A graph theoretic approach for generating T-shaped floor plans

Abstract

A non-rectangular floor plan (NRFP) is one with a rectilinear exterior boundary containing rectangular modules. An NRFP is identified as a T-shaped floor plan if the rectilinear exterior boundary forms a T-shape with two concave corners. A T-shaped floor plan is further classified as aligned or non-aligned based on the alignment of its two concave corners. In this work, we aim to investigate graph-theoretic characteristics of properly triangulated plane graphs (PTPGs) for the existence of corresponding aligned and non-aligned T-shaped floor plans. Also, we provide an O(n3) algorithm for generating T-shaped floor plans (both aligned and non-aligned) for any PTPG with six or fewer corner-implying paths (CIPs), if they exist. Moreover, we claim that the resultant T-shaped floor plans are non-trivial. A T-shaped floor plan is considered non-trivial if the count of concave corners (two) at its exterior boundary can only be lowered by disrupting the modules' horizontal and vertical adjacencies.