Department of Mathematics

Permanent URI for this collectionhttp://localhost:4000/handle/123456789/1920

Browse

Filters

2014 - 2019132020 - 202529

Settings

Author: search.filters.author.Shekhawat, KrishnendraSubject: search.filters.subject.Mathematics

Search Results

Now showing 1 - 10 of 42
  • No Thumbnail Available
    Item
    Automated generation of circulations within a floorplan
    (CUP, 2025-04) Shekhawat, Krishnendra
    Various factors are considered when designing a floorplan layout, including the plan’s outer boundary, room shape and size, adjacency, privacy, and circulation space, among others. While graph-theoretic approaches have proven effective for floorplan generation, existing algorithms generally focus on defining the boundary of the plan or different room shapes, lacking the investigation of designing circulation space within a floorplan. However, the circulation design in architectural planning is a crucial factor that affects the functionality and efficiency of areas within a building. This paper presents a graph-theoretic approach for integrating circulation within a floorplan. In this study, we use plane graphs to represent floorplans and develop graph algorithms to incorporate various types of circulation within a floorplan as follows: i. The first phase generates a spanning circulation, that is, a corridor leading to each room using a circulation graph. ii. Subsequently, using an approximation algorithm, the circulation space is minimized, that is, generation of minimum circulation space covering all the rooms, thereby enhancing space utilization in the floorplan. iii. Furthermore, customized circulations are generated to cater to user preferences, distinguishing between public and private spaces within the floorplan. In addition to the theoretical framework, we have implemented our algorithms in Python and developed a user-friendly graphical interface (GUI), enabling seamless integration of our algorithms into architectural design processes.
  • No Thumbnail Available
    Item
    Linear-time algorithm for generating L-shaped floorplans using canonical ordering technique
    (Springer, 2025-05) Shekhawat, Krishnendra
    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.
  • No Thumbnail Available
    Item
    Existence and construction of a C-shaped module within a floorplan
    (Elsevier, 2025-06) Shekhawat, Krishnendra
    For a given graph, this paper presents a graph-theoretic approach for creating a floorplan with a specific module, i.e., a C-shaped module. Unlike traditional methods that only consider boundary layouts for floorplan generation, this research considers constraints related to constructing the desired modules. The central objective is to explore how graph theoretic properties can ensure the integration of C-shaped modules within floorplans that have rectangular boundaries. A key innovation lies in introducing the concept of non-triviality for these modules, which becomes crucial for achieving the desired non-trivial C-shaped module (a non-trivial module means that it cannot be transformed into other shaped modules by stretching or shrinking its module walls, i.e. if its module walls are stretched or shrinked, then either the bends of its neighboring modules may increase or the given adjacency may not be preserved). The proposed solution involves a linear-time algorithm based on the concept of canonical labeling. The algorithm introduces prioritized canonical labeling to generate a non-trivial C-shaped module within the floorplan. It operates on a given plane triangulated graph (PTG) that contains at least one interior . The paper outlines the algorithm and establishes the essential conditions for constructing a non-trivial C-shaped module within the floorplan of a given plane triangulated graph (PTG) G. Notably, the algorithm's simplicity and ease of implementation set it apart. In future work, we will focus on generating the existence and construction of other desired shaped modules for the given input graphs.
  • No Thumbnail Available
    Item
    Automated generation of floorplans with non-rectangular rooms
    (Elsevier, 2023-05) Shekhawat, Krishnendra
    Existing approaches (in particular graph theoretic) for generating floorplans focus on constructing floorplans for given adjacencies without considering boundary layout or room shapes. With recent developments in designs, it is demanding to consider multiple constraints while generating floorplan layouts. In this paper, we study graph theoretic properties which guarantee the presence of different shaped rooms within the floorplans. Further, we present a graph-algorithms based application, developed in Python, for generating floorplans with given input room shapes. The proposed application is useful in creating floorplans for a given graph with desired room shapes mainly, L, T, F, C, staircase, and plus-shape. Here, the floorplan boundary is always rectangular. In future,we aim to extend this work to generate any (rectilinear) room shape and floor plan boundary for a given graph.
  • No Thumbnail Available
    Item
    An algorithm for customizing slicing floor plan design
    (Springer, 2023) Shekhawat, Krishnendra
    This paper proposes a linear time algorithm for the customization of a slicing floor plan design, which can be done by customizing its modules in the following two ways: —-by modifying the aspect ratio or by modifying either its width or height while retaining its area,-by modifying its area while keeping either of its aspect ratio or initial width or height. Both of the aforementioned approaches demonstrate that a slicing floor plan can be generated for any aspect ratio and area while preserving the module adjacencies of the original floor plan. A demonstration has been provided for a devised prototype to validate the viability of the aforementioned approaches
  • No Thumbnail Available
    Item
