TY - JOUR AU - Agarwal, Pankaj K. AU - Ko, Shao-Heng AU - Munagala, Kamesh AU - Taylor, Erin PY - 2022/06/28 Y2 - 2024/03/28 TI - Locally Fair Partitioning JF - Proceedings of the AAAI Conference on Artificial Intelligence JA - AAAI VL - 36 IS - 5 SE - AAAI Technical Track on Game Theory and Economic Paradigms DO - 10.1609/aaai.v36i5.20401 UR - https://ojs.aaai.org/index.php/AAAI/article/view/20401 SP - 4752-4759 AB - We model the societal task of redistricting political districts as a partitioning problem: Given a set of n points in the plane, each belonging to one of two parties, and a parameter k, our goal is to compute a partition P of the plane into regions so that each region contains roughly s = n/k points. P should satisfy a notion of "local" fairness, which is related to the notion of core, a well-studied concept in cooperative game theory. A region is associated with the majority party in that region, and a point is unhappy in P if it belongs to the minority party. A group D of roughly s contiguous points is called a deviating group with respect to P if majority of points in D are unhappy in P. The partition P is locally fair if there is no deviating group with respect to P.This paper focuses on a restricted case when points lie in 1D. The problem is non-trivial even in this case. We consider both adversarial and "beyond worst-case" settings for this problem. For the former, we characterize the input parameters for which a locally fair partition always exists; we also show that a locally fair partition may not exist for certain parameters. We then consider input models where there are "runs" of red and blue points. For such clustered inputs, we show that a locally fair partition may not exist for certain values of s, but an approximate locally fair partition exists if we allow some regions to have smaller sizes. We finally present a polynomial-time algorithm for computing a locally fair partition if one exists. ER -