Fair Railway Network Design

When designing a public transportation network in a country, one may want to minimise the sum of travel duration of all inhabitants. This corresponds to a purely utilitarian view and does not involve any fairness consideration, as the resulting network will typically benefit the capital city and/or large central cities while leaving some peripheral cities behind. On the other hand, a more egalitarian view will allow some people to travel between peripheral cities without having to go through a central city. We define a model, propose algorithms for computing solution networks, and report on experiments based on real data.

Scaling up graph homomorphism for classification via sampling

Feature generation is an open topic of investigation in graph machine learning. In this paper, we study the use of graph homomorphism density features as a scalable alternative to homomorphism numbers which retain similar theoretical properties and ability to take into account inductive bias. For this, we propose a high-performance implementation of a simple sampling algorithm which computes additive approximations of homomorphism densities. In the context of graph machine learning, we demonstrate in experiments that simple linear models trained on sample homomorphism densities can achieve performance comparable to graph neural networks on standard graph classification datasets. Finally, we show in experiments on synthetic data that this algorithm scales to very large graphs when implemented with Bloom filters.

The shortest way to visit all metro lines in a city

What if $\{$a tourist, a train addict, Dr. Sheldon Cooper, somebody who likes to waste time$\}$ wants to visit all metro lines or carriages in a given network in a minimum number of steps? We study this problem with an application to the metro network of Paris and Tokyo, proposing optimal solutions thanks to mathematical programming tools. Quite surprisingly, it appears that you can visit all 16 Parisian metro lines in only 26 steps (we denote by a step the act of taking the metro from one station to an adjacent one). Perhaps even more surprisingly, adding the 5 RER lines to these 16 lines does not increase the size of the best solution. It is also possible to visit the 13 lines of (the dense network of) Tokyo with only 15 steps.