    Construction of non-rectangular floor plans for properly triangulated planar graphs
    (Springer, 2024-10) Shekhawat, Krishnendra
    A majority of previous research on the problem of floor planning has been limited to constructing floor plans with rectangular exterior boundaries. It includes rectangular floor plans (RFPs) (Kozminski and Kinnen in IEEE Trans-Actions Circuits Syst 35:1401–1416, 1988, [1]) for properly triangulated plane graphs (PTPGs) having four or fewer corner implying paths (CIPs), where both the modules and exterior boundary are considered rectangular, and orthogonal floor plans (OFPs) (Liao et al in J Algorithms 2:441–451, 2003, [2]) for the remaining graphs (which do not possess RFPs), where the exterior boundary is rectangular but modules are taken of rectilinear shapes (L-shaped, T-shaped, Z-shaped, etc.). As an alternative to OFPs, sometimes floor plans containing rectilinear external boundaries and rectangular modules can also be obtained, known as non-rectangular floor plans (Raveena Shekhawat in Theor Comput Sci 942:57–92, 2023, [3]). This work aims to investigate non-rectangular floor plans (NRFPs) providing the best alternative solution in terms of the least number of concave corners (comparing with the number of bends in OFPs) for the PTPGs having more than four CIPs. We present a linear time algorithm to construct NRFPs with the least possible number of concave corners at the exterior boundary corresponding to the PTPGs with more than four CIPs. Further, we claim that the obtained NRFPs are non-trivial. An NRFP is considered non-trivial if the count of concave corners at its exterior boundary cannot be lowered without disrupting the horizontal and vertical adjacencies of the modules. In addition, we demonstrate that it is always feasible to produce an NRFP with precisely concave corners for any PTPG with k; CIPs.
  • No Thumbnail Available
    Item
    Generation of dimensioned floor plans for a given boundary layout
    (SSCE, 2024) Shekhawat, Krishnendra
    In literature, the generation of floor plans has mainly been confined to dimensionless floor plans with rectangular boundaries having no open spaces within the floor plan. In this paper, the user is allowed to construct a dimensioned boundary using slant, horizontal and vertical line segments, where dimensioned open spaces can be drawn within the boundary layout. Once the boundary is finalized, it can be partitioned into dimensioned blocks using vertical and horizontal dissections. Each block can be further partitioned into dimensioned rooms which results in a dimensioned floor plan F for the given boundary layout. The dissection method employed is based on the slicing tree approach, which results in floor plans that are amenable to slicing and consist of non-rectangular rooms, offering the potential for open spaces within floor plan F. As a preliminary step towards automation, we have developed an interactive user interface for generating dissected dimensioned floor plans.
  • No Thumbnail Available
    Item
    A graph theoretic approach for generating T-shaped floor plans
    (Elsevier, 2024-10) Shekhawat, Krishnendra
    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 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.
  • No Thumbnail Available
    Item
    Automated generation of floor plans with minimum bends
    (CUP, 2025-02) Shekhawat, Krishnendra
    The generation of floor plan layouts has been extensively studied in recent years, driven by the need for efficient and functional architectural designs. Despite significant advancements, existing methods often face limitations when dealing with specific input adjacency graphs or room shapes and boundary layouts. When adjacency graphs contain separating triangles, the floor plan must include rectilinear rooms (non-rectangular rooms with concave corners). From a design perspective, minimizing corners or bends in rooms is crucial for functionality and aesthetics. In this article, we present a Python-based application called G-Drawer for automatically generating floor plans with a minimum number of bends. G-Drawer takes any plane triangulated graph as an input and outputs a floor plan layout with minimum bends. It prioritizes generating a rectangular floor plan (RFP); if an RFP is not feasible, it then generates an orthogonal floor plan or an irregular floor plan. G-Drawer modifies orthogonal drawing techniques based on flow networks and applies them on the dual graph of a given PTG to generate the required floor plans. The results of this article demonstrate the efficacy of G-Drawer in creating efficient floor plans. However, in future, we need to work on generating multiple dimensioned floor plans having non-rectangular rooms as well as non-rectangular boundary. These enhancements will address both mathematical and architectural challenges, advancing the automated generation of floor plans toward more practical and versatile applications.
  • No Thumbnail Available
    Item
    Non-trivial self-organised floor plans: an optimisation strategy
    (Springer, 2025-01) Shekhawat, Krishnendra
    We present a novel workflow where non-rectangular floor plans (NRFPs), namely plans with at least one concave corner, are self-generated using a model that directly encodes key optimisation factors on spatial quality and energy consumption, with non-rectangular building envelopes. The modelling considers a number of key factors including architectural and urban quality, net zero factors and adherence to general residents’ feedback from previous studies. We provide evidence that the proposed workflow outperforms a number of optimisation solvers generally used in computational design, in those cases where solar radiation is most needed. Our study combines a syntactic approach with a computational one with a novel workflow to encode tangible and intangible factors to improve a specific class of non-trivial floor plans (L-shaped).