Edges as Nodes - a New Approach to Timetable Information

In this paper we suggest a new approach to timetable information by introducing the ``edge-converted graph'' of a timetable. Using this model we present simple algorithms that solve the earliest arrival problem (EAP) and the minimum number of transfers problem (MNTP). For constant-degree graphs this yields linear-time algorithms for EAP and MNTP which improves upon the known \emph{Dijkstra}-based approaches. We also test the performance of our algorithms against the classical algorithms for EAP and MNTP in the time-expanded model

Generation of the transport service offer with application to timetable planning considering constraints due to maintenance work

Line planning is an important step in strategic timetable planning in public transport. In this step the transport offer for the customer is generated by the public transport operator, whereby the resulting costs for the operator should be as deep as possible. Mathematical models for line planning allow to create optimized line plans quickly. Planners can use these models to rate and select different alternatives. This is particularly valuable under the aspect of increasing maintenance and construction tasks of the railway infrastructure. We show, that in this case, it is possible to create functional requirements for automated timetable creation from the result of line planning step. The practical use of the involved models is illustrated by a real application example

Phase Synchronization in Railway Timetables

Timetable construction belongs to the most important optimization problems in public transport. Finding optimal or near-optimal timetables under the subsidiary conditions of minimizing travel times and other criteria is a targeted contribution to the functioning of public transport. In addition to efficiency (given, e.g., by minimal average travel times), a significant feature of a timetable is its robustness against delay propagation. Here we study the balance of efficiency and robustness in long-distance railway timetables (in particular the current long-distance railway timetable in Germany) from the perspective of synchronization, exploiting the fact that a major part of the trains run nearly periodically. We find that synchronization is highest at intermediate-sized stations. We argue that this synchronization perspective opens a new avenue towards an understanding of railway timetables by representing them as spatio-temporal phase patterns. Robustness and efficiency can then be viewed as properties of this phase pattern

Time-dependent stochastic shortest path(s) algorithms for a scheduled transportation network

Following on from our work concerning travellers’ preferences in public transportation networks (Wu and Hartley, 2004), we introduce the concept of stochasticity to our algorithms. Stochasticity greatly increases the complexity of the route finding problem, so greater algorithmic efficiency becomes imperative. Public transportation networks (buses, trains) have two important features: edges can only be traversed at certain points in time and the weights of these edges change in a day and have an uncertainty associated with them. These features determine that a public transportation network is a stochastic and time-dependent network. Finding multiple shortest paths in a both stochastic and time-dependent network is currently regarded as the most difficult task in the route finding problems (Loui, 1983). This paper discusses the use of k-shortest-paths (KSP) algorithms to find optimal route(s) through a network in which the edge weights are defined by probability distributions. A comprehensive review of shortest path(s) algorithms with probabilistic graphs was conducted

Combining Relational Algebra, SQL, Constraint Modelling, and Local Search

The goal of this paper is to provide a strong integration between constraint modelling and relational DBMSs. To this end we propose extensions of standard query languages such as relational algebra and SQL, by adding constraint modelling capabilities to them. In particular, we propose non-deterministic extensions of both languages, which are specially suited for combinatorial problems. Non-determinism is introduced by means of a guessing operator, which declares a set of relations to have an arbitrary extension. This new operator results in languages with higher expressive power, able to express all problems in the complexity class NP. Some syntactical restrictions which make data complexity polynomial are shown. The effectiveness of both extensions is demonstrated by means of several examples. The current implementation, written in Java using local search techniques, is described. To appear in Theory and Practice of Logic Programming (TPLP)Comment: 30 pages, 5 figure

Trip-Based Public Transit Routing Using Condensed Search Trees

We study the problem of planning Pareto-optimal journeys in public transit networks. Most existing algorithms and speed-up techniques work by computing subjourneys to intermediary stops until the destination is reached. In contrast, the trip-based model focuses on trips and transfers between them, constructing journeys as a sequence of trips. In this paper, we develop a speed-up technique for this model inspired by principles behind existing state-of-the-art speed-up techniques, Transfer Pattern and Hub Labelling. The resulting algorithm allows us to compute Pareto-optimal (with respect to arrival time and number of transfers) 24-hour profiles on very large real-world networks in less than half a millisecond. Compared to the current state of the art for bicriteria queries on public transit networks, this is up to two orders of magnitude faster, while increasing preprocessing overhead by at most one order of magnitude

Trip-Based Public Transit Routing

We study the problem of computing all Pareto-optimal journeys in a public transit network regarding the two criteria of arrival time and number of transfers taken. We take a novel approach, focusing on trips and transfers between them, allowing fine-grained modeling. Our experiments on the metropolitan network of London show that the algorithm computes full 24-hour profiles in 70 ms after a preprocessing phase of 30 s, allowing fast queries in dynamic scenarios.Comment: Minor corrections, no substantial changes. To be presented at ESA 201

Multi-Paradigm Reasoning for Access to Heterogeneous GIS

Accessing and querying geographical data in a uniform way has become easier in recent years. Emerging standards like WFS turn the web into a geospatial web services enabled place. Mediation architectures like VirGIS overcome syntactical and semantical heterogeneity between several distributed sources. On mobile devices, however, this kind of solution is not suitable, due to limitations, mostly regarding bandwidth, computation power, and available storage space. The aim of this paper is to present a solution for providing powerful reasoning mechanisms accessible from mobile applications and involving data from several heterogeneous sources. By adapting contents to time and location, mobile web information systems can not only increase the value and suitability of the service itself, but can substantially reduce the amount of data delivered to users. Because many problems pertain to infrastructures and transportation in general and to way finding in particular, one cornerstone of the architecture is higher level reasoning on graph networks with the Multi-Paradigm Location Language MPLL. A mediation architecture is used as a “graph provider” in order to transfer the load of computation to the best suited component – graph construction and transformation for example being heavy on resources. Reasoning in general can be conducted either near the “source” or near the end user, depending on the specific use case. The concepts underlying the proposal described in this paper are illustrated by a typical and concrete scenario for web applications

Deriving query suggestions for site search

Modern search engines have been moving away from simplistic interfaces that aimed at satisfying a user's need with a single-shot query. Interactive features are now integral parts of web search engines. However, generating good query modification suggestions remains a challenging issue. Query log analysis is one of the major strands of work in this direction. Although much research has been performed on query logs collected on the web as a whole, query log analysis to enhance search on smaller and more focused collections has attracted less attention, despite its increasing practical importance. In this article, we report on a systematic study of different query modification methods applied to a substantial query log collected on a local website that already uses an interactive search engine. We conducted experiments in which we asked users to assess the relevance of potential query modification suggestions that have been constructed using a range of log analysis methods and different baseline approaches. The experimental results demonstrate the usefulness of log analysis to extract query modification suggestions. Furthermore, our experiments demonstrate that a more fine-grained approach than grouping search requests into sessions allows for extraction of better refinement terms from query log files. © 2013 ASIS&T