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73
Shortest Paths Algorithms: Theory And Experimental Evaluation
 Mathematical Programming
, 1993
"... . We conduct an extensive computational study of shortest paths algorithms, including some very recent algorithms. We also suggest new algorithms motivated by the experimental results and prove interesting theoretical results suggested by the experimental data. Our computational study is based on se ..."
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Cited by 177 (15 self)
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. We conduct an extensive computational study of shortest paths algorithms, including some very recent algorithms. We also suggest new algorithms motivated by the experimental results and prove interesting theoretical results suggested by the experimental data. Our computational study is based on several natural problem classes which identify strengths and weaknesses of various algorithms. These problem classes and algorithm implementations form an environment for testing the performance of shortest paths algorithms. The interaction between the experimental evaluation of algorithm behavior and the theoretical analysis of algorithm performance plays an important role in our research. Andrew V. Goldberg was supported in part by ONR Young Investigator Award N0001491J1855, NSF Presidential Young Investigator Grant CCR8858097 with matching funds from AT&T, DEC, and 3M, and a grant from Powell Foundation. This work was done while Boris V. Cherkassky was visiting Stanford University Compu...
Computing the shortest path: A* search meets graph theory
, 2005
"... We study the problem of finding a shortest path between two vertices in a directed graph. This is an important problem with many applications, including that of computing driving directions. We allow preprocessing the graph using a linear amount of extra space to store auxiliary information, and usi ..."
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Cited by 150 (8 self)
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We study the problem of finding a shortest path between two vertices in a directed graph. This is an important problem with many applications, including that of computing driving directions. We allow preprocessing the graph using a linear amount of extra space to store auxiliary information, and using this information to answer shortest path queries quickly. Our approach uses A ∗ search in combination with a new graphtheoretic lowerbounding technique based on landmarks and the triangle inequality. We also develop new bidirectional variants of A ∗ search and investigate several variants of the new algorithms to find those that are most efficient in practice. Our algorithms compute optimal shortest paths and work on any directed graph. We give experimental results showing that the most efficient of our new algorithms outperforms previous algorithms, in particular A ∗ search with Euclidean bounds, by a wide margin on road networks. We also experiment with several synthetic graph families.
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 72 (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.
Shortest path algorithms: An evaluation using real road networks
 Transportation Science
, 1998
"... The classic problem of finding the shortest path over a network has been the target of many research efforts over the years. These research efforts have resulted in a number of different algorithms and a considerable amount of empirical findings with respect to performance. Unfortunately, prior rese ..."
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Cited by 69 (1 self)
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The classic problem of finding the shortest path over a network has been the target of many research efforts over the years. These research efforts have resulted in a number of different algorithms and a considerable amount of empirical findings with respect to performance. Unfortunately, prior research does not provide a clear direction for choosing an algorithm when one faces the problem of computing shortest paths on real road networks. Most of the computational testing on shortest path algorithms has been based on randomly generated networks, which may not have the characteristics of real road networks. In this paper, we provide an objective evaluation of 15 shortest path algorithms using a variety of real road networks. Based on the evaluation, a set of recommended algorithms for computing shortest paths on real road networks is identified. This evaluation should be particularly useful to researchers and practitioners in operations research, management science, transportation, and Geographic Information Systems. The computation of shortest paths is an important task in many network and transportation related analyses. The development, computational testing, and efficient implementation of shortest path algorithms have remained important research topics within related disciplines such as operations
Discrete dynamic shortest path problems in transportation applications: Complexity and algorithms with optimal run time
 234 I. Chabini. Minimum expected travel times in stochastic timedependent networks revisited. Internal Report. MIT
, 1999
"... A solution is provided for what appears to be a 30yearold problem dealing with the discovery of the most efficient algorithms possible to compute alltoone shortest paths in discrete dynamic networks. This problem lies at the heart of efficient solution approaches to dynamic network models that a ..."
