Christos D. Zaroliagis

Efficient models for timetable information in public transportation systems

We consider two approaches that model timetable information in public transportation systems as shortest-path problems in weighted graphs. In the time-expanded approach, every event at a station, e.g., the departure of a train, is modeled as a node in the graph, while in the time-dependent approach the graph contains only one node per station. Both approaches have been recently considered for (a simplified version of) the earliest arrival problem, but little is known about their relative performance. Thus far, there are only theoretical arguments in favor of the time-dependent approach. In this paper, we provide the first extensive experimental comparison of the two approaches. Using several real-world data sets, we evaluate the performance of the basic models and of several new extensions towards realistic modeling. Furthermore, new insights on solving bicriteria optimization problems in both models are presented. The time-expanded approach turns out to be more robust for modeling more complex scenarios, whereas the time-dependent approach shows a clearly better performance.

Robust and Online Large-Scale Optimization

Robustness and Recoverability: New Concepts.- The Concept of Recoverable Robustness, Linear Programming Recovery, and Railway Applications.- Recoverable Robustness in Shunting and Timetabling.- Light Robustness.- Incentive-Compatible Robust Line Planning.- A Bicriteria Approach for Robust Timetabling.- Robust Timetabling and Route Planning.- Meta-heuristic and Constraint-Based Approaches for Single-Line Railway Timetabling.- Engineering Time-Expanded Graphs for Faster Timetable Information.- Time-Dependent Route Planning.- The Exact Subgraph Recoverable Robust Shortest Path Problem.- Efficient Timetable Information in the Presence of Delays.- Robust Planning under Scarce Resources.- Integrating Robust Railway Network Design and Line Planning under Failures.- Effective Allocation of Fleet Frequencies by Reducing Intermediate Stops and Short Turning in Transit Systems.- Shunting for Dummies: An Introductory Algorithmic Survey.- Integrated Gate and Bus Assignment at Amsterdam Airport Schiphol.- Online Planning: Delay and Disruption Management.- Mining Railway Delay Dependencies in Large-Scale Real-World Delay Data.- Rescheduling Dense Train Traffic over Complex Station Interlocking Areas.- Online Train Disposition: To Wait or Not to Wait?.- Disruption Management in Passenger Railway Transportation.

Planar Spanners and Approximate Shortest Path Queries among Obstacles in the Plane

We consider the problem of finding an obstacle-avoiding path between two points s and t in the plane, amidst a set of disjoint polygonal obstacles with a total of n vertices. The length of this path should be within a small constant factor c of the length of the shortest possible obstacle-avoiding s-t path measured in the L p -metric. Such an approximate shortest path is called a c-short path, or a short path with stretch factor c. The goal is to preprocess the obstacle-scattered plane by creating an efficient data structure that enables fast reporting of a c-short path (or its length). In this paper, we give a family of algorithms for the above problem that achieve an interesting trade-off between the stretch factor, the query time and the preprocessing bounds. Our main results are algorithms that achieve logarithmic length query time, after subquadratic time and space preprocessing.

Using Multi-level Graphs for Timetable Information in Railway Systems

In many fields of application, shortest path finding problems in very large graphs arise. Scenarios where large numbers of on-line queries for shortest paths have to be processed in real-time appear for example in traffic information systems. In such systems, the techniques considered to speed up the shortest path computation are usually based on precomputed information. One approach proposed often in this context is a space reduction, where precomputed shortest paths are replaced by single edges with weight equal to the length of the corresponding shortest path. In this paper, we give a first systematic experimental study of such a space reduction approach. We introduce the concept of multi-level graph decomposition. For one specific application scenario from the field of timetable information in public transport, we perform a detailed analysis and experimental evaluation of shortest path computations based on multi-level graph decomposition.

Shortest paths in digraphs of small treewidth. Part I, Sequential algorithms

Abstract. We consider the problem of preprocessing an n -vertex digraph with real edge weights so that subsequent queries for the shortest path or distance between any two vertices can be efficiently answered. We give algorithms that depend on the treewidth of the input graph. When the treewidth is a constant, our algorithms can answer distance queries in O(α(n)) time after O(n) preprocessing. This improves upon previously known results for the same problem. We also give a dynamic algorithm which, after a change in an edge weight, updates the data structure in time O(nβ) , for any constant 0 < β < 1 . Furthermore, an algorithm of independent interest is given: computing a shortest path tree, or finding a negative cycle in linear time.

