Linear-time construction of floor plans for plane triangulations

This paper focuses on a novel approach for producing a floor plan (FP), either a rectangular (RFP) or an orthogonal (OFP) based on the concept of orthogo nal drawings, which satisfies the adjacency relations given by any bi-connected plane triangulation G. Previous algorithms for constructing a FP are primarily restricted to the cases given below: (i) A bi-connected plane triangulation without separating triangles (STs) and with at most 4 corner implying paths (CIPs), known as properly triangulated planar graph (PTPG). (ii) A bi-connected plane triangulation with an exterior face of length 3 and no CIPs, known as maximal planar graph (MPG). The FP obtained in the above two cases is a RFP or an OFP respectively. In this paper, we present the construction of a FP (RFP if exists, else an OFP), for a bi-connected plane triangulation G in linear-time.