P is allowed to repeat vertices and edges. We call each path ..."
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Cited by 5 (0 self)
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In this paper we study a variant of the shortest path problem in graphs: given a weighted graph G and vertices s and t, and given a set X of forbidden paths in G, find a shortest st path P such that no path in X is a subpath of P. Path P is allowed to repeat vertices and edges. We call each path in X an exception, and our desired path a shortest exception avoiding path. We formulate a new version of the problem where the algorithm has no a priori knowledge of X, and finds out about an exception x ∈ X only when a path containing x fails. This situation arises in computing shortest paths in optical networks. We give an algorithm that finds a shortest exception avoiding path in time polynomial in G  and X. The main idea is to run Dijkstra’s algorithm incrementally after replicating vertices when an exception is discovered.
Dynamic Algorithms for the Shortest Path Routing Problem: Learning AutomataBased Solutions
 IEEE Transactions on Systems, Man, and Cybernetics
, 2005
"... Abstract—This paper presents the first Learning Automatonbased solution to the dynamic single source shortest path problem. It involves finding the shortest path in a singlesource stochastic graph topology where there are continuous probabilistic updates in the edgeweights. The algorithm is signi ..."
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Abstract—This paper presents the first Learning Automatonbased solution to the dynamic single source shortest path problem. It involves finding the shortest path in a singlesource stochastic graph topology where there are continuous probabilistic updates in the edgeweights. The algorithm is significantly more efficient than the existing solutions, and can be used to find the “statistical” shortest path tree in the “average ” graph topology. It converges to this solution irrespective of whether there are new changes in edgeweights taking place or not. In such random settings, the proposed learning automata solution converges to the set of shortest paths. On the other hand, the existing algorithms will fail to exhibit such a behavior, and would recalculate the affected shortest paths after each weightchange. The important contribution of the proposed algorithm is that all the edges in a stochastic graph are not probed, and even if they are, they are not all probed equally often. Indeed, the algorithm attempts to almost always probe only those edges that will be included in the shortest path graph, while probing the other edges minimally. This increases the performance of the proposed algorithm. All the algorithms were tested in environments where edgeweights change stochastically, and where the graph topologies undergo multiple simultaneous edgeweight updates. Its superiority in terms of the average number of processed nodes, scanned edges and the time per update operation, when compared with the existing algorithms, was experimentally established. The algorithm can be applicable in domains ranging from ground transportation to aerospace, from civilian applications to military, from spatial database applications to telecommunications networking. Index Terms—Algorithm, dynamic, routing, shortest path. I.