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) can be modeled by CDCs admitting junction trees
and we also obtain MIP formulations of SOSk. 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