Balancing Notions of Equity: Trade-offs Between Fair Portfolio Sizes and Achievable Guarantees

Swati Gupta, Jai Moondra, Mohit Singh

Abstract: Motivated by fairness concerns, we study existence and computation of portfolios, defined as: given an optimization problem with feasible solutions 𝓓, a class C of fairness objective functions, a set X ⊆ 𝓓 of feasible solutions is an α-approximate portfolio if for each objective f ⊆ C, there is an α-approximation for f in X. We study the trade-off between the size |X | of the portfolio and its approximation factor α for various combinatorial problems, such as scheduling, covering, and facility location, and choices of C as top-k, ordered and symmetric monotonic norms. Our results include: (i) an α-approximate portfolio of size for ordered norms and lower bounds of size for the problem of scheduling identical jobs on d unidentical machines, (ii) O (log n )-approximate O (log n )-sized portfolios for facility location on n points for symmetric monotonic norms, and (iii) logO (r2) d-size O (1)-approximate portfolios for ordered norms and O (log d )-approximate for symmetric monotonic norms for covering polyhedra with a constant r number of constraints. The latter result uses our novel OrderAndCount framework that obtains an exponential improvement in portfolio sizes compared to current state-of-the-art, which may be of independent interest.Acknowledgements. This work was supported by NSF Grants CCF-2106444, CCF-1910423, 2112533, NSF CAREER Grant 2239824, and the Georgia Tech ARC-ACO Fellowship.

External IDs:dblp:conf/soda/0001MS25