Department of Mathematics

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

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Now showing 1 - 10 of 10
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    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.
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    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.
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    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.
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    Algorithm for constructing an optimally connected rectangular floor plan
    (Elsevier, 2014-09) Shekhawat, Krishnendra
    In most applications, such as urbanism and architecture, randomly utilizing given spaces is certainly not favorable. This study proposes an explicit algorithm for utilizing the given spaces inside a rectangle with satisfactory results. In the literature, connectivity is not considered as a criterion for floor plan design, but it is deemed essential in architecture. For example, dining rooms are preferably connected to kitchens, toilets should be connected to many rooms, and each bedroom should be separated from the other rooms. This paper describes adjacency among spaces and proves that the obtained rectangular floor plan is one of the best ones in terms of connectivity. An architectural and mathematical object called extra spaces is introduced by the proposed algorithm and is subsequently examined in this work.
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    Automated space allocation using mathematical techniques
    (