Shortest Paths in Time-Dependent FIFO Networks

Dehne, Frank; Omran, Masoud T.; Sack, Jörg-Rüdiger

doi:10.1007/s00453-010-9461-6

Cited by 36 publications

(27 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Such queries can be dealt with by range searches, which compute the travel time function between two points. There exist Dijkstra-based algorithms [71] for this problem, and most speedup techniques can be adapted to deal with this as well [32,72].…”

Section: Time-dependencementioning

confidence: 99%

Route Planning in Transportation Networks

Bast

Delling

Goldberg

et al. 2016

Lecture Notes in Computer Science

463

388

View full text Add to dashboard Cite

We survey recent advances in algorithms for route planning in transportation networks. For road networks, we show that one can compute driving directions in milliseconds or less even at continental scale. A variety of techniques provide different trade-offs between preprocessing effort, space requirements, and query time. Some algorithms can answer queries in a fraction of a microsecond, while others can deal efficiently with real-time traffic. Journey planning on public transportation systems, although conceptually similar, is a significantly harder problem due to its inherent time-dependent and multicriteria nature. Although exact algorithms are fast enough for interactive queries on metropolitan transit systems, dealing with continent-sized instances requires simplifications or heavy preprocessing. The multimodal route planning problem, which seeks journeys combining schedule-based transportation (buses, trains) with unrestricted modes (walking, driving), is even harder, relying on approximate solutions even for metropolitan inputs. *

show abstract

Section: Time-dependencementioning

confidence: 99%

Route Planning in Transportation Networks

Bast

Delling

Goldberg

et al. 2016

Lecture Notes in Computer Science

463

388

View full text Add to dashboard Cite

show abstract

“…In [48], it has been shown that within the same time complexity, for a given start time at s, not only the minimum travel time to d can be computed, but it is also possible to obtain the slope of the function at that time. This can be used in Algorithm Aprx-B as a heuristic improvement to reduce the number of computations by using the function tangent rather than lines connecting consecutive sample points.…”

Section: Discussionmentioning

confidence: 99%

“…We study two variants of the problem [47,48]. First, we consider networks in which the availability of links, changes over time.…”

Section: Problemsmentioning

confidence: 99%

“…Our new algorithm [47,48] is based on the idea that instead of building all earliest arrival time functions to all nodes in the network, we calculate only the earliest arrival time function to destination node d. An outline of our method is given in algorithm A lin . In the remainder, we discuss our method in more detail.…”

Section: A New Algorithm For Instances With Polynomial Size Outputmentioning

confidence: 99%

“…Dehne et al proposed an exact output-sensitive algorithm for this problem [47,48] that, in most cases, improves upon existing algorithms. They also provide an approximation algorithm.…”

Section: Time-dependent Shortest Pathsmentioning

confidence: 99%

See 2 more Smart Citations

Path Problems in Geographic Information Systems

Omran¹

View full text Add to dashboard Cite

Path problems are among the most widely studied problems in graph theory. Various versions of the problem with distinct real world applications have been proposed and studied (Shortest Path, Longest Path, Hamiltonian Path, Traveling Salesperson Problem, among others). The shortest path problem for a network (or directed graph) is a fundamental problem in graph theory with applications related to Navigation/Transportation Systems, Computer Networks, VLSI Design, Social Networks, and many other networks. Unlike in well-studied conventional static shortest path problems, the characteristics of underlying networks may change over time in many real-world applications. An efficient solution to the Shortest Path problem, should therefore take the dynamics of the underlying graph into consideration. In this thesis, we study a dynamic version of the Shortest Path Problem in which travel times on links of the underlying graph change over time, and present improved and easily implemented exact and approximation algorithms.With theoretical improvements in time-dependent shortest path computation and technical advancements in the provision of real-time traffic data, many travelers these days use and rely on navigation systems and time-dependent shortest path computation in their everyday lives. For example, GoogleMaps provides advice on best routes by using current traffic conditions and historical route data to keep users out of traffic jams. This may, however, compromise users' privacy since untrusted Location Based Services (LBS) are able to use inference attacks to gain access to sensitive information about users, such as their driving habits, health conditions they may have, their sexual orientation, or details about their lifestyle. In this dissertation, we propose a heuristic algorithm that protects the privacy of users who submit frequent location based queries to a Location Based Service.Although, shortest paths are preferred in most applications related to navigation and transportation, they can easily be inferred and regenerated, and should therefore be avoided in applications where user security is paramount. For example, a traveling VIP is more concerned about the security of her path rather than its length. We study the traveling VIP problem in which the goal is to randomly select a path from k candidate source-destination paths. When links are shared between many paths security is compromised and security guards may have to be placed on such links. The number of shared edges, then, should be minimized to reduce the costs associated with security guards who must be assigned to each shared link. We show that this problem is hard to approximate, and propose an approximation algorithm which has been experimentally evaluated on various networks.

show abstract

Time‐dependent shortest paths with discounted waits

Omer

Poss

2019

Networks

View full text Add to dashboard Cite

We study a variant of the shortest path problem in a congested environment. In this setting, the travel time of each arc is represented by a piecewise continuous affine function of departure time. Besides, the driver is allowed to wait at nodes to avoid wasting time in traffic. While waiting, the driver is able to perform useful tasks for her job or herself, so the objective is to minimize only driving time. Although optimal solutions may contain cycles and pseudo‐polynomially many arcs, we provide a representation of the solutions that is polynomial in the absolute value of the inverse of the slopes as well as in the dimensions of the graph. We further prove that the problem is NP‐Hard when the slopes are integer. We introduce a restriction of the problem where waits must be integer and propose pseudo‐polynomial algorithms for the latter. We also provide a pseudo‐FPTAS, polynomial in the ratio between the bound on the total waiting time and the minimum travel time. Finally, we discuss harder variants of the problem and show their inapproximability.

show abstract

Shortest Paths in Time-Dependent FIFO Networks

Cited by 36 publications

References 20 publications

Route Planning in Transportation Networks

Route Planning in Transportation Networks

Path Problems in Geographic Information Systems

Time‐dependent shortest paths with discounted waits

Contact Info

Product

Resources

About