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18
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 76 (6 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.
Computing PointtoPoint Shortest Paths from External Memory
"... We study the ALT algorithm [19] for the pointtopoint shortest path problem in the context of road networks. We suggest improvements to the algorithm itself and to its preprocessing stage. We also develop a memoryefficient implementation of the algorithm that runs on a Pocket PC. It stores graph d ..."
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Cited by 56 (6 self)
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We study the ALT algorithm [19] for the pointtopoint shortest path problem in the context of road networks. We suggest improvements to the algorithm itself and to its preprocessing stage. We also develop a memoryefficient implementation of the algorithm that runs on a Pocket PC. It stores graph data in a flash memory card and uses RAM to store information only for the part of the graph visited by the current shortest path computation. The implementation works even on very large graphs, including that of the North America road network, with almost 30 million vertices.
A Simple Shortest Path Algorithm with Linear Average Time
"... We present a simple shortest path algorithm. If the input lengths are positive and uniformly distributed, the algorithm runs in linear time. The worstcase running time of the algorithm is O(m + n log C), where n and m are the number of vertices and arcs of the input graph, respectively, and C i ..."
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Cited by 39 (7 self)
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We present a simple shortest path algorithm. If the input lengths are positive and uniformly distributed, the algorithm runs in linear time. The worstcase running time of the algorithm is O(m + n log C), where n and m are the number of vertices and arcs of the input graph, respectively, and C is the ratio of the largest and the smallest nonzero arc length.
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 bound ..."
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Cited by 27 (3 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...
Shortest Path Algorithms: Engineering Aspects
 In Proc. ESAAC ’01, Lecture Notes in Computer Science
, 2001
"... We review shortest path algorithms based on the multilevel bucket data structure [6] and discuss the interplay between theory and engineering choices that leads to e#cient implementations. Our experimental results suggest that the caliber heuristic [17] and adaptive parameter selection give an ..."
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Cited by 23 (4 self)
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We review shortest path algorithms based on the multilevel bucket data structure [6] and discuss the interplay between theory and engineering choices that leads to e#cient implementations. Our experimental results suggest that the caliber heuristic [17] and adaptive parameter selection give an e#cient algorithm, both on typical and on hard inputs, for a wide range of arc lengths.
A Practical Shortest Path Algorithm with Linear Expected Time
 SUBMITTED TO SIAM J. ON COMPUTING
, 2001
"... We present an improvement of the multilevel bucket shortest path algorithm of Denardo and Fox [9] and justify this improvement, both theoretically and experimentally. We prove that if the input arc lengths come from a natural probability distribution, the new algorithm runs in linear average time ..."
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Cited by 16 (8 self)
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We present an improvement of the multilevel bucket shortest path algorithm of Denardo and Fox [9] and justify this improvement, both theoretically and experimentally. We prove that if the input arc lengths come from a natural probability distribution, the new algorithm runs in linear average time while the original algorithm does not. We also describe an implementation of the new algorithm. Our experimental data suggests that the new algorithm is preferable to the original one in practice. Furthermore, for integral arc lengths that fit into a word of today's computers, the performance is close to that of breadthfirst search, suggesting limitations on further practical improvements.
A Continuous Query System for Dynamic Route Planning
"... Abstract—In this paper, we address the problem of answering continuous route planning queries over a road network, in the presence of updates to the delay (cost) estimates of links. A simple approach to this problem would be to recompute the best path for all queries on arrival of every delay update ..."
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Cited by 16 (0 self)
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Abstract—In this paper, we address the problem of answering continuous route planning queries over a road network, in the presence of updates to the delay (cost) estimates of links. A simple approach to this problem would be to recompute the best path for all queries on arrival of every delay update. However, such a naive approach scales poorly when there are many users who have requested routes in the system. Instead, we propose two new classes of approximate techniques – Kpaths and proximity measures to substantially speed up processing of the set of designated routes specified by continuous route planning queries in the face of incoming traffic delay updates. Our techniques work through a combination of precomputation of likely good paths and by avoiding complete recalculations on every delay update, instead only sending the user new routes when delays change significantly. Based on an experimental evaluation with 7,000 drives from real taxi cabs, we found that the routes delivered by our techniques are within 5 % of the best shortest path and have run times an order of magnitude or less compared to a naive approach. I.
Experimental Evaluation of a New Shortest Path Algorithm (Extended Abstract)
, 2002
"... We evaluate the practical eciency of a new shortest path algorithm for undirected graphs which was developed by the rst two authors. This algorithm works on the fundamental comparisonaddition model. Theoretically, this new algorithm outperforms Dijkstra's algorithm on sparse graphs for t ..."
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Cited by 12 (4 self)
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We evaluate the practical eciency of a new shortest path algorithm for undirected graphs which was developed by the rst two authors. This algorithm works on the fundamental comparisonaddition model. Theoretically, this new algorithm outperforms Dijkstra's algorithm on sparse graphs for the allpairs shortest path problem, and more generally, for the problem of computing singlesource shortest paths from !(1) different sources. Our extensive experimental analysis demonstrates that this is also the case in practice. We present results which show the new algorithm to run faster than Dijkstra's on a variety of sparse graphs when the number of vertices ranges from a few thousand to a few million, and when computing singlesource shortest paths from as few as three different sources.
PointtoPoint Shortest Path Algorithms with Preprocessing
"... This is a survey of some recent results on pointtopoint shortest path algorithms. This classical optimization problem received a lot of attention lately and significant progress has been made. After an overview of classical results, we study recent heuristics that solve the problem while examinin ..."
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Cited by 7 (0 self)
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This is a survey of some recent results on pointtopoint shortest path algorithms. This classical optimization problem received a lot of attention lately and significant progress has been made. After an overview of classical results, we study recent heuristics that solve the problem while examining only a small portion of the input graph; the graph can be very big. Note that the algorithms we discuss find exact shortest paths. These algorithms are heuristic because they perform well only on some graph classes. While their performance has been good in experimental studies, no theoretical bounds are known to support the experimental observations. Most of these algorithms have been motivated by finding paths in large road networks. We start by reviewing the classical Dijkstra’s algorithm and its bidirectional variant, developed in 1950’s and 1960’s. Then we review A* search, an AI technique developed in 1970’s. Next we turn our attention to modern results which are based on preprocessing the graph. To be practical, preprocessing needs to be reasonably fast and not use too much space. We discuss landmark and reachbased algorithms as well as their combination.
HeaponTop Priority Queues
 TR 96042, NEC RESEARCH INSTITUTE
, 1996
"... We introduce the heapontop (hot) priority queue data structure that combines the multilevel bucket data structure of Denardo and Fox [9] and a heap. We use the new data structure to obtain an O(m+n(logC) 1 3 +ffl ) expected time implementation of Dijkstra's shortest path algorithm [11], im ..."
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Cited by 4 (2 self)
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We introduce the heapontop (hot) priority queue data structure that combines the multilevel bucket data structure of Denardo and Fox [9] and a heap. We use the new data structure to obtain an O(m+n(logC) 1 3 +ffl ) expected time implementation of Dijkstra's shortest path algorithm [11], improving the previous bounds.