Maximizing coverage while ensuring fairness: a tale of conflicting objective

TL;DR

This paper introduces a combinatorial optimization framework that balances fairness and coverage in maximum coverage problems by using coloring constraints to minimize discrepancies among different groups, providing new approximation algorithms.

Contribution

It formulates a novel combinatorial framework for fairness in maximum coverage problems and develops approximation algorithms to balance fairness with coverage.

Findings

Developed randomized and deterministic approximation algorithms.

Framework effectively balances fairness and coverage objectives.

Addresses conflicting goals in combinatorial optimization.

Abstract

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