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90
Incremental A*
 In Proceedings of the Neural Information Processing Systems
, 2002
"... Incremental search techniques find optimal solutions to series of similar search tasks much faster than is possible by solving each search task from scratch. While researchers have developed incremental versions of uninformed search methods, we develop an incremental version of A*. ..."
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Cited by 37 (17 self)
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Incremental search techniques find optimal solutions to series of similar search tasks much faster than is possible by solving each search task from scratch. While researchers have developed incremental versions of uninformed search methods, we develop an incremental version of A*.
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 35 (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].
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 35 (4 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
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 28 (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.
A Memetic Algorithm for OSPF Routing
, 2002
"... this paper, we extend the GA by adding to it a local improvement procedure, resulting in a memetic algorithm (MA). We compare the MA with an optimized version of the GA and show that the MA not only finds better solutions, but also converges to a given solution in less time ..."
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Cited by 28 (6 self)
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this paper, we extend the GA by adding to it a local improvement procedure, resulting in a memetic algorithm (MA). We compare the MA with an optimized version of the GA and show that the MA not only finds better solutions, but also converges to a given solution in less time
New Dynamic SPT Algorithm based on a BallandString Model
, 1999
"... A key functionality in today's widely used interior gateway routing protocols such as OSPF and ISIS involves the computation of a shortest path tree (SPT). In many existing commercial routers, the computation of an SPT is done from scratch following changes in the link states of the network. As the ..."
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Cited by 25 (0 self)
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A key functionality in today's widely used interior gateway routing protocols such as OSPF and ISIS involves the computation of a shortest path tree (SPT). In many existing commercial routers, the computation of an SPT is done from scratch following changes in the link states of the network. As there may coexist multiple SPTs in a network with a set of given link states, such recomputation of an entire SPT not only is inefficient but also causes frequent unnecessary changes in the topology of an existing SPT and creates routing instability. This paper presents a new dynamic SPT algorithm that makes use of the structure of the previously computed SPT. Our algorithm is derived by recasting the SPT problem into an optimization problem in a dual linear programming framework, which can also be interpreted using a ballandstring model. In this model, the increase (or decrease) of an edge weight in the tree corresponds to the lengthening (or shortening) of a string. By stretching the strings...
Fully Dynamic Output Bounded Single Source Shortest Path Problem (Extended Abstract)
 In ACMSIAM Symposium on Discrete Algorithms
"... ) Abstract We consider the problem of maintaining the distances and the shortest paths from a single source in either a directed or an undirected graph with positive real edge weights, handling insertions, deletions and cost updates of edges. We propose fully dynamic algorithms with optimal space ..."
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Cited by 24 (4 self)
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) Abstract We consider the problem of maintaining the distances and the shortest paths from a single source in either a directed or an undirected graph with positive real edge weights, handling insertions, deletions and cost updates of edges. We propose fully dynamic algorithms with optimal space requirements and query time. The cost of update operations depends on the class of the considered graph and on the number of vertices that, due to an edge modification, either change their distance from the source or change their parent in the shortest path tree. In the case of graphs with bounded genus (including planar graphs), bounded degree graphs, bounded treewidth graphs and finearplanar graphs with bounded fi, the update procedures require O(log n) amortized time per vertex update, while for general graphs with n vertices and m edges they require O( p m log n) amortized time per vertex update. The solution is based on a dynamization of Dijkstra's algorithm [6] and requires simple ...
Speeding Up the Calculation of Heuristics for Heuristic SearchBased Planning
, 2002
"... Heuristic searchbased planners, such as HSP 2.0, solve STRIPSstyle planning problems efficiently but spend about eighty percent of their planning time on calculating the heuristic values. In this paper, we systematically evaluate alternative methods for calculating the heuristic values for HSP 2.0 ..."
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Cited by 22 (2 self)
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Heuristic searchbased planners, such as HSP 2.0, solve STRIPSstyle planning problems efficiently but spend about eighty percent of their planning time on calculating the heuristic values. In this paper, we systematically evaluate alternative methods for calculating the heuristic values for HSP 2.0 and demonstrate that the resulting planning times differ substantially. HSP 2.0 calculates each heuristic value by solving a relaxed planning problem with a dynamic programming method similar to value iteration. We identify two different approaches for speeding up the calculation of heuristic values, namely to order the value updates and to reuse information from the calculation of previous heuristic values. We then show how these two approaches can be combined, resulting in our PINCH method. PINCH outperforms both of the other approaches individually as well as the methods used by HSP 1.0 and HSP 2.0 for most of the large planning problems tested. In fact, it speeds up the planning time of HSP 2.0 by up to eighty percent in several domains and, in general, the amount of savings grows with the size of the domains, allowing HSP 2.0 to solve larger planning problems than was possible before in the same amount of time and without changing its overall operation.
Optimal Traversal of Directed Hypergraphs
, 1992
"... A directed hypergraph is defined by a set of nodes and a set of hyperarcs, each connecting a set of source nodes to a single target node. Directed hypergraphs are used in several contexts to model different combinatorial structures, such as functional dependencies [Ull82], Horn clauses in proposi ..."
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Cited by 21 (2 self)
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A directed hypergraph is defined by a set of nodes and a set of hyperarcs, each connecting a set of source nodes to a single target node. Directed hypergraphs are used in several contexts to model different combinatorial structures, such as functional dependencies [Ull82], Horn clauses in propositional calculus [AI91], ANDOR graphs [Nil82], Petri nets [Pet62]. A hyperpath, similarly to the notion of path in directed graphs, consists of a connection among nodes using hyperarcs. Unlike paths in graphs, hyperpaths are suitable of different definitions of measure, corresponding to different concepts arising in various applications. In this paper we consider the problem of finding minimal hyperpaths according to several measures. We show that some of these problems are, not surprisingly, NPhard. However, if the measure function on hyperpaths matches certain conditions (which we define as valuebased measure functions) , the problem turns out to be solvable in polynomial time. We...
Fast replanning for navigation in unknown terrain
 Transactions on Robotics
"... Abstract—Mobile robots often operate in domains that are only incompletely known, for example, when they have to move from given start coordinates to given goal coordinates in unknown terrain. In this case, they need to be able to replan quickly as their knowledge of the terrain changes. Stentz ’ Fo ..."
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Cited by 21 (7 self)
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Abstract—Mobile robots often operate in domains that are only incompletely known, for example, when they have to move from given start coordinates to given goal coordinates in unknown terrain. In this case, they need to be able to replan quickly as their knowledge of the terrain changes. Stentz ’ Focussed Dynamic A (D) is a heuristic search method that repeatedly determines a shortest path from the current robot coordinates to the goal coordinates while the robot moves along the path. It is able to replan faster than planning from scratch since it modifies its previous search results locally. Consequently, it has been extensively used in mobile robotics. In this article, we introduce an alternative to D that determines the same paths and thus moves the robot in the same way but is algorithmically different. D Lite is simple, can be rigorously analyzed, extendible in multiple ways, and is at least as efficient as D. We believe that our results will make Dlike replanning methods even more popular and enable robotics researchers to adapt them to additional applications. Index Terms—A, D (Dynamic A), navigation in unknown terrain, planning with the freespace assumption, replanning, search, sensorbased path planning. I.