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Cited by 66 (1 self)
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A solution is provided for what appears to be a 30yearold problem dealing with the discovery of the most efficient algorithms possible to compute alltoone shortest paths in discrete dynamic networks. This problem lies at the heart of efficient solution approaches to dynamic network models that arise in dynamic transportation systems, such as intelligent transportation systems (ITS) applications. The alltoone dynamic shortest paths problem and the onetoall fastest paths problems are studied. Early results are revisited and new properties are established. The complexity of these problems is established, and solution algorithms optimal for run time are developed. A new and simple solution algorithm is proposed for alltoone, all departure time intervals, shortest paths problems. It is proved, theoretically, that the new solution algorithm has an optimal run time complexity that equals the complexity of the problem. Computer implementations and experimental evaluations of various solution algorithms support the theoretical findings and demonstrate the efficiency of the proposed solution algorithm. The findings should be of major benefit to research and development activities in the field of dynamic management, in particular realtime management, and to control of largescale ITSs.
Shortest Path Algorithms in Transportation Models: Classical and Innovative Aspects
, 1998
"... Shortest Path Problems are among the most studied network flow optimization problems, with interesting applications in various fields. One such field is transportation, where shortest path problems of different kinds need to be solved. Due to the nature of the application, transportation scientists ..."
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Cited by 63 (3 self)
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Shortest Path Problems are among the most studied network flow optimization problems, with interesting applications in various fields. One such field is transportation, where shortest path problems of different kinds need to be solved. Due to the nature of the application, transportation scientists need very flexible and efficient shortest path procedures, both from the running time point of view, and also for the memory requirements. Since no "best" algorithm currently exists for every kind of transportation problem, research in this field has recently moved to the design and implementation of "ad hoc" shortest path procedures, which are able to capture the peculiarities of the problems under consideration. The aim of this work is to present in a unifying framework both the main algorithmic approaches that have been proposed in the past years for solving the shortest path problems arising most frequently in the transportation field, and also some important implementation techniques ...
NegativeCycle Detection Algorithms
 MATHEMATICAL PROGRAMMING
, 1996
"... We study the problem of finding a negative length cycle in a network. An algorithm for the negative cycle problem combines a shortest path algorithm and a cycle detection strategy. We study various combinations of shortest path algorithms and cycle detection strategies and find the best combinations ..."
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Cited by 53 (5 self)
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We study the problem of finding a negative length cycle in a network. An algorithm for the negative cycle problem combines a shortest path algorithm and a cycle detection strategy. We study various combinations of shortest path algorithms and cycle detection strategies and find the best combinations. One of our discoveries is that a cycle detection strategy of Tarjan greatly improves practical performance of a classical shortest path algorithm, making it competitive with the fastest known algorithms on a wide range of problems. As a part of our study, we develop problem families for testing negative cycle algorithms.
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 51 (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.
A Bundle Type DualAscent Approach to Linear Multicommodity MinCost Flow Problems
"... We present a Cost Decomposition approach for the linear Multicommodity MinCost Flow problem, where the mutual capacity constraints are dualized and the resulting Lagrangean Dual is solved with a dualascent algorithm belonging to the class of Bundle methods. Although decomposition approaches to bl ..."
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Cited by 36 (15 self)
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We present a Cost Decomposition approach for the linear Multicommodity MinCost Flow problem, where the mutual capacity constraints are dualized and the resulting Lagrangean Dual is solved with a dualascent algorithm belonging to the class of Bundle methods. Although decomposition approaches to blockstructured Linear Programs have been reported not to be competitive with generalpurpose software, our extensive computational comparison shows that, when carefully implemented, a decomposition algorithm can outperform several other approaches, especially on problems where the number of commodities is “large ” with respect to the size of the graph. Our specialized Bundle algorithm is characterized by a new heuristic for the trust region parameter handling, and embeds a specialized Quadratic Program solver that allows the efficient implementation of strategies for reducing the number of active Lagrangean variables. We also exploit the structural properties of the singlecommodity MinCost Flow subproblems to reduce the overall computational cost. The proposed approach can be easily extended to handle variants of the problem.