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.
翻译:近年来,确保计算问题的公平性已成为一个“美元”专题,并受到公平资源分配和社会正义考虑的推动。从若干角度,例如利用优化、游戏理论或机器学习框架,有可能将公平性纳入计算问题之中。在本文件中,我们从“美元”的优化角度处理将公平性纳入考虑的问题。我们制定了一个组合优化框架,适合研究人员在近似算法和相关领域进行分析,将公平性纳入最大覆盖问题,作为2美元相互冲突的目标之间的相互作用。公平性通过使用彩色限制,将选定组合所涵盖不同颜色要素的数量之间的差异最小化,从而在覆盖范围中实现。这与文献中广泛研究的通常差异性差异性最小化问题形成对照,因为(通常两种)颜色是给美元,但需要选择,以最大限度地减少个人设定的美元的最大颜色差异。我们的主要结果是一组随机和确定性近似于公平性和覆盖面的估算值。