arXiv subjects

Krishnendra Shekhawat

Publications and source records attributed to Krishnendra Shekhawat.

12 recordsLinked to original sources

arXiv2026

DPLAN: Minimal Connectivity to Floorplan Generation

Automated floor plan generation is an important problem in computational architectural design. The goal is to construct a floor plan from user-defined room numbers and door requirements. The user specifies which rooms must share a door and which rooms must not be adjacent. However, these requirements do not determine the exact placement or shape of the rooms. The task is therefore to arrange the rooms in a single floor plan so that all required door connections are satisfied and no rooms overlap. To address this problem, we propose DPLAN (Door Connectivity to Floor Plan Generation), a graph-based prototype that generates floor plans from door and non-adjacency constraints. The framework operates in three stages. First, the user-defined graph is examined and, if disconnected, additional edges are added to connect its components. Second, a bi-connected plane triangulation is constructed to ensure the existence of a floor plan without overlapping rooms or empty spaces. Third, the triangulated graph is transformed into floor plans. For rectangular floor plans (RFPs), separating triangles are removed by modifying edges without adding new vertices, thereby avoiding the creation of extra rooms. For orthogonal floor plans (OFPs), separating triangles are removed by introducing additional vertices, allowing rectilinear room shapes. By enforcing both door and non-adjacency requirements, the framework generates floor plans that satisfy the given constraints. The method is implemented in Python and includes a prototype for interactive constraint specification and floor plan visualization. Currently, the framework supports rectangular plot boundaries. Future work includes support for non-rectangular plots, dimension-based scaling, and circulation modeling.

cs.CG↗

arXiv2026

Area-universality in Outerplanar Graphs

A rectangular floorplan is a partition of a rectangle into smaller rectangles such that no four rectangles meet at a single point. Rectangular floorplans arise naturally in a variety of applications, including VLSI design, architectural layout, and cartography, where efficient and flexible spatial subdivisions are required. A central concept in this domain is that of area-universality: a floorplan (or more generally, a rectangular layout) is area-universal if, for any assignment of target areas to its constituent rectangles, there exists a combinatorially equivalent layout that realizes these areas. In this paper, we investigate the structural conditions under which an outerplanar graph admits an area-universal rectangular layout. We establish a necessary and sufficient condition for area-universality in this setting, thereby providing a complete characterization of admissible outerplanar graphs. Furthermore, we present an algorithmic construction that guarantees that the resulting layout is always area-universal.

cs.CG↗

arXiv2026

Algorithmic Design and Graph-Based Classification for Rectilinear-Shaped Modules in Floor Plans

We present a graph-theoretic framework for constructing floor plans that support non-rectangular modules, with particular emphasis on L-shaped and T-shaped geometries. Unlike traditional approaches that primarily focus on rectangular modules and outer boundary constraints, our method explicitly incorporates structural restrictions that arise when realizing more complex module shapes within rectangular floor-plan representations. The framework is based on triangulated graphs and investigates how algorithmic graph theory techniques can be used to embed L and T-shaped modules while preserving prescribed adjacencies. We show that not every triangulated graph admits such realizations and identify structural limitations that prevent the existence of the desired module geometries. To capture these limitations, we introduce a shape-preservation constraint that ensures module geometries cannot be altered through boundary deformation, as such changes would either increase the combinatorial complexity of neighboring modules or violate adjacency relationships. We propose a linear-time construction algorithm based on a prioritized canonical ordering that realizes L and T-shaped modules in graphs containing at least one internal K4, or two internal K4 subgraphs satisfying specific existence conditions. The algorithm is simple, constructive, and directly implementable, making it suitable for practical floor-plan generation workflows. We conclude by discussing extensions to additional module shapes and broader classes of supporting graph structures.

math.CO↗

arXiv2022

End-to-end Graph-constrained Vectorized Floorplan Generation with Panoptic Refinement

