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41
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 19 (0 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.
Dynamic Shortest Paths Minimizing Travel Times and Costs
 Networks
, 2001
"... In this paper, we study dynamic shortest path problems, which is to determine a shortest path from a specified source node to every other node in the network where arc travel times change dynamically. We consider two problems: the minimum time walk problem (which is to find a walk with the minimum t ..."
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Cited by 18 (0 self)
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In this paper, we study dynamic shortest path problems, which is to determine a shortest path from a specified source node to every other node in the network where arc travel times change dynamically. We consider two problems: the minimum time walk problem (which is to find a walk with the minimum travel time) and the minimum cost walk problem (which is to find a walk with the minimum travel cost). The minimum time walk problem is known to be polynomially solvable for a class of networks called FIFO networks. This paper makes the following contributions: (i) we show that the minimum cost walk problem is an NPcomplete problem; (ii) we develop a pseudopolynomialtime algorithm to solve the minimum cost walk problem (for integer travel times); and (iii) we develop a polynomialtime algorithm for the minimum time walk problem arising in road networks with traffic lights.
Adaptive fastest path computation on a road network: A traffic mining approach
 In Proc. 2007 Int. Conf. on Very Large Data Bases (VLDB’07
, 2007
"... Efficient fastest path computation in the presence of varying speed conditions on a large scale road network is an essential problem in modern navigation systems. Factors affecting road speed, such as weather, time of day, and vehicle type, need to be considered in order to select fast routes that m ..."
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Cited by 18 (2 self)
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Efficient fastest path computation in the presence of varying speed conditions on a large scale road network is an essential problem in modern navigation systems. Factors affecting road speed, such as weather, time of day, and vehicle type, need to be considered in order to select fast routes that match current driving conditions. Most existing systems compute fastest paths based on road Euclidean distance and a small set of predefined road speeds. However, “History is often the best teacher”. Historical traffic data or driving patterns are often more useful than the simple Euclidean distancebased computation because people must have good reasons to choose these routes, e.g., they may want to avoid those that pass through high crime areas at night or that likely encounter accidents, road construction, or traffic jams. In this paper, we present an adaptive fastest path algorithm capable of efficiently accounting for important driving and speed patterns mined from a large set of traffic data. The algorithm is based on the following observations: (1) The hierarchy of roads can be used to partition the road network into areas, and different path precomputation strategies can be used at the area level, (2) we can limit our route search strategy to edges and path segments that are actually frequently traveled in the data, and (3) drivers usually traverse the road network through the largest roads available given the distance of the trip, except if there are small roads with a significant speed advantage over the large ones. Through an extensive experimental evaluation on real road networks we show that our algorithm provides desirable (short and wellsupported) routes, and that it is significantly faster than competing methods.
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 17 (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
Stochastic shortest paths via quasiconvex maximization
 PROCEEDINGS OF EUROPEAN SYMPOSIUM OF ALGORITHMS
, 2006
"... We consider the problem of finding shortest paths in a graph with independent randomly distributed edge lengths. Our goal is to maximize the probability that the path length does not exceed a given threshold value (deadline). We give a surprising exact n Θ(log n) algorithm for the case of normally ..."
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Cited by 15 (7 self)
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We consider the problem of finding shortest paths in a graph with independent randomly distributed edge lengths. Our goal is to maximize the probability that the path length does not exceed a given threshold value (deadline). We give a surprising exact n Θ(log n) algorithm for the case of normally distributed edge lengths, which is based on quasiconvex maximization. We then prove average and smoothed polynomial bounds for this algorithm, which also translate to average and smoothed bounds for the parametric shortest path problem, and extend to a more general nonconvex optimization setting. We also consider a number other edge length distributions, giving a range of exact and approximation schemes.
ContinuousTime Dynamic Shortest Path Algorithms
, 1999
"... We consider the problem of computing shortest paths through a dynamic network – a network with timevarying characteristics, such as arc travel times and costs, which are known for all values of time. Many types of networks, most notably transportation networks, exhibit such predictable dynamic beha ..."
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Cited by 13 (1 self)
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We consider the problem of computing shortest paths through a dynamic network – a network with timevarying characteristics, such as arc travel times and costs, which are known for all values of time. Many types of networks, most notably transportation networks, exhibit such predictable dynamic behavior over the course of time. Dynamic shortest path problems are currently solved in practice by algorithms which operate within a discretetime framework. In this thesis, we introduce a new set of algorithms for computing shortest paths in continuoustime dynamic networks, and demonstrate for the first time in the literature the feasibility and the advantages of solving dynamic shortest path problems in continuous time. We assume that all timedependent network data functions are given as piecewise linear functions of time, a representation capable of easily modeling most common dynamic problems. Additionally, this form of
A Directed Hypergraph Model for Random Time Dependent Shortest Paths
 EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
, 1998
"... We consider routing problems in dynamic networks where arc travel times are both random and time dependent. The problem of finding the best route to a fixed destination is formulated in terms of shortest hyperpaths on a suitable timeexpanded directed hypergraph. The latter problem can be solved in ..."
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Cited by 12 (5 self)
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We consider routing problems in dynamic networks where arc travel times are both random and time dependent. The problem of finding the best route to a fixed destination is formulated in terms of shortest hyperpaths on a suitable timeexpanded directed hypergraph. The latter problem can be solved in linear time, with respect to the size of the hypergraph, for several definitions of hyperpath length. Different criteria for ranking routes can be modeled by suitable definitions of hyperpath length. We also show that the problem becomes intractable if a constraint on the route structure is imposed.
Minimum Time and Minimum Cost Path Problems in Street Networks With Periodic Traffic Lights
"... This paper investigates minimum time and minimum cost path problems in street networks regulated by periodic traffic lights. We show that the minimum time path problem is polynomially solvable. On the other hand, minimum cost path problems are generally NPhard. Special, realistic, cases which are ..."
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Cited by 10 (1 self)
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This paper investigates minimum time and minimum cost path problems in street networks regulated by periodic traffic lights. We show that the minimum time path problem is polynomially solvable. On the other hand, minimum cost path problems are generally NPhard. Special, realistic, cases which are polynomially solvable are discussed. Dynamic shortest path problems often arise in transportation applications. Several models have been defined and analyzed depending on the properties of the travel time and of the cost functions (e.g., continuous or discrete), on the possibility of waiting at the nodes (e.g., no waiting, waiting at each node, waiting only at the origin nodes), on the presence of time windows associated with the nodes, etc. For more details about shortest path problems in dynamic transportation networks, see KIRBY and POTTS (1969); DESROSIERS, PELLETIER and SOUMIS (1983); ORDA<
A Concept of Communication Distance And Its Application to Six Situations in Mobile Environments
 IEEE Transactions on Mobile Computing
, 2005
"... Wireless networks combined with location technology create new problems and call for new decision aids. As a precursor to the development of these decision aids, a concept of communication distance is developed and applied to six situations. This concept allows travel time and bandwidth to be combin ..."
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Cited by 8 (3 self)
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Wireless networks combined with location technology create new problems and call for new decision aids. As a precursor to the development of these decision aids, a concept of communication distance is developed and applied to six situations. This concept allows travel time and bandwidth to be combined in a single measure so that many problems can be mapped onto a weighted graph and solved through shortest path algorithms. The paper looks at the problem of intercepting an outofcommunication team member and describes ways of using planning to reduce communication distance in anticipation of a break in connection. The concept is also applied to ad hoc radio networks. A way of performing route planning using a bandwidth map is developed and analyzed. The general implications of the work to transportation planning are discussed.