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22
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 67 (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 ...
Geometric SpeedUp Techniques for Finding Shortest Paths in Large Sparse Graphs
, 2003
"... In this paper, we consider Dijkstra's algorithm for the single source single target shortest paths problem in large sparse graphs. The goal is to reduce the response time for online queries by using precomputed information. For the result of the preprocessing, we admit at most linear space. ..."
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Cited by 59 (15 self)
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In this paper, we consider Dijkstra's algorithm for the single source single target shortest paths problem in large sparse graphs. The goal is to reduce the response time for online queries by using precomputed information. For the result of the preprocessing, we admit at most linear space. We assume that a layout of the graph is given. From this layout, in the preprocessing, we determine for each edge a geometric object containing all nodes that can be reached on a shortest path starting with that edge. Based on these geometric objects, the search space for online computation can be reduced significantly. We present an extensive experimental study comparing the impact of different types of objects. The test data we use are traffic networks, the typical field of application for this scenario.
Finding fastest paths on a road network with speed patterns
 In Proc. Int. Conf. on Data Engineering (ICDE’06
, 2006
"... This paper proposes and solves the TimeInterval All Fastest Path (allFP) query. Given a userdefined leaving or arrival time interval I, a source node s and an end node e, allFP asks for a set of all fastest paths from s to e, one for each subinterval of I. Note that the query algorithm should fin ..."
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Cited by 45 (0 self)
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This paper proposes and solves the TimeInterval All Fastest Path (allFP) query. Given a userdefined leaving or arrival time interval I, a source node s and an end node e, allFP asks for a set of all fastest paths from s to e, one for each subinterval of I. Note that the query algorithm should find a partitioning of I into subintervals. Existing methods can only be used to solve a very special case of the problem, when the leaving time is a single time instant. A straightforward solution to the allFP query is to run existing methods many times, once for every time instant in I. This paper proposes a solution based on novel extensions to the A * algorithm. Instead of expanding the network many times, we expand once. The travel time on a path is kept as a function of leaving time. Methods to combine traveltime functions are provided to expand a path. A novel lowerbound estimator for travel time is proposed. Performance results reveal that our method is more efficient and more accurate than the discretetime approach. 1
Vehicle dispatching with timedependent travel times

, 2003
"... Most of the models for vehicle routing reported in the literature assume constant travel times. Clearly, ignoring the fact that the travel time between two locations does not depend only on the distance traveled, but on many other factors including the time of the day, impact the application of thes ..."
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Cited by 38 (1 self)
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Most of the models for vehicle routing reported in the literature assume constant travel times. Clearly, ignoring the fact that the travel time between two locations does not depend only on the distance traveled, but on many other factors including the time of the day, impact the application of these models to realworld problems. In this paper, we present a model based on timedependent travel speeds which satisfies the "firstinâfirstout" property. An experimental evaluation of the proposed model is performed in a static and a dynamic setting, using a parallel tabu search heuristic. It is shown that the timedependent model provides substantial improvements over a model based on fixed travel times.
Finding timedependent shortest paths over large graphs
 In Proc. EDBT
, 2008
"... The spatial and temporal databases have been studied widely and intensively over years. In this paper, we study how to answer queries of finding the best departure time that minimizes the total travel time from a place to another, over a road network, where the traffic conditions dynamically change ..."
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Cited by 35 (1 self)
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The spatial and temporal databases have been studied widely and intensively over years. In this paper, we study how to answer queries of finding the best departure time that minimizes the total travel time from a place to another, over a road network, where the traffic conditions dynamically change from time to time. We study a generalized form of this problem, called the timedependent shortestpath problem. A timedependent graph GT is a graph that has an edgedelay function, wi,j(t), associated with each edge (vi, vj), to be stored in a database. The edgedelay function wi,j(t) specifies how much time it takes to travel from node vi to node vj, if it departs from vi at time t. A userspecified query is to ask the minimumtraveltime path, from a source node, vs, to a destination node, ve, over the timedependent graph, GT, with the best departure time to be selected from a time interval T. We denote this user query as LTT(vs, ve, T) over GT. The challenge of this problem is the added complexity due to the time dependency in the timedependent graph. That is, edge delays are not constants, and can vary from time to time. In this paper, we propose a novel algorithm to find the minimumtraveltime path with the best departure time for a LTT(vs, ve, T) query over a large graph GT. Our approach outperforms existing algorithms in terms of both time complexity in theory and efficiency in practice. We will discuss the design of our algorithm, together with its correctness and complexity. We conducted extensive experimental studies over large graphs and will report our findings. 1.
