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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 58 (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
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 51 (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 46 (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.
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...
Three Fastest Shortest Path Algorithms on Real Road Networks: Data Structures and Procedures
, 1997
"... It is well known that computing shortest paths over a network is an important task in many network and transportation related analyses. Choosing an adequate algorithm from the numerous algorithms reported in the literature is a critical step in many applications involving real road networks. In a re ..."
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Cited by 12 (0 self)
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It is well known that computing shortest paths over a network is an important task in many network and transportation related analyses. Choosing an adequate algorithm from the numerous algorithms reported in the literature is a critical step in many applications involving real road networks. In a recent study, a set of three shortest path algorithms that run fastest on real road networks has been identified. These three algorithms are: 1) the graph growth algorithm implemented with two queues, 2) the Dijkstra algorithm implemented with approximate buckets, and 3) the Dijkstra algorithm implemented with double buckets. As a sequel to that study, this paper reviews and summarizes these three algorithms, and demonstrates the data structures and procedures related to the algorithms. This paper should be particularly useful to researchers and practitioners in transportation, GIS, operations research and management sciences.
Choosing a Shortest Path Algorithm
, 1995
"... Computation of shortest paths is an integral component of many applications such as transportation planning and VLSI design. Frequently, a shortest path algorithm is selected for a given application based on the performance of the algorithm for a set of test networks. The performance of this algorit ..."
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Cited by 5 (4 self)
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Computation of shortest paths is an integral component of many applications such as transportation planning and VLSI design. Frequently, a shortest path algorithm is selected for a given application based on the performance of the algorithm for a set of test networks. The performance of this algorithm, however, can be significantly different for networks not included in the test set. Therefore, it is necessary to recognize when an algorithm has poor performance. In this paper, we develop a theoretical indicator, H that can be used to identify algorithms with poor performance. We show that using this theoretical guideline can result in reducing execution time significantly for various transportation networks. 1 Introduction Significant research has focused on developing fast shortest path algorithms. The relative performance of these algorithms, however, varies considerably for different networks, thereby making algorithm selection difficult. To address this problem, we derive a theo...
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 3 (1 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.
SPT_L shortest path algorithms: review, new proposals and some experimental results
, 1999
"... This paper presents in a unified framework the most efficient shortest path algorithms of the List class to highlight strategies for handling the candidate node set as well as issues related to the efficient implementation of such strategies. A deep analysis of the strategies which inspired two of t ..."
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Cited by 2 (0 self)
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This paper presents in a unified framework the most efficient shortest path algorithms of the List class to highlight strategies for handling the candidate node set as well as issues related to the efficient implementation of such strategies. A deep analysis of the strategies which inspired two of the most robust algorithms for the shortest path tree problem, due to Tarjan [27] and to Goldberg and Radzik [18], allows the proposal of some variants. A computational study of such variants is conducted on the same test problem families used in [6], in order to validate "a posteriori" the implementation choices. The experimental data suggest that all of the new variants are robust in practice and, for each of the tested problem families, at least one of the new variants either improves the performance or performs as well as both benchmark algorithms. 1 Under grants MURSTCofinanziato 1997 and CNRGNIM. 2 This work was done while the author was visiting the Department of Computer Science...
A Computational Study Of Parallel Algorithms For The AllPairs Shortest Path Problem
, 1994
"... This paper presents experiences from the implementation of parallel algorithms for the allpairs shortest path problem. A brief survey of the problem is given and efficient techniques for exploiting the memory hierarchy of parallel computers are described. Comparing the algorithms at a practical ..."
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Cited by 1 (1 self)
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This paper presents experiences from the implementation of parallel algorithms for the allpairs shortest path problem. A brief survey of the problem is given and efficient techniques for exploiting the memory hierarchy of parallel computers are described. Comparing the algorithms at a practical level, the importance of issues such as synchronisation and data locality is established. 1 Introduction The problem of finding the shortest path in a graph is one of the most important problems in operations research. It arises in many applications and, as a result, has been the subject of numerous studies which provide solutions for both sequential [7] and parallel [3] computers. This paper deals with algorithms for solving the allpairs shortest path problem (i.e. finding the shortest paths between all pairs of nodes in a graph) on parallel computers. While theoretical measures of the performance of these algorithms are rather well described, it is well known that for parallel implement...
Computing AllPairs Shortest Paths by Leveraging Low Treewidth
, 2012
"... We present two new and efficient algorithms for computing allpairs shortest paths. The algorithms operate on directed graphs with real (possibly negative) weights. They make use of directed path consistency along a vertex ordering d. Both algorithms run in O(n²) wd time, where wd is the graph width ..."
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Cited by 1 (0 self)
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We present two new and efficient algorithms for computing allpairs shortest paths. The algorithms operate on directed graphs with real (possibly negative) weights. They make use of directed path consistency along a vertex ordering d. Both algorithms run in O(n²) wd time, where wd is the graph width induced by this vertex ordering. For graphs of constant treewidth, this yields O(n²) time, which is optimal. On chordal graphs, the algorithms run in O (nm) time. In addition, we present a variant that exploits graph separators to arrive at a run time of O(nw² d + n²) sd on general graphs, where sd ≤ wd is the size of the largest minimal separator induced by the vertex ordering d. We show empirically that on both constructed and realistic benchmarks, in many cases the algorithms outperform Floyd–Warshall’s as well as Johnson’s algorithm, which represent the current state of the art with a run time of O(n³) and O(nm + n² log n) , respectively. Our algorithms can be used for spatial and temporal reasoning, such as for the Simple Temporal Problem, which underlines their relevance to the planning and scheduling community.