Maximizing coverage while ensuring fairness: a tale of conflicting objective
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Abolfazl Asudeh and Tanya Berger-Wolf and Bhaskar DasGupta and Anastasios Sidiropoulos
2020
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 combinatorialoptimization
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 apriori 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.
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