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18
An Incremental Algorithm for a Generalization of the ShortestPath Problem
, 1992
"... The grammar problem, a generalization of the singlesource shortestpath problem introduced by Knuth, is to compute the minimumcost derivation of a terminal string from each nonterminal of a given contextfree grammar, with the cost of a derivation being suitably defined. This problem also subsume ..."
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Cited by 116 (1 self)
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The grammar problem, a generalization of the singlesource shortestpath problem introduced by Knuth, is to compute the minimumcost derivation of a terminal string from each nonterminal of a given contextfree grammar, with the cost of a derivation being suitably defined. This problem also subsumes the problem of finding optimal hyperpaths in directed hypergraphs (under varying optimization criteria) that has received attention recently. In this paper we present an incremental algorithm for a version of the grammar problem. As a special case of this algorithm we obtain an efficient incremental algorithm for the singlesource shortestpath problem with positive edge lengths. The aspect of our work that distinguishes it from other work on the dynamic shortestpath problem is its ability to handle "multiple heterogeneous modifications": between updates, the input graph is allowed to be restructured by an arbitrary mixture of edge insertions, edge deletions, and edgelength changes.
On the Computational Complexity of Dynamic Graph Problems
 THEORETICAL COMPUTER SCIENCE
, 1996
"... ..."
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.
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 ...
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.
Experimental Analysis of Dynamic Algorithms for the Single Source Shortest Path Problem
 ACM Jounal of Experimental Algorithmics
, 1997
"... In this paper we propose the first experimental study of the fully dynamic single source shortest paths problem on directed graphs with positive real edge weights. In particular, we perform an experimental analysis of three different algorithms: Dijkstra's algorithm, and the two output bounded al ..."
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Cited by 19 (2 self)
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In this paper we propose the first experimental study of the fully dynamic single source shortest paths problem on directed graphs with positive real edge weights. In particular, we perform an experimental analysis of three different algorithms: Dijkstra's algorithm, and the two output bounded algorithms proposed by Ramalingam and Reps in [31] and by Frigioni, MarchettiSpaccamela and Nanni in [18], respectively. The main goal of this paper is to provide a first experimental evidence for: (a) the effectiveness of dynamic algorithms for shortest paths with respect to a traditional static approach to this problem; (b) the validity of the theoretical model of output boundedness to analyze dynamic graph algorithms. Beside random generated graphs, useful to capture the "asymptotic" behavior of algorithms, we also develope experiments by considering a widely used graph from the real world, i.e., the Internet graph. Work partially supported by the ESPRIT Long Term Research Project...
Anytime Search in Dynamic Graphs
"... Agents operating in the real world often have limited time available for planning their next actions. Producing optimal plans is infeasible in these scenarios. Instead, agents must be satisfied with the best plans they can generate within the time available. One class of planners wellsuited to this ..."
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Cited by 17 (5 self)
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Agents operating in the real world often have limited time available for planning their next actions. Producing optimal plans is infeasible in these scenarios. Instead, agents must be satisfied with the best plans they can generate within the time available. One class of planners wellsuited to this task are anytime planners, which quickly find an initial, highly suboptimal plan, and then improve this plan until time runs out. A second challenge associated with planning in the real world is that models are usually imperfect and environments are often dynamic. Thus, agents need to update their models and consequently plans over time. Incremental planners, which make use of the results of previous planning efforts to generate a new plan, can substantially speed up each planning episode in such cases. In this paper, we present an A*based anytime search algorithm that produces significantly better solutions than current approaches, while also providing suboptimality bounds on the quality of the solution at any point in time. We also present an extension of this algorithm that is both anytime and incremental. This extension improves its current solution while deliberation time allows and is able to incrementally repair its solution when changes to the world model occur. We provide a number of theoretical and experimental results and demonstrate the effectiveness of the approaches in a robot navigation domain involving two physical systems. We believe that the simplicity, theoretical properties, and generality of the presented methods make them well suited to a range of search problems involving large, dynamic graphs.
Improved Algorithms for Dynamic Shortest Paths
, 2000
"... We describe algorithms for finding shortest paths and distances in outerplanar and planar digraphs that exploit the particular topology of the input graph. An important feature of our algorithms is that they can work in a dynamic environment, where the cost of any edge can be changed or the edge ca ..."
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Cited by 15 (3 self)
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We describe algorithms for finding shortest paths and distances in outerplanar and planar digraphs that exploit the particular topology of the input graph. An important feature of our algorithms is that they can work in a dynamic environment, where the cost of any edge can be changed or the edge can be deleted. In the case of outerplanar digraphs, our data structures can be updated after any such change in only logarithmic time. A distance query is also answered in logarithmic time. In the case of planar digraphs, we give an interesting tradeoff between preprocessing, query, and update times depending on the value of a certain topological parameter of the graph. Our results can be extended to nvertex digraphs of genus O(n1−ε) for any ε>0.
Dynamic Graph Algorithms
, 2000
"... INTRODUCTION Dynamic graph algorithms are algorithms that maintain properties of a (possibly edgeweighted) graph while the graph is changing. These algorithms are potentially useful in a number of application areas, including communication networks, VLSI design, distributed computing, and graphics, ..."
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Cited by 11 (0 self)
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INTRODUCTION Dynamic graph algorithms are algorithms that maintain properties of a (possibly edgeweighted) graph while the graph is changing. These algorithms are potentially useful in a number of application areas, including communication networks, VLSI design, distributed computing, and graphics, where the underlying graphs are subject to dynamic changes. Efficient dynamic graph algorithms are also used as subroutines in algorithms that build and modify graphs as part of larger tasks, e.g., the algorithm for constructing Voronoi diagrams by building planar subdivisions. GLOSSARY Update: an operation that changes the graph. The primitive updates considered in the literature are edge insertions and deletions and, in the case of edgeweighted graphs, changes in edge weights. Query: a request for information about the property being maintained. For example, if the property is planarity, a query simply asks whether the graph is currently
Incremental heuristic search in artificial intelligence
 Artificial Intelligence Magazine
"... Incremental search reuses information from previous searches to find solutions to a series of similar search problems potentially faster than is possible by solving each search problem from scratch. This is important since many artificial intelligence systems have to adapt their plans continuously t ..."
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Cited by 8 (5 self)
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Incremental search reuses information from previous searches to find solutions to a series of similar search problems potentially faster than is possible by solving each search problem from scratch. This is important since many artificial intelligence systems have to adapt their plans continuously to changes in (their knowledge of) the world. In this article, we therefore give an overview of incremental search, focusing on Lifelong Planning A*, and outline some of its possible applications in artificial intelligence. Overview It is often important that searches be fast. Artificial intelligence has developed several ways of speeding up searches by trading off the search time and the cost of the resulting path. This includes using inadmissible heuristics (Pohl