On tackling reverse convex constraints for non-overlapping of unequal circles

We study the unequal circle-circle non-overlapping constraints, a form of reverse convex constraints that often arise in optimization models for cutting and packing applications. The feasible region induced by the intersection of circle-circle non-overlapping constraints is highly non-convex, and standard approaches to construct convex relaxations for spatial branch-and-bound global optimization of such models typically yield … Read more

A simple branching scheme for Vertex Coloring Problems

We present a branching scheme for some Vertex Coloring Problems based on a new graph operator called extension. The extension operator is used to generalize the branching scheme proposed by Zykov for the basic problem to a broad class of coloring problems, such as the graph multicoloring, where each vertex requires a multiplicity of colors, … Read more