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Graph cut problems are fundamental in combinatorial optimization, and are a central object of study in both theory and practice. Further, the study of 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 demographic and 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.
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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 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.
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- PAR ID:
- 10384608
- Date Published:
- Journal Name:
- Algorithmica
- ISSN:
- 0178-4617
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s00453-022-01072-1
