The Bipartite Boolean Quadric Polytope

Relaxations and Cutting Planes for Linear Programs with Complementarity Constraints

“…In fact, this special case of BQP corresponding to a complete bipartite graph is also called bipartite BQP, and its structural properties have been recently studied in [33]. Using this definition, by (27), we have the following relaxation for conv(S T ) : conv(S T ) ⊆ conv({(y y y, q q q, q q q, v v…”

“…The polyhedral structure of BQP for a series-parallel or an acyclic graph were studied originally by Padberg [28]. More recently, Sripratak et al [33] studied valid inequalities for BQP over a complete bipartite graph, which is particularly interesting for our setting and they coined it as bipartite boolean quadric polytope. In that paper, the authors proposed a few families of valid inequalities, e.g., odd-cycle inequalities, rounded clique inequalities, rounded cut inequalities, etc., among which odd-cycle inequalities are the only family of inequalities that can be facet-defining.…”

“…The last type of cuts we added comes from BQP 2|T |,n . As recently studied by Sripratak et al [33], a few families of valid inequalities have been proposed. However, the odd-cycle inequalities are the only inequalities that can be facetdefining for BQP 2|T |,n , while all the other inequalities therein, e.g., rounded clique inequalities, rounded cut inequalities are actually valid for the linear relaxation given by the McCormick constraints.…”