Optimization Techniques for Solving the Minimum Red--Blue Separating Set Problem with an Application to Human--AI Text Separation

arXiv cs.AINovember 2, 2026en

arXiv cs.AI

AI Global Wire

arXiv:2610.41081v1 Announce Type: new Abstract: We study the so-called Minimum Red''Blue Separating Set Problem (MRBSSP) which arises from computational geometry. In particular, we propose a compact Set-Cover ILP formulation, safe preprocessing rules, a Greedy Randomized Adaptive Search Procedure (GRASP), and two exact approaches: one is based on Logic-Based Benders Decomposition (LBBD) approach, and the second represents a novel Branch-and-Benders-Cut (BBC) approach. These two exact approaches are compared to ILP--alongside GRASP and the Variable Neighborhood Search (VNS) from literature. Experiments on 250 random graphs with up to 500 vertices reveal complementary strengths: ILP yields the

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