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Amy Babay, Michael Dinitz, Prathyush Sambaturu, Aravind Srinivasan, Leonidas Tsepenekas, Anil Vullikanti

Graph cut problems form a fundamental problem type in combinatorial optimization, and are a central object of study in both theory and practice. In addition, the study of fairness in Algorithmic Design and Machine Learning has recently received significant attention, with many different notions proposed and analyzed in a variety of contexts. In this paper we initiate the study of fairness for graph cut problems by giving the first fair definitions for them, and subsequently we demonstrate appropriate algorithmic techniques that yield a rigorous theoretical analysis. Specifically, we incorporate two different definitions of fairness, namely demographic and probabilistic individual fairness, in a particular cut problem modeling disaster containment scenarios. Our results include a variety of approximation algorithms with provable theoretical guarantees.

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Improving the explainability of the results from machine learning methods has become an important research goal. Here, we study the problem of making clusters more interpretable by extending a recent approach of [Davidson et al., NeurIPS 2018] for constructing succinct representations for clusters. Given a set of objects $S$, a partition $\pi$ of $S$ (into clusters), and a universe $T$ of tags such that each element in $S$ is associated with a subset of tags, the goal is to find a representative set of tags for each cluster such that those sets are pairwise-disjoint and the total size of all the representatives is minimized. Since this problem is NP-hard in general, we develop approximation algorithms with provable performance guarantees for the problem. We also show applications to explain clusters from datasets, including clusters of genomic sequences that represent different threat levels.

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