Local Search for Fair Max-Min Diversification
This study addresses the max-min diversification problem subject to partition constraints, aiming to maximize the diversity of selected points while strictly satisfying cardinality limits for each color class. By integrating local search techniques with parameterized algorithm design, the proposed approach handles combinatorial optimization and fairness constraints in metric spaces. This work presents the first constant-factor approximation algorithm for this problem, achieving a running time of f(m)·poly(n) while exactly satisfying all constraints in polynomial time. It overcomes limitations of prior methods that suffered from high approximation ratios, exponential time complexity, or merely expected constraint satisfaction. By unifying parameterized polynomial-time computation with constant approximation guarantees, the framework is further generalized to accommodate arbitrary upper- and lower-bound constraints on subset colors.