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42
Generalized bestfirst search strategies and the optimality of A*
 JOURNAL OF THE ACM
, 1985
"... This paper reports several properties of heuristic bestfirst search strategies whose scoring functions f depend on all the information available from each candidate path, not merely on the current cost g and the estimated completion cost h. It is shown that several known properties of A * retain t ..."
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Cited by 161 (12 self)
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This paper reports several properties of heuristic bestfirst search strategies whose scoring functions f depend on all the information available from each candidate path, not merely on the current cost g and the estimated completion cost h. It is shown that several known properties of A * retain their form (with the minmax offplaying the role of the optimal cost), which helps establish general tests of admissibility and general conditions for node expansion for these strategies. On the basis of this framework the computational optimality of A*, in the sense of never expanding a node that can be skipped by some other algorithm having access to the same heuristic information that A* uses, is examined. A hierarchy of four optimality types is defined and three classes of algorithms and four domains of problem instances are considered. Computational performances relative to these algorithms and domains are appraised. For each classdomain combination, we then identify the strongest type of optimality that exists and the algorithm for achieving it. The main results of this paper relate to the class of algorithms that, like A*, return optimal solutions (i.e., admissible) when all cost estimates are optimistic (i.e., h 5 h*). On this class, A * is shown to be not optimal and it is also shown that no optimal algorithm exists, but if the performance tests are confirmed to cases in which the estimates are also consistent, then A * is indeed optimal. Additionally, A * is also shown to be optimal over a subset of the latter class containing all bestfirst algorithms that are guided by pathdependent evaluation functions.
Bidirectional Expansion For Keyword Search On Graph Databases
, 2005
"... Relational, XML and HTML data can be represented as graphs with entities as nodes and relationships as edges. Text is associated with nodes and possibly edges. Keyword search on such graphs has received much attention lately. A central problem in this scenario is to e#ciently extract from the ..."
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Cited by 117 (5 self)
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Relational, XML and HTML data can be represented as graphs with entities as nodes and relationships as edges. Text is associated with nodes and possibly edges. Keyword search on such graphs has received much attention lately. A central problem in this scenario is to e#ciently extract from the data graph a small number of the "best" answer trees. A Backward Expanding search, starting at nodes matching keywords and working up toward confluent roots, is commonly used for predominantly textdriven queries. But it can perform poorly if some keywords match many nodes, or some node has very large degree. In this paper
Fast exact and approximate geodesics on meshes
 ACM Trans. Graph
, 2005
"... The computation of geodesic paths and distances on triangle meshes is a common operation in many computer graphics applications. We present several practical algorithms for computing such geodesics from a source point to one or all other points efficiently. First, we describe an implementation of th ..."
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Cited by 67 (0 self)
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The computation of geodesic paths and distances on triangle meshes is a common operation in many computer graphics applications. We present several practical algorithms for computing such geodesics from a source point to one or all other points efficiently. First, we describe an implementation of the exact “single source, all destination ” algorithm presented by Mitchell, Mount, and Papadimitriou (MMP). We show that the algorithm runs much faster in practice than suggested by worst case analysis. Next, we extend the algorithm with a merging operation to obtain computationally efficient and accurate approximations with bounded error. Finally, to compute the shortest path between two given points, we use a lowerbound property of our approximate geodesic algorithm to efficiently prune the frontier of the MMP algorithm, thereby obtaining an exact solution even more quickly.
Reach for A∗: Efficient pointtopoint shortest path algorithms
 IN WORKSHOP ON ALGORITHM ENGINEERING & EXPERIMENTS
, 2006
"... We study the pointtopoint shortest path problem in a setting where preprocessing is allowed. We improve the reachbased approach of Gutman [16] in several ways. In particular, we introduce a bidirectional version of the algorithm that uses implicit lower bounds and we add shortcut arcs which reduc ..."
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Cited by 60 (5 self)
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We study the pointtopoint shortest path problem in a setting where preprocessing is allowed. We improve the reachbased approach of Gutman [16] in several ways. In particular, we introduce a bidirectional version of the algorithm that uses implicit lower bounds and we add shortcut arcs which reduce vertex reaches. Our modifications greatly reduce both preprocessing and query times. The resulting algorithm is as fast as the best previous method, due to Sanders and Schultes [27]. However, our algorithm is simpler and combines in a natural way with A∗ search, which yields significantly better query times.
Geometric SpeedUp Techniques for Finding Shortest Paths in Large Sparse Graphs
, 2003
"... In this paper, we consider Dijkstra's algorithm for the single source single target shortest paths problem in large sparse graphs. The goal is to reduce the response time for online queries by using precomputed information. For the result of the preprocessing, we admit at most linear space. We as ..."
