Modeling Combinatorial Disjunctive Constraints via Junction Trees


We introduce techniques to build small ideal mixed-integer programming (MIP) formulations of combinatorial disjunctive constraints (CDCs) via the independent branching scheme. We present a novel pairwise IB-representable class of CDCs, CDCs admitting junction trees, and provide a combinatorial procedure to build MIP formulations for those constraints. Generalized special ordered sets (SOSk\text{SOS} k) can be modeled by CDCs admitting junction trees and we also obtain MIP formulations of SOSk\text{SOS} k. Furthermore, we provide a novel ideal extended formulation of any combinatorial disjunctive constraints with fewer auxiliary binary variables with an application in planar obstacle avoidance

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