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Shortest Paths in TimeDependent FIFO Networks Using Edge Load Forecasts
, 2009
"... We study the problem of finding shortest paths in timedependent networks with edge load forecasts where the behavior of each edge is modeled as a timedependent arrival function with FIFO property. Here, we present a new algorithm that computes for a given start node s and destination node d, the sh ..."
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We study the problem of finding shortest paths in timedependent networks with edge load forecasts where the behavior of each edge is modeled as a timedependent arrival function with FIFO property. Here, we present a new algorithm that computes for a given start node s and destination node d, the shortest paths and earliest arrival times for all possible starting times. Our algorithm runs in time O((Fd + λ)(E  + V log V )) where Fd is the output size (number of linear pieces needed to represent the earliest arrival time function) and λ is the input size (number of linear pieces needed to represent the local earliest arrival time functions for all edges in the network). Our method improves significantly on the best previously known algorithm which requires time O(FmaxV E) where Fmax ≥ Fd is the maximum number of linear pieces needed to represent the earliest arrival time function between the start node s to any node in the network. It has been conjectured that there are cases where Fmax is of superpolynomial size; however, even in such cases, Fd might still be of linear size. In such cases, our algorithm would take polynomial time to find the solution, while other methods require superpolynomial time. Both of the above methods are not useful in practice for graphs where Fd is of superpolynomial size. For such graphs, we present the first approximation method to compute for all possible starting times at s, the earliest arrival times at d within error at most ǫ. Our algorithm runs in time O ( ∆ (E  + V log V )) where ∆ is the difference beǫ tween the earliest arrival times at d for the latest and earliest starting times at s.
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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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
Energyoptimal routes for electric vehicles
 In Proceedings of the 21st ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, SIGSPATIAL’13
, 2013
"... Abstract. We study the problem of electric vehicle route planning, where an important aspect is computing paths that minimize energy consumption. Thereby, any method must cope with specific properties, such as recuperation, battery constraints (over and undercharging), and frequently changing cost ..."
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Abstract. We study the problem of electric vehicle route planning, where an important aspect is computing paths that minimize energy consumption. Thereby, any method must cope with specific properties, such as recuperation, battery constraints (over and undercharging), and frequently changing cost functions (e. g., due to weather conditions). This work presents a practical algorithm that quickly computes energyoptimal routes for networks of continental scale. Exploiting multilevel overlay graphs [26, 31], we extend the Customizable Route Planning approach [8] to our scenario in a sound manner. This includes the efficient computation of profile queries and the adaption of bidirectional search to battery constraints. Our experimental study uses detailed consumption data measured from a production vehicle (Peugeot iOn). It reveals for the network of Europe that a new cost function can be incorporated in about five seconds, after which we answer random queries within 0.3ms on average. Additional evaluation on an artificial but realistic [22, 36] vehicle model with unlimited range demonstrates the excellent scalability of our algorithm: Even for longrange queries across Europe it achieves query times below 5ms on average—fast enough for interactive applications. Altogether, our algorithm exhibits faster query times than previous approaches, while improving (metricdependent) preprocessing time by three orders of magnitude. 1
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"... A model for solving the dynamic vehicle dispatching problem with customer uncertainty and time dependent link travel time Un modelo para resolver el problema dinámico de despacho de vehículos con incertidumbre de clientes y con tiempos de viaje en arcos ..."
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A model for solving the dynamic vehicle dispatching problem with customer uncertainty and time dependent link travel time Un modelo para resolver el problema dinámico de despacho de vehículos con incertidumbre de clientes y con tiempos de viaje en arcos
© IDOSI Publications, 2008 New Method for Finding Optimal Path in Dynamic Networks
"... Abstract: Nowadays, urban traffic congestion is a complicated and ubiquitous problem. Continuous changes of traffic congestion with respect to the time lead to change the travel times of transportation network. These changes show the importance of time in transportation analyses in addition to the l ..."
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Abstract: Nowadays, urban traffic congestion is a complicated and ubiquitous problem. Continuous changes of traffic congestion with respect to the time lead to change the travel times of transportation network. These changes show the importance of time in transportation analyses in addition to the location. So determining the optimal path in a timedependent transportation network is a challenging task.This article proposes the spatial analysis of finding the optimal path between two specific locations in a network that its traffic congestion changes continuously. Conventional algorithms are analyzed, and their features and constraints are evaluated. Then, a new method based on the partitioning spacetime is presented. In the proposed method, some heuristic functions which are extracted from graph features have been used to guide the solution in each partition. Finally, a business model for collecting traffic data is introduced. Using this model could help the traffic managers to have realtime traffic data in different times and locations. Also, it could help the users to obtain the best route in their urban trips using GIS analyses like finding the optimal path.
Distance Oracles for TimeDependent Networks
"... Abstract. We present the first approximate distance oracle for sparse directed networks with timedependent arctraveltimes determined by continuous, piecewise linear, positive functions possessing the FIFO property. Our approach precomputes (1 + ε)−approximate distance summaries from selected la ..."
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Abstract. We present the first approximate distance oracle for sparse directed networks with timedependent arctraveltimes determined by continuous, piecewise linear, positive functions possessing the FIFO property. Our approach precomputes (1 + ε)−approximate distance summaries from selected landmark vertices to all other vertices in the network, and provides two sublineartime query algorithms that deliver constant and (1+σ)−approximate shortesttraveltimes, respectively, for arbitrary origindestination pairs in the network. Our oracle is based only on the sparsity of the network, along with two quite natural assumptions about traveltime functions which allow the smooth transition towards asymmetric and timedependent distance metrics. 1
Snapshot Centrality Indices in Dynamic FIFO Networks
 J MATH MODEL ALGOR
, 2011
"... The article introduces the concept of snapshot dynamic indices as centrality measures to analyse how the importance of nodes changes over time in dynamic networks. In particular, the dynamic stresssnapshot and dynamic betweenness snapshot are investigated. We present theoretical results on dynamic ..."
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The article introduces the concept of snapshot dynamic indices as centrality measures to analyse how the importance of nodes changes over time in dynamic networks. In particular, the dynamic stresssnapshot and dynamic betweenness snapshot are investigated. We present theoretical results on dynamic shortest paths in firstin firstout dynamic networks, and then introduce some algorithms for computing these indices in the discretetime case. Finally, we present some experimental results exploring the algorithms’ efficiency and illustrating the variation of the dynamic betweenness snapshot index for some sample dynamic networks.
Shortest Paths and Probabilities on TimeDependent Graphs Applications to Transport Networks
, 2012
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
A Landmark Algorithm for the Timedependent . . .
, 2008
"... The shortest path problem is one of the most classical problem in combinatorial optimization problem which, given an edgeweighted graph and two vertices, asks to find a path between the two vertices of the minimum length. In this thesis, we consider a generalization of the shortest path problem in ..."
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The shortest path problem is one of the most classical problem in combinatorial optimization problem which, given an edgeweighted graph and two vertices, asks to find a path between the two vertices of the minimum length. In this thesis, we consider a generalization of the shortest path problem in which the edge length is timevariable, which we call the timedependent shortest path problem. This kind