Leon Peeters

Algorithms for Centrality Indices

The usefulness of centrality indices stands or falls with the ability to compute them quickly. This is a problem at the heart of computer science, and much research is devoted to the design and analysis of efficient algorithms. For example, shortest-path computations are well understood, and these insights are easily applicable to all distance based centrality measures. This chapter is concerned with algorithms that efficiently compute the centrality indices of the previous chapters.

The computational complexity of delay management

Delay management for public transport consists of deciding whether vehicles should wait for delayed transferring passengers, with the objective of minimizing the overall passenger discomfort. This paper classifies the computational complexity of delay management problems with respect to various structural parameters, such as the maximum number of passenger transfers, the graph topology, and the capability of trains to reduce delays. Our focus is to distinguish between polynomially solvable and nP-complete problem variants. To that end, we show that even fairly restricted versions of the delay management problem are hard to solve.

Railway Delay Management: Exploring Its Algorithmic Complexity

We consider delay management in railway systems. Given delayed trains, we want to find a waiting policy for the connecting trains minimizing the weighted total passenger delay. If there is a single delayed train and passengers transfer at most twice along fixed routes, or if the railway network has a tree structure, the problem can be solved by reduction to min-cut problems. For delayed passenger flows on a railway network with a path structure, the problem can be solved to optimality by dynamic programming. If passengers are allowed to adapt their route to the waiting policy, the decision problem is strongly \(\mathcal{NP}\)-complete.

Online delay management on a single train line

We provide competitive analyses for the online delay management problem on a single train line. The passengers that want to connect to the train line might arrive delayed at the connecting stations, and these delays happen in an online setting. Our objective is to minimize the total passenger delay on the train line. We relate this problem to the Ski-Rental problem and present a family of 2-competitive online algorithms. Further, we show that no online algorithm for this problem can be better than Golden Ratio competitive, and that no online algorithm can be competitive if the objective accounts only for the optimizable passenger delay.

Online single machine batch scheduling

We are concerned with the problem of safely storing a history of actions that happen rapidly in real time, such as in “buy” and “sell” orders in stock exchange trading. This leads to a single-family scheduling problem with batching on a single machine, with a setup time and job release times, under batch availability. We investigate the objective of minimizing the total flow time in an online setting. On the positive side, we propose a 2-competitive algorithm for the case of identical job processing times, and we prove a lower bound that comes close. With general processing times, our lower bound shows that online algorithms are inevitably bad in the worst case.

Optimal placement of ad-hoc devices under a VCG-style routing protocol

Motivated by a routing protocol with VCG-style side payments, this paper investigates the combinatorial problem of placing new devices in an ad-hoc network such that the resulting shortest path distances are minimum. Here, distances reflect transmission costs that are quadratic in Euclidean distance. We show that the general problem of placing multiple new wireless devices, either with different or identical transmission ranges, is NP-hard under multiple communication requests. On the positive side, we provide polynomial-time algorithms for the cases with only one new device and/or one communication request. To that end, we define geometric objects that capture the general geometric structure of wireless networks.

Railway Delay Management

We consider delay management in railway systems. Given delayed trains, we want to find a waiting policy for the connecting trains minimizing the weighted total passenger delay. If there is a single delayed train and passengers transfer at most twice along fixed routes, or if the railway network has a tree structure, the problem can be solved by reduction to min-cut problems. For delayed passenger flows on a railway network with a path structure, the problem can be solved to optimality by dynamic programming. If passengers are allowed to adapt their route to the waiting policy, the decision problem is strongly NP-complete.