Combining SpeedUp Techniques for ShortestPath Computations
 In Proc. 3rd Workshop on Experimental and Efficient Algorithms. LNCS
, 2004
"... Computing a shortest path from one node to another in a directed graph is a very common task in practice. This problem is classically solved by Dijkstra's algorithm. Many techniques are known to speed up this algorithm heuristically, while optimality of the solution can still be guaranteed. ..."
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Cited by 29 (7 self)
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Computing a shortest path from one node to another in a directed graph is a very common task in practice. This problem is classically solved by Dijkstra's algorithm. Many techniques are known to speed up this algorithm heuristically, while optimality of the solution can still be guaranteed. In most studies, such techniques are considered individually.
Lagrangian Relaxation and Enumeration for Solving Constrained
 ShortestPath Problems, Operations Research Department, Naval Postgraduate School
, 2003
"... Recently published research indicates that a vertexlabeling algorithm based on dynamicprogramming concepts is the most efficient procedure available for solving constrained shortestpath problems (CSPPs), i.e., shortestpath problems with one or more side constraints on the total “weight ” of the ..."
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Cited by 23 (6 self)
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Recently published research indicates that a vertexlabeling algorithm based on dynamicprogramming concepts is the most efficient procedure available for solving constrained shortestpath problems (CSPPs), i.e., shortestpath problems with one or more side constraints on the total “weight ” of the optimal path. However, we investigate an alternative procedure that Lagrangianises the side constraints, optimises the resulting Lagrangian function and then closes any duality gap through enumeration of nearshortest paths. These paths are measured with respect to Lagrangianmodified edge lengths, and “nearshortest ” implies ɛoptimal, with ɛ equal to the duality gap. Our recently developed procedure for enumerating nearshortestpaths leads to an algorithm for CSPP that, empirically, proves to be an order of magnitude faster than the most recent vertexlabeling algorithm. 1
FATES: Finding A Time dEpendent Shortest path
 In Proceedings of the 4th International Conference on Mobile Data Management
, 2003
"... Abstract. We model a moving object as a sizable physical entity equipped with GPS, wireless communication capability, and a computer. Based on a grid model, we develop a distributed system, FATES, to manage data for moving objects in a twodimensional space. The system is used to provide timedepend ..."
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Cited by 15 (0 self)
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Abstract. We model a moving object as a sizable physical entity equipped with GPS, wireless communication capability, and a computer. Based on a grid model, we develop a distributed system, FATES, to manage data for moving objects in a twodimensional space. The system is used to provide timedependent shortest paths for moving objects. The performance study shows that FATES yields shorter average trip time when there is a more congested route than any other routes in the domain space. 1
Dynamic Shortest Paths Containers
, 2004
"... Using a set of geometric containers to speed up shortest path queries in a weighted graph has been proven a useful tool for dealing with large sparse graphs. Given a layout of a graph G =(V,E), we store, for each edge (u, v) ∈ E, the bounding box of all nodes t ∈ V for which a shortest utpath sta ..."
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Cited by 9 (3 self)
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Using a set of geometric containers to speed up shortest path queries in a weighted graph has been proven a useful tool for dealing with large sparse graphs. Given a layout of a graph G =(V,E), we store, for each edge (u, v) ∈ E, the bounding box of all nodes t ∈ V for which a shortest utpath starts with (u, v). Shortest path queries can then be answered by Dijkstra’s algorithm restricted to edges where the corresponding bounding box contains the target. In this paper, we present new algorithms as well as an empirical study for the dynamic case of this problem, where edge weights are subject to change and the bounding boxes have to be updated. We evaluate the quality and the time for different update strategies that guarantee correct shortest paths in an interesting application to railway information systems, using realworld data from six European countries.
On the Complexity of TimeDependent Shortest Paths
"... We investigate the complexity of shortest paths in timedependent graphs, in which the costs of edges vary as a function of time, and as a result the shortest path between two nodes s and d can change over time. Our main result is that when the edge cost functions are (polynomialsize) piecewise line ..."
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Cited by 4 (0 self)
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We investigate the complexity of shortest paths in timedependent graphs, in which the costs of edges vary as a function of time, and as a result the shortest path between two nodes s and d can change over time. Our main result is that when the edge cost functions are (polynomialsize) piecewise linear, the shortest path from s to d can change Θ(log n) n times, settling a severalyearold conjecture of Dean [Technical Reports, 1999, 2004]. We also show that the complexity is polynomial if the slopes of the linear function come from a restricted class, present an outputsensitive algorithm for the general case, and describe a scheme for a (1 + ɛ)approximation of the travel time function in nearquadratic space. Finally, despite the fact that the arrival time function may have superpolynomial complexity, we show that a minimum delay path for any departure time interval can be computed in polynomial time. 1