Area minimization in a three-sided switchbox by sliding the modules

An optimal algorithm for minimizing the number of columns (width) in a three-sided switchbox, when the modules are allowed to slide, is presented. The proposed algorithm runs in O(mn+e log e) time, where m and n are the number of terminals on the top and on the bottom, and e is the total number of feasible alignments (e⩽mn). The movable-module model considered is a generalization, and a realistic version, of the (previously studied) movable-terminal model