Maximizing Coverage While Ensuring Fairness: A Tale of Conflicting Objectives

Ensuring fairness in computational problems has emerged as a $key$ topic during recent years, buoyed by considerations for equitable resource distributions and social justice. It $is$ possible to incorporate from several perspectives, such using optimization, game-theoretic or machine learning frameworks. In this paper we address the problem of incorporation $combinatorial$ $optimization$ perspective. We formulate combinatorial optimization framework, suitable analysis researchers approximation algorithms related areas, that incorporates maximum coverage an interplay between $two$ conflicting objectives. Fairness is imposed coloring constraints $minimizes$ discrepancies number elements different colors covered selected sets; contrast usual discrepancy minimization studied extensively literature where (usually two) are $not$ given $a$ $priori$ but need be minimize color $each$ individual set. Our main results set randomized deterministic attempts $simultaneously$ approximate both framework.