Optimal slicing of plane point placements

Abstract

An algorithm for finding an optimal floor plan among all slicing structures consistent with a given plane point placement is presented. Here, consistent means that each slice corresponds with a rectangular subset of the point placement and that its child slices are ordered according to the coordinates on the associated axis. An optimal floor plan among these slicing structures is one that minimizes an object function, while satisfying the shape constraints of all blocks represented by the points. The object function must be a non-decreasing function of the height and the width of the floor plan. Area is just one such function. The algorithm is proven to be of polynomial time complexity in case all shape constraints are integer stair case functions.