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Cited by 53 (14 self)
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In this paper, we consider Dijkstra's algorithm for the single source single target shortest paths problem in large sparse graphs. The goal is to reduce the response time for online queries by using precomputed information. For the result of the preprocessing, we admit at most linear space. We assume that a layout of the graph is given. From this layout, in the preprocessing, we determine for each edge a geometric object containing all nodes that can be reached on a shortest path starting with that edge. Based on these geometric objects, the search space for online computation can be reduced significantly. We present an extensive experimental study comparing the impact of different types of objects. The test data we use are traffic networks, the typical field of application for this scenario.
A Computational Study of Routing Algorithms for Realistic Transportation Networks
 ACM JOURNAL OF EXPERIMENTAL ALGORITHMS
, 1998
"... We carry out an experimental analysis of a number of shortest path (routing) algorithms investigated in the context of the TRANSIMS (TRansportation ANalysis and SIMulation System) project. The main focus of the paper is to study how various heuristic as well as exact solutions and associated data ..."
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Cited by 42 (22 self)
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We carry out an experimental analysis of a number of shortest path (routing) algorithms investigated in the context of the TRANSIMS (TRansportation ANalysis and SIMulation System) project. The main focus of the paper is to study how various heuristic as well as exact solutions and associated data structures affect the computational performance of the software developed for realistic transportation networks. For this purpose we have used a road network representing with high degree of resolution the Dallas FtWorth urban area. We discuss and experimentally analyze various onetoone shortest path algorithms. These include classical exact algorithms studied in the literature as well as heuristic solutions that are designed to take into account the geometric structure of the input instances. Computational results are provided to empirically compare the efficiency of various algorithms. Our studies indicate that a modified Dijkstra's algorithm is computationally fast and an ex...
A scalable distributed parallel breadthfirst search algorithm on bluegene/l
 In SC ’05: Proceedings of the 2005 ACM/IEEE conference on Supercomputing
, 2005
"... Many emerging largescale data science applications require searching large graphs distributed across multiple memories and processors. This paper presents a distributed breadthfirst search (BFS) scheme that scales for random graphs with up to three billion vertices and 30 billion edges. Scalability ..."
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Cited by 39 (2 self)
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Many emerging largescale data science applications require searching large graphs distributed across multiple memories and processors. This paper presents a distributed breadthfirst search (BFS) scheme that scales for random graphs with up to three billion vertices and 30 billion edges. Scalability was tested on IBM BlueGene/L with 32,768 nodes at the Lawrence Livermore National Laboratory. Scalability was obtained through a series of optimizations, in particular, those that ensure scalable use of memory. We use 2D (edge) partitioning of the graph instead of conventional 1D (vertex) partitioning to reduce communication overhead. For Poisson random graphs, we show that the expected size of the messages is scalable for both 2D and 1D partitionings. Finally, we have developed efficient collective communication functions for the 3D torus architecture of BlueGene/L that also take advantage of the structure in the problem. The performance and characteristics of the algorithm are measured and reported. 1
Bidirectional Heuristic Search Reconsidered
 Journal of Artificial Intelligence Research
, 1997
"... The assessment of bidirectional heuristic search has been incorrect since it was first published more than a quarter of a century ago. For quite a long time, this search strategy did not achieve the expected results, and there was a major misunderstanding about the reasons behind it. Although there ..."
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Cited by 32 (2 self)
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The assessment of bidirectional heuristic search has been incorrect since it was first published more than a quarter of a century ago. For quite a long time, this search strategy did not achieve the expected results, and there was a major misunderstanding about the reasons behind it. Although there is still widespread belief that bidirectional heuristic search is afflicted by the problem of search frontiers passing each other, we demonstrate that this conjecture is wrong. Based on this finding, we present both a new generic approach to bidirectional heuristic search and a new approach to dynamically improving heuristic values that is feasible in bidirectional search only. These approaches are put into perspective with both the traditional and more recently proposed approaches in order to facilitate a better overall understanding. Empirical results of experiments with our new approaches show that bidirectional heuristic search can be performed very efficiently and also with limited mem...
Artificial Intelligence Search Algorithms
 In Algorithms and Theory of Computation Handbook
, 1996
"... Introduction Search is a universal problemsolving mechanism in artificial intelligence (AI). In AI problems, the sequence of steps required for solution of a problem are not known a priori, but often must be determined by a systematic trialanderror exploration of alternatives. The problems that h ..."
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Cited by 25 (0 self)
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Introduction Search is a universal problemsolving mechanism in artificial intelligence (AI). In AI problems, the sequence of steps required for solution of a problem are not known a priori, but often must be determined by a systematic trialanderror exploration of alternatives. The problems that have been addressed by AI search algorithms fall into three general classes: singleagent pathfinding problems, twoplayer games, and constraintsatisfaction problems. Classic examples in the AI literature of pathfinding problems are the slidingtile puzzles, including the 3 \Theta 3 Eight Puzzle (see Fig. 1) and its larger relatives the 4 \Theta 4 Fifteen Puzzle, and 5 \Theta 5 TwentyFour Puzzle. The Eight Puzzle consists of a 3 \Theta 3 square frame containing eight numbered square tiles, and an empty position called the blank. The legal operators are to slide any tile that is h