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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 150 (14 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...
Faster algorithms for the shortest path problem
, 1990
"... Efficient implementations of Dijkstra's shortest path algorithm are investigated. A new data structure, called the radix heap, is proposed for use in this algorithm. On a network with n vertices, mn edges, and nonnegative integer arc costs bounded by C, a onelevel form of radix heap gives a t ..."
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Cited by 108 (9 self)
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Efficient implementations of Dijkstra's shortest path algorithm are investigated. A new data structure, called the radix heap, is proposed for use in this algorithm. On a network with n vertices, mn edges, and nonnegative integer arc costs bounded by C, a onelevel form of radix heap gives a time bound for Dijkstra's algorithm of O(m + n log C). A twolevel form of radix heap gives a bound of O(m + n log C/log log C). A combination of a radix heap and a previously known data structure called a Fibonacci heap gives a bound of O(m + n /log C). The best previously known bounds are O(m + n log n) using Fibonacci heaps alone and O(m log log C) using the priority queue structure of Van Emde Boas et al. [17].
Faster approximation algorithms for the unit capacity concurrent flow problem with applications to routing and finding sparse cuts
 SIAM Journal on Computing
, 1994
"... Abstract. This paper describes new algorithms for approximately solving the concurrent multicommodity flow problem with uniform capacities. These algorithms are much faster than algorithms discovered previously. Besides being an important problem in its own right, the uniformcapacity concurrent flo ..."
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Cited by 84 (20 self)
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Abstract. This paper describes new algorithms for approximately solving the concurrent multicommodity flow problem with uniform capacities. These algorithms are much faster than algorithms discovered previously. Besides being an important problem in its own right, the uniformcapacity concurrent flow problem has many interesting applications. Leighton and Rao used uniformcapacity concurrent flow to find an approximately "sparsest cut " in a graph and thereby approximately solve a wide variety of graph problems, including minimum feedback arc set, minimum cut linear arrangement, and minimum area layout. However, their method appeared to be impractical as it required solving a large linear program. This paper shows that their method might be practical by giving an O(m log m) expectedtime randomized algorithm for their concurrent flow problem on an medge graph. Raghavan and Thompson used uniformcapacity concurrent flow to solve approximately a channel width minimization problem in very large scale integration. An O (k 3/2 (m + n log n)) expectedtime randomized algorithm and an O (k min {n, k} (m + n log n) log k) deterministic algorithm is given for this problem when the channel width is f2 (log n), where k denotes the number of wires to be routed in an nnode, medge network. Key words, multicommodity flow, approximation, concurrent flow, graph separators, VLSI routing AMS subject classification. 68Q25, 90C08, 90C27 1. Introduction. The
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 65 (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
Scaling Algorithms for Network Problems
, 1985
"... This paper gives algorithms for network problems that work by scaling the numeric parameters. Assume all parameters are integers. Let n, m, and N denote the number of vertices, number of edges, and largest parameter of the network, respectively. A scaling algorithm for maximum weight matching on a b ..."
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Cited by 63 (2 self)
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This paper gives algorithms for network problems that work by scaling the numeric parameters. Assume all parameters are integers. Let n, m, and N denote the number of vertices, number of edges, and largest parameter of the network, respectively. A scaling algorithm for maximum weight matching on a bipartite graph runs in O(n3 % log N) time. For appropriate N this improves the traditional Hungarian method, whose most efftcient implementation is O(n(m + n log n)). The speedup results from finding augmenting paths in batches. The matching algorithm gives similar improvements for the following problems: singlesource shortest paths for arbitrary edge lengths (Bellman’s algorithm); maximum weight degreeconstrained subgraph; minimum cost flow on a cl network. Scaling gives a simple maximum value flow algorithm that matches the best known bound (Sleator and Tarjan’s algorithm) when log N = O(log n). Scaling also gives a good algorithm for shortest paths on a directed graph with nonnegative edge lengths (Dijkstra’s algorithm).
Finding the Hidden Path: Time Bounds for AllPairs Shortest Paths
, 1993
"... We investigate the allpairs shortest paths problem in weighted graphs. We present an algorithmthe Hidden Paths Algorithmthat finds these paths in time O(m* n+n² log n), where m is the number of edges participating in shortest paths. Our algorithm is a practical substitute for Dijkstra&ap ..."
