The almost square rectangle packing problem involves packing all rectangles with sizes 1 × 2 to n × (n + 1) (almost squares) into an enclosing rectangle with minimal area. This extends the previously studied square packing problem by adding an additional degree of freedom for each rectangle, deciding in which orientation the item should be packed. We show how to extend the model and search stra...

In this paper we investigate separation problems for classes of inequalities valid for the polytope associated with the Steiner tree packing problem , a problem that arises, e. g., in VLSI routing. The separation problem for Steiner partition inequalities is NP-hard in general. We show that it can be solved in polynomial time for those instances that come up in switchbox routing. Our algorithm ...