Ben Bals

Ben Bals, Joakim Blikstad, Greg Bodwin et al.

For many popular graph metric sparsifiers, such as spanners, emulators, and preservers, simple and elegant greedy algorithms are known that achieve state-of-the-art or existentially optimal tradeoffs between size and quality. The goal of this paper is to develop and analyze comparable greedy algorithms for nearby objects in graph metric augmentation. We show the following: - A simple greedy algorithm for shortcut sets achieves the state-of-the-art size/hopbound tradeoff recently proved by Kogan and Parter (2022), up to $O(\log n)$ factors in the size. Moreover, with an additional preprocessing step, the greedy algorithm subpolynomially improves on the previous size bounds in some range of parameters. - The same greedy algorithm was already known to be existentially optimal for the size/hopbound tradeoff for hopsets, by an analysis of Berman, Raskhodnikova, and Ruan (2010) introduced for transitive-closure spanners. We provide a completely different analysis showing that the algorithm is also existentially optimal (up to $O(\log n)$ factors) for the matching hopset problem, in which one has a budget of roughly $O(m)$ additional edges (for an $m$-edge input graph).

Sebastian Angrick, Ben Bals, Niko Hastrich et al.

Human lives are increasingly influenced by algorithms, which therefore need to meet higher standards not only in accuracy but also with respect to explainability. This is especially true for high-stakes areas such as real estate valuation. Unfortunately, the methods applied there often exhibit a trade-off between accuracy and explainability. One explainable approach is case-based reasoning (CBR), where each decision is supported by specific previous cases. However, such methods can be wanting in accuracy. The unexplainable machine learning approaches are often observed to provide higher accuracy but are not scrutable in their decision-making. In this paper, we apply evolutionary algorithms (EAs) to CBR predictors in order to improve their performance. In particular, we deploy EAs to the similarity functions (used in CBR to find comparable cases), which are fitted to the data set at hand. As a consequence, we achieve higher accuracy than state-of-the-art deep neural networks (DNNs), while keeping interpretability and explainability. These results stem from our empirical evaluation on a large data set of real estate offers where we compare known similarity functions, their EA-improved counterparts, and DNNs. Surprisingly, DNNs are only on par with standard CBR techniques. However, using EA-learned similarity functions does yield an improved performance.