Linear-time algorithm for generating L-shaped floorplans using canonical ordering technique

Abstract

L-shaped floorplans are defined by rectangular modules enclosed within a rectilinear outer boundary, forming an L-shape that can not be altered through simple extension or contraction of a boundary wall. The boundary of such floorplans comprises five convex corners and one concave corner. The concave corner on the boundary of the plan can not be converted into a convex corner without altering the horizontal and vertical adjacency among the modules. This paper introduces a linear-time algorithm based on canonical ordering to generate L-shaped floorplans from properly triangulated plane graphs (PTPGs). Here, modules in the floorplan correspond to the nodes of the given graph, while edges in the graph represent wall adjacency between modules. The proposed algorithm assigns a unique labeling to the given graph, ensuring the presence of a concave corner on the resulting floorplan’s boundary. Simple boundary wall extensions or contractions cannot eliminate this concave corner. It also produces multiple L-shaped floorplans corresponding to the given PTPG, with variations mainly on their concave corners, highlighting the unique configurations possible within the same boundary constraints. Our algorithm offers simplicity over existing methods and is easy to implement. Additionally, we have implemented the algorithm in Python, enabling easy integration for generating L-shaped floorplans in various architectural and VLSI circuit design applications.