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35
Directed Hypergraphs And Applications
, 1992
"... We deal with directed hypergraphs as a tool to model and solve some classes of problems arising in Operations Research and in Computer Science. Concepts such as connectivity, paths and cuts are defined. An extension of the main duality results to a special class of hypergraphs is presented. Algorith ..."
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Cited by 100 (5 self)
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We deal with directed hypergraphs as a tool to model and solve some classes of problems arising in Operations Research and in Computer Science. Concepts such as connectivity, paths and cuts are defined. An extension of the main duality results to a special class of hypergraphs is presented. Algorithms to perform visits of hypergraphs and to find optimal paths are studied in detail. Some applications arising in propositional logic, AndOr graphs, relational data bases and transportation analysis are presented. January 1990 Revised, October 1992 ( * ) This research has been supported in part by the "Comitato Nazionale Scienza e Tecnologia dell'Informazione", National Research Council of Italy, under Grant n.89.00208.12, and in part by research grants from the National Research Council of Canada. 1 Dipartimento di Informatica, Università di Pisa, Italy 2 Département d'Informatique et de Recherche Opérationnelle, Université de Montréal, Canada 2 INTRODUCTION Hypergraphs, a generaliz...
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 ...
Adaptive leastexpected time paths in stochastic, timevarying transportation and data networks
 Networks
"... In congested transportation and data networks, travel (or transmission) times are timevarying quantities that are at best known a priori with uncertainty. In such stochastic, timevarying (or STV) networks, one can choose to use the a priori leastexpected time (LET) path or one can make improved r ..."
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Cited by 28 (0 self)
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In congested transportation and data networks, travel (or transmission) times are timevarying quantities that are at best known a priori with uncertainty. In such stochastic, timevarying (or STV) networks, one can choose to use the a priori leastexpected time (LET) path or one can make improved routing decisions en route as traversal times on traveled arcs are experienced and arrival times at intermediate locations are revealed. In this context, for a given origin–destination pair at a specific departure time, a single path may not provide an adequate solution, because the optimal path depends on intermediate information concerning experienced traversal times on traveled arcs. Thus, a set of strategies, referred to as hyperpaths, are generated to provide directions to the destination node conditioned upon arrival times at intermediate locations. In this paper, an efficient labelsettingbased algorithm is presented for determining the adaptive LET hyperpaths in STV networks. Such a procedure is useful in making critical routing decisions in Intelligent Transportation Systems (ITS) and data communication networks. A sidebyside comparison of this procedure with a labelcorrectingbased algorithm for solving the same problem is made. Results of extensive computational tests to assess and compare the performance of both algorithms, as well as to investigate the characteristics of the resulting hyperpaths, are presented. An illustrative example of both procedures is provided. © 2001 John Wiley & Sons, Inc.
The Optimal Path Problem
, 1999
"... : In this paper, the optimal path problem will be studied from a global point of view and having no restrictions imposed on the network. The concepts of boundness and finiteness will be presented for the general problem and will be studied in two particular cases. Special emphasis will be given to ..."
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Cited by 28 (3 self)
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: In this paper, the optimal path problem will be studied from a global point of view and having no restrictions imposed on the network. The concepts of boundness and finiteness will be presented for the general problem and will be studied in two particular cases. Special emphasis will be given to the optimality principle since it allows one to design a class of algorithms  the labelling algorithms  which determine an optimal path when the weak optimality principle is satisfied. Its importance will be stressed by two problems which, in its turn, are similar in their description and completly different in what concerns their resolution. Keywords: network, path, optimality principle, labelling algorithms. 1 Introduction In the optimal path problem, a real function is considered which assigns a value to each path that can be defined between a given pair of nodes in a given network; a path with the best value in a subset of paths between that pair of nodes is what has to be determin...
Deviation Algorithms For Ranking Shortest Paths
, 1999
"... The shortest path problem is a classical network problem that has been extensively studied. The problem of determining not only the shortest path, but also listing the K shortest paths (for a given integer K ? 1) is also a classical one but has not been studied so intensively, despite its obvious p ..."