The automatic generation of floorplans given user inputs has great potential in architectural design and has recently been explored in the computer vision community. However, the majority of existing methods synthesize floorplans in the format of rasterized images, which are difficult to edit or customize. In this paper, we aim to synthesize floorplans as sequences of 1-D vectors, which eases user interaction and design customization. To generate high fidelity vectorized floorplans, we propose a novel two-stage framework, including a draft stage and a multi-round refining stage. In the first stage, we encode the room connectivity graph input by users with a graph convolutional network (GCN), then apply an autoregressive transformer network to generate an initial floorplan sequence. To polish the initial design and generate more visually appealing floorplans, we further propose a novel panoptic refinement network(PRN) composed of a GCN and a transformer network. The PRN takes the initial generated sequence as input and refines the floorplan design while encouraging the correct room connectivity with our proposed geometric loss. We have conducted extensive experiments on a real-world floorplan dataset, and the results show that our method achieves state-of-the-art performance under different settings and evaluation metrics.

cs.CV↗

arXiv2022

A Theory of L-shaped Floor-plans

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.

cs.DM↗

arXiv2021

A Theory of Rectangularly Dualizable Graphs

A plane graph is called a rectangular graph if each of its edges can be oriented either horizontally or vertically, each of its interior regions is a four-sided region and all interior regions can be fitted in a rectangular enclosure. Only planar graphs can be dualized. If the dual of a plane graph is a rectangular graph, then the plane graph is a rectangularly dualizable graph. In 1985, Koźmiński and Kinnen presented a necessary and sufficient condition for the existence of a rectangularly dualizable graph for a separable connected plane graph. In this paper, we present a counter example for which the conditions given by them for separable connected plane graphs fail and hence, we derive a necessary and sufficient condition for a plane graph to be a rectangularly dualizable graph.

math.CO↗

arXiv2021

Rectangularly Dualizable Graphs: Area-Universality

A plane graph is called a rectangular graph if each of its edges can be oriented either horizontally or vertically, each of its interior regions is a four-sided region and all interior regions can be fitted in a rectangular enclosure. If the dual of a plane graph is a rectangular graph, then the plane graph is a rectangularly dualizable graph. A rectangular dual is it area-universal if any assignment of areas to each of its regions can be realized by a combinatorially weak equivalent rectangular dual. It is still unknown that there exists no polynomial time algorithm to construct an area-universal rectangular dual for a rectangularly dualizable graph . In this paper, we describe a class of rectangularly dualizable graphs wherein each graph can be realized by an area-universal rectangular dual. We also present a polynomial time algorithm for its construction.

math.CO↗

arXiv2021

Transformations of Rectangular Dualizable Graphs

A plane graph is said to be a rectangular graph if each of its edges can be oriented horizontal or vertical, its internal regions are four-sided and it has a rectangular enclosure. If dual of a planar graph is a rectangular graph, then the graph is said to be a rectangular dualizable graph (RDG). In this paper, we present adjacency transformations between RDGs and present polynomial time algorithms for their transformations. An RDG $\mathcal{G}=(V, E)$ is called maximal RDG (MRDG) if there does not exist an RDG $\mathcal{G'}=(V, E')$ with $E' \supset E$. An RDG $\mathcal{G}=(V, E)$ is said to be an edge-reducible if there exists an RDG $\mathcal{G'}=(V, E')$ such that $E\supset E'$. If an RDG is not edge-reducible, it is said to be an edge-irreducible RDG. We show that there always exists an MRDG for a given RDG. We also show that an MRDG is edge-reducible and can always be transformed to a minimal one (an edge-irreducible RDG).

math.CO↗

arXiv2020

GPLAN: Computer-Generated Dimensioned Floorplans for given Adjacencies

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.

cs.CG↗

arXiv2020

A linear time algorithm for constructing orthogonal floor plans with minimum number of bends

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 ρ- 2 \leq B_{min} \leq ρ+ 1 and ρis 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.

cs.CG↗

arXiv2019

Automated Generation of Dimensioned Rectangular Floorplans

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.

cs.CG↗

arXiv2015

Connectivity Algorithm

In this work, for the given adjacency matrix of a graph, we present an algorithm which checks the connectivity of a graph and computes all of its connected components. Also, it is mathematically proved that the algorithm presents all the desired results.

cs.DS↗