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Existing graph theoretic approaches are mainly restricted to floor-plans with rectangular boundary. In this paper, we introduce floor-plans with $L$-shaped boundary (boundary with only one concave corner). To ensure the L-shaped boundary, we introduce the concept of non-triviality of a floor-plan. A floor-plan with a rectilinear boundary with at least one concave corner is non-trivial if the number of concave corners can not be reduced, without affecting the modules adjacencies within it. Further, we present necessary and sufficient conditions for the existence of a non-trivial L-shaped floor-plan corresponding to a properly triangulated planar graph (PTPG) $G$. Also, we develop an $O(n^2)$ algorithm for its construction, if it exists., Comment: 35 pages, 61 figures

In this paper, we present GPLAN, software aimed at constructing dimensioned floorplan layouts based on graph-theoretical and optimization techniques. GPLAN takes user requirements as input in the following two forms: i. Adjacency graph: It allows user to draw an adjacency graph on a GUI(graphical user interface) corresponding to which GPLAN produces a set of dimensioned floorplans with a rectangular boundary, where each floorplan is topologically distinct from others. ii. Dimensionless layout: Here, user can draw any layout with rectangular or non-rectangular boundary on a GUI and GPLAN transforms it into a dimensioned floorplan while preserving adjacencies, positions, shapes of the rooms. The above approaches represent different ways of inserting adjacencies and GPLAN generate dimensioned floorplans corresponding to the given adjacencies. The larger aim is to provide alternative platforms to user for producing dimensioned floorplans for all given (architectural) constraints, which can be further refined by architects.

Let G = (V, E) be a planar triangulated graph (PTG) having every face triangular. A rectilinear dual or an orthogonal floor plan (OFP) of G is obtained by partitioning a rectangle into \mid V \mid rectilinear regions (modules) where two modules are adjacent if and only if there is an edge between the corresponding vertices in G. In this paper, a linear-time algorithm is presented for constructing an OFP for a given G such that the obtained OFP has B_{min} bends, where a bend in a concave corner in an OFP. Further, it has been proved that at least B_{min} bends are required to construct an OFP for G, where \rho - 2 \leq B_{min} \leq \rho + 1 and \rho is the sum of the number of leaves of the containment tree of G and the number of K_4 (4-vertex complete graph) in G.

This paper proposes a methodology for the automated construction of rectangular floorplans (RFPs) while addressing dimensional constraints and adjacency relations. Here, adjacency relations are taken in the form of a dimensionless rectangular arrangement (RA) ensuring the existence of a RFP, while dimensional constraints are given in terms of minimum width and aspect ratio range for each room. A linear optimization model is then presented to obtain a feasible dimensioned RFP for user-defined constraints. A GUI is also developed for the automated generation of RFPs. The proposed model is able to generate feasible solutions for every possible RA in a reasonable amount of time. From the architectural perspective, this work can be seen as a re-generation of well-known architectural plans with modified dimensions. In the end, the regeneration of existing legacy RFPs (corresponding to the user-defined dimensions) has been demonstrated, taking their image as input.