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Cited by 63 (0 self)
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We investigate the allpairs shortest paths problem in weighted graphs. We present an algorithmthe Hidden Paths Algorithmthat finds these paths in time O(m* n+n² log n), where m is the number of edges participating in shortest paths. Our algorithm is a practical substitute for Dijkstra's algorithm. We argue that m* is likely to be small in practice, since m* = O(n log n) with high probability for many probability distributions on edge weights. We also prove an Ω(mn) lower bound on the running time of any pathcomparison based algorithm for the allpairs shortest paths problem. Pathcomparison based algorithms form a natural class containing the Hidden Paths Algorithm, as well as the algorithms of Dijkstra and Floyd. Lastly, we consider generalized forms of the shortest paths problem, and show that many of the standard shortest paths algorithms are effective in this more general setting.
Discrete Choice Methods And Their Applications To Short Term Travel Decisions
, 1999
"... Introduction Modeling travel behavior is a key aspect of demand analysis, where aggregate demand is the accumulation of individuals' decisions. In this chapter, we focus on "shortterm" travel decisions. The most important shortterm travel decisions include choice of destination fo ..."
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Cited by 58 (17 self)
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Introduction Modeling travel behavior is a key aspect of demand analysis, where aggregate demand is the accumulation of individuals' decisions. In this chapter, we focus on "shortterm" travel decisions. The most important shortterm travel decisions include choice of destination for a nonwork trip, choice of travel mode, choice of departure time and choice of route. It is important to note that shortterm decisions are conditional on longterm travel and mobility decisions such as car ownership and residential and work locations. The analysis of travel behavior is typically disaggregate, meaning that the models represent the choice behavior of individual travelers. Discrete choice analysis is the methodology used to analyze and predict travel decisions. Therefore, we begin this chapter with a review of the theoretical and practical aspects of discrete choice models. After a brief discussion of general assumptions, we introduce the random utility model, which is the most c
Scaling algorithms for the shortest paths problem
 In SODA ’93: Proceedings of the fourth annual ACMSIAM Symposium on Discrete algorithms
, 1993
"... Abstract. We describe a new method for designing scaling algorithms for the singlesource shortest paths problem and use this method to obtain an O (Vcfftn log N) algorithm for the problem. (Here n and m are the number of nodes and arcs in the input network and N is essentially the absolute value of ..."
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Cited by 55 (5 self)
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Abstract. We describe a new method for designing scaling algorithms for the singlesource shortest paths problem and use this method to obtain an O (Vcfftn log N) algorithm for the problem. (Here n and m are the number of nodes and arcs in the input network and N is essentially the absolute value of the most negative arc length; arc lengths are assumed to be integral.) This improves previous bounds for the problem. The method extends to related problems. Key words, shortest paths problem, graph theory, networks, scaling AMS subject classifications. 68Q20, 68Q25, 68R10, 05C70 1. Introduction. In
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 54 (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 ...
The Ordered Queue And The Optimality Of The Watershed Approaches
 In Mathematical Morphology and its Applications to Image and Signal Processing
, 2000
"... This work reviews the watershed in the graph framework of a shortestpath forest problem using a lexicographic path cost formulation. This formulation reects the behavior of the ordered queuebased watershed algorithm. This algorithm is compared with our proposed shortestpath forest (IFT{Image Fore ..."
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Cited by 52 (23 self)
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This work reviews the watershed in the graph framework of a shortestpath forest problem using a lexicographic path cost formulation. This formulation reects the behavior of the ordered queuebased watershed algorithm. This algorithm is compared with our proposed shortestpath forest (IFT{Image Foresting Transform), concluding that the watershed is a special case of that. Recently many dierent watershed approaches are being used. We point out that in some cases the watershed algorithm does not keep the optimality of the shortestpath forest solution unless the IFT algorithm is used. The main dierence between the algorithms is related to permanently labeling a pixel when inserting or removing it from the queue. The watershed based on the pixel dissimilarity using IFT can segment onepixel width regions while keeping the optimality of the shortestpath forest solution.