Wencheng Bao

Wencheng Bao, Eleftheria Kontou, Chrysafis Vogiatzis

We propose a betweenness centrality measure and algorithms for stochastic networks, where edges can fail and weights vary across realizations, making the most central node random. Our approach models the sequence of reported central nodes as an absorbing Markov chain and measures node importance by the share of pre-absorption time spent at each node. This produces a way to study centrality under uncertainty, which can then be estimated with Monte Carlo simulation. We also analyze robustness when the transition kernel is only approximately known, using row-wise perturbations to assess sensitivity and potential ranking changes. The framework further admits extensions to weighted rewards and restricted candidate sets without altering the Markov chain formulation. Experiments on Erdős-Rényi, Watts-Strogatz, and Les Misérables networks with stochastic edges show that the method identifies a small set of dominant nodes, reveals stable versus sensitive rankings under perturbations, and supports reward-based and structure-constrained variants.

Wencheng Bao, Shi Feng

Mainstream navigation software, like Google and Apple Maps, often lacks the ability to provide routes prioritizing safety. However, safety remains a paramount concern for many. Our aim is to strike a balance between safety and efficiency. To achieve this, we're devising an Integer Programming model that takes into account both the shortest path and the safest route. We will harness machine learning to derive safety coefficients, employing methodologies such as generalized linear models, linear regression, and recurrent neural networks. Our evaluation will be based on the Root Mean Square Error (RMSE) across various subway stations, helping us identify the most accurate model for safety coefficient estimation. Furthermore, we'll conduct a comprehensive review of different shortest-path algorithms, assessing them based on time complexity and real-world data to determine their appropriateness in merging both safety and time efficiency.