Fair Disaster Containment via Graph-Cut Problems
This work addresses fairness in algorithmic design for disaster containment, representing an incremental advance by applying existing fairness notions to a new combinatorial optimization context.
The paper tackles the problem of incorporating fairness into graph cut problems for disaster containment, introducing the first fair definitions and developing approximation algorithms with provable theoretical guarantees.
Graph cut problems are fundamental in Combinatorial Optimization, and are a central object of study in both theory and practice. Furthermore, the study of \emph{fairness} in Algorithmic Design and Machine Learning has recently received significant attention, with many different notions proposed and analyzed for 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 notions of fairness, namely \emph{demographic} and \emph{probabilistic individual} fairness, in a particular cut problem that models disaster containment scenarios. Our results include a variety of approximation algorithms with provable theoretical guarantees.