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Cited by 17 (5 self)
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The shortest path problem is a classical network problem that has been extensively studied. The problem of determining not only the shortest path, but also listing the K shortest paths (for a given integer K ? 1) is also a classical one but has not been studied so intensively, despite its obvious practical interest. Two different types of problems are usually considered: the unconstrained and the constrained K shortest paths problem. While in the former no restriction is considered in the definition of a path, in the constrained K shortest paths problem all the paths have to satisfy some condition  for example, to be loopless. In this paper new algorithms are proposed for the unconstrained problem, which compute a super set of the K shortest paths. It is also shown that ranking loopless paths does not hold in general the Optimality Principle and how the proposed algorithms for the unconstrained problem can be adapted for ranking loopless paths. Keywords: Network, tree, path, path d...
Parallel asynchronous labelcorrecting methods for shortest paths
 Journal of Optimization Theory and Applications
, 1996
"... Abstract. In this paper we develop parallel asynchronous implementations of some known and some new label correcting methods for finding a shortest path from a single origin to all the other nodes of a directed graph. We compare these implementations on a shared memory multiprocessor, the Alliant FX ..."
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Cited by 16 (2 self)
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Abstract. In this paper we develop parallel asynchronous implementations of some known and some new label correcting methods for finding a shortest path from a single origin to all the other nodes of a directed graph. We compare these implementations on a shared memory multiprocessor, the Alliant FX/80, using several types of randomly generated problems. Excellent (sometimes superlinear) speedup is achieved with some of the methods, and it is found that the asynchronous versions of these methods are substantially faster than their synchronous counterparts.
Intelligent Route Finding: Combining Knowledge, Cases and An Efficient Search Algorithm
 In Proceedings of the 12th European Conference on Artificial Intelligence
, 1996
"... : One of the major road transportation problems is route finding. With the massive and complicated road network of a modern city (or country), finding a good route to travel from one place to another is not a simple task. In Network Theory, this is a shortest path problem. Shortest path algorithms a ..."
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Cited by 10 (0 self)
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: One of the major road transportation problems is route finding. With the massive and complicated road network of a modern city (or country), finding a good route to travel from one place to another is not a simple task. In Network Theory, this is a shortest path problem. Shortest path algorithms are often used to solve the problem. However, these algorithms are wasteful in terms of computation when applied to the route finding task. They may also produce routes that are not suitable for human drivers. Furthermore, finding a route only solves part of the route finding problem. Accepting user's feedback and learning from past experiences are also crucial to the success of a route finding system. In this paper, we present an integrated approach of using knowledge about the road network, past cases and an efficient search algorithm for route finding. This technique not only substantially reduces the time and space required in computation, but also produces humanoriented and personalized ...
Dual Algorithms for the Shortest Path Tree Problem
, 1997
"... We consider dual approaches for the Shortest Path Tree Problem. After a brief introduction to the problem, we review the most important dual algorithms which have been described in the literature for its solution, and propose a new family of dual ascent algorithms. In these algorithms, "local" an ..."
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Cited by 8 (3 self)
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We consider dual approaches for the Shortest Path Tree Problem. After a brief introduction to the problem, we review the most important dual algorithms which have been described in the literature for its solution, and propose a new family of dual ascent algorithms. In these algorithms, "local" and "global" dual updating operations are performed at the nodes in order to enlarge a partial shortest path tree, which at the beginning contains only the root node, until a shortest path tree is found. Several kinds of dual updating operations are proposed, which allow one to derive different dual algorithms from a general schema. One of them, in particular, which is based only on global operations, can be viewed as a dual interpretation of Dijkstra's classical algorithm. Due to their structure, all the proposed approaches are suitable for parallel implementations. They are also suitable for reoptimization approaches, when the computation of shortest paths from different root nodes i...