Geometric containers for efficient shortest-path computation

A fundamental approach in finding efficiently best routes or optimal itineraries in traffic information systems is to reduce the search space (part of graph visited) of the most commonly used shortest path routine (Dijkstras algorithm) on a suitably defined graph. We investigate reduction of the search space while simultaneously retaining data structures, created during a preprocessing phase, of size linear (i.e., optimal) to the size of the graph. We show that the search space of Dijkstras algorithm can be significantly reduced by extracting geometric information from a given layout of the graph and by encapsulating precomputed shortest-path information in resulted geometric objects (containers). We present an extensive experimental study comparing the impact of different types of geometric containers using test data from real-world traffic networks. We also 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 geometric containers have to be updated and show that our new methods are two to three times faster than recomputing everything from scratch. Finally, in an appendix, we discuss the software framework that we developed to realize the implementations of all of our variants of Dijkstras algorithm. Such a framework is not trivial to achieve as our goal was to maintain a common code base that is, at the same time, small, efficient, and flexible, as we wanted to enhance and combine several variants in any possible way.

Multiobjective Optimization: Improved FPTAS for Shortest Paths and Non-Linear Objectives with Applications

Abstract We provide an improved FPTAS for multiobjective shortest paths—a fundamental (NP-hard) problem in multiobjective optimization—along with a new generic method for obtaining FPTAS to any multiobjective optimization problem with non-linear objectives. We show how these results can be used to obtain better approximate solutions to three related problems, multiobjective constrained [optimal] path and non-additive shortest path, that have important applications in QoS routing and in traffic optimization. We also show how to obtain a FPTAS to a natural generalization of the weighted multicommodity flow problem with elastic demands and values that models several realistic scenarios in transportation and communication networks.

A Parallel Priority Queue with Constant Time Operations

We present a parallel priority queue that supports the following operations in constant time:parallel insertionof a sequence of elements ordered according to key,parallel decrease keyfor a sequence of elements ordered according to key,deletion of the minimum key element, anddeletion of an arbitrary element. Our data structure is the first to support multi-insertion and multi-decrease key in constant time. The priority queue can be implemented on the EREW PRAM and can perform any sequence ofnoperations inO(n) time andO(mlogn) work,mbeing the total number of keyes inserted and/or updated. A main application is a parallel implementation of Dijkstras algorithm for the single-source shortest path problem, which runs inO(n) time andO(mlogn) work on a CREW PRAM on graphs withnvertices andmedges. This is a logarithmic factor improvement in the running time compared with previous approaches.

Algorithmic Methods for Railway Optimization

We present an interactive application to assist planners in adding new trains on a complex railway network. It includes many trains with different characteristics, whose timetables cannot be modified because they are already in circulation. The application builds the timetable for new trains linking the available time slots to trains to be scheduled. A very flexible interface allows the user to specify the parameters of the problem. The resulting problem is formulated as a CSP and efficiently solved. The solving method carries out the search assigning values to variables in a given order verifying the satisfaction of constraints where these are involved. When a constraint is not satisfied, a guided backtracking is done. Finally, the resulting timetable is delivered to the user who can interact with it, guaranteeing the traffic constraint satisfaction.

An Experimental Study of Basic Communication Protocols in Ad-hoc Mobile Networks

We investigate basic communication protocols in ad-hoc mobile networks. We follow the semi-compulsory approach according to which a small part oft he mobile users, the support Σ, thatmoves in a predetermined way is used as an intermediate pool for receiving and delivering messages. Under this approach, we present a new semi-compulsory protocol called the runners in which the members of Σ perform concurrent and continuous random walks and exchange any information given to them by senders when they meet. We also conduct a comparative experimental study ofthe runners protocol with another existing semi-compulsory protocol, called the snake, in which the members of Σ move in a coordinated way and always remain pairwise adjacent. The experimental evaluation has been carried out in a new generic framework that we developed to implement protocols for mobile computing. Our experiments showed that for both protocols only a small support is required for efficient communication, and that the runners protocol outperforms the snake protocol in almost all types ofi nputs we considered.