Marc Nunkesser

Constant-factor approximation for minimum-weight (connected) dominating sets in unit disk graphs

For a given graph with weighted vertices, the goal of the minimum-weight dominating set problem is to compute a vertex subset of smallest weight such that each vertex of the graph is contained in the subset or has a neighbor in the subset. A unit disk graph is a graph in which each vertex corresponds to a unit disk in the plane and two vertices are adjacent if and only if their disks have a non-empty intersection. We present the first constant-factor approximation algorithm for the minimum-weight dominating set problem in unit disk graphs, a problem motivated by applications in wireless ad-hoc networks. The algorithm is obtained in two steps: First, the problem is reduced to the problem of covering a set of points located in a small square using a minimum-weight set of unit disks. Then, a constant-factor approximation algorithm for the latter problem is obtained using enumeration and dynamic programming techniques exploiting the geometry of unit disks. Furthermore, we also show how to obtain a constant-factor approximation algorithm for the minimum-weight connected dominating set problem in unit disk graphs.

Multistage methods for freight train classification

In this article, we study the train classification problem. Train classification basically is the process of rearranging the cars of a train in a specified order, which can be regarded as a special sorting problem. This sorting is done in a special railway installation called a classification yard, and a classification process is described by a classification schedule. In this article, we develop a novel encoding of classification schedules, which allows characterizing train classification methods simply as classes of schedules. Applying this efficient encoding, we achieve a simpler, more precise analysis of well-known classification methods. Furthermore, we elaborate a valuable optimality condition inherent in our encoding, which we succesfully apply to obtain tight lower bounds for the length of schedules in general and to develop new classification methods. Finally, we present complexity results and algorithms to derive optimal schedules for several real-world settings. Together, our theoretical results provide a solid foundation for improving train classification in practice.

Efficient algorithms for the double traveling salesman problem with multiple stacks

In this paper we investigate theoretical properties of the Double Traveling Salesman Problem with Multiple Stacks. In particular, we provide polynomial time algorithms for different subproblems when the stack size limit is relaxed. Since these algorithms can represent building blocks for more complex methods, we also include them in a simple heuristic which we test experimentally. We finally analyze the impact of handling the stack size limit, and we propose repair procedures. The theoretical investigation highlights interesting structural properties of the problem, and our computational results show that the single components of the heuristic can be successfully incorporated in more complex algorithms or bounding techniques.

Mining Railway Delay Dependencies in Large-Scale Real-World Delay Data

The propagation of delays between trains has a considerable impact on railway operations. Ideally, planners would like to create timetables that avoid such propagation as much as possible. To improve existing timetables, tools for automatic detection of systematic dependencies of delays among trains would be of great aid. We present efficient algorithms to detect two of the most important types of dependencies, namely dependencies due to resource conflicts and due to maintained connections. We give experimental results on real-world data that demonstrate the practical applicability of our algorithms.

Optimizing the Cargo Express Service of Swiss Federal Railways

The Cargo Express service of Swiss Federal Railways (SBB Cargo) offers fast overnight transportation of goods between selected train stations in Switzerland and is operated as a hub-and-spoke system with two hubs. We present three different models for planning the operation of this service as a whole. All models capture the underlying optimization problem with a high level of detail: Traffic routing, train routing, makeup, scheduling, and locomotive assignment are all addressed. At the same time we respect hard constraints like tight service time windows and train capacities, and we avoid hub overloading. We describe our approaches for obtaining provably good quality solutions. Our algorithmic techniques involve branch-and-cut, branch-and-price, and problem-specific exact and heuristic acceleration methods. We conclude our study with computational results on realistic data.

Scheduling Additional Trains on Dense Corridors

Every train schedule entails a certain risk of delay. When adding a new train to an existing timetable, planners have to take the expected risk of delay of the trains into account. Typically, this can be a very laborious task involving detailed simulations. We propose to predict the risk of a planned train using a series of linear regression models on the basis of extensive real world delay data of trains. We show how to integrate these models into a combinatorial shortest path model to compute a set of Pareto optimal train schedules with respect to risk and travel time. We discuss the consequences of different model choices and notions of risk with respect to the algorithmic complexity of the resulting combinatorial problems. Finally, we demonstrate the quality of our models on real world data of Swiss Federal Railways.

An Algorithmic View on OVSF Code Assignment

The combinatorial core of the OVSF code assignment problem that arises in UMTS is to assign some nodes of a complete binary tree of height h (the code tree) to n simultaneous connections, such that no two assigned nodes (codes) are on the same root-to-leaf path. Each connection requires a code on a specified level. The code can change over time as long as it is still on the same level. We consider the one-step code assignment problem: Given an assignment, move the minimum number of codes to serve a new request. Minn and Siu proposed the so-called DCA-algorithm to solve the problem optimally. We show that DCA does not always return an optimal solution, and that the problem is NP-hard. We give an exact n O( h)-time algorithm, and a polynomial time greedy algorithm that achieves approximation ratio Θ(h). Finally, we consider the online code assignment problem for which we derive several results.

Joint base station scheduling

Consider a scenario where base stations need to send data to users with wireless devices. Time is discrete and slotted into synchronous rounds. Transmitting a data item from a base station to a user takes one round. A user can receive the data item from any of the base stations. The positions of the base stations and users are modeled as points in Euclidean space. If base station b transmits to user u in a certain round, no other user within distance at most ||b−u||2 from b can receive data in the same round due to interference phenomena. The goal is to minimize, given the positions of the base stations and users, the number of rounds until all users have their data. We call this problem the Joint Base Station Scheduling Problem (JBS) and consider it on the line (1D-JBS) and in the plane (2D-JBS). For 1D-JBS, we give a 2-approximation algorithm and polynomial optimal algorithms for special cases. We model transmissions from base stations to users as arrows (intervals with a distinguished endpoint) and show that their conflict graphs, which we call arrow graphs, are a subclass of the class of perfect graphs. For 2D-JBS, we prove NP-hardness and discuss an approximation algorithm.

Combinational Aspects of Move Up Crews

In railway planning, a frequent problem is that a delayed train necessarily delays its crew. To prevent delay propagation along the crew‘s succeeding trips, a move-up crew may take over the rest of the crew‘s duty on time. We address two problems in this context: First, during the planning stage, one has to make a tradeoff between robustness gained and additional costs incurred by introducing move-up crews. We suggest different heuristics to solve this problem, depending on the size of the instance. Second, during operations, dispatchers have to make optimal crew swap decisions, i.e., use available move-up crews to minimize overall passenger delay. For the local case, we give an efficient algorithm. However, optimizing crew swaps over the whole railway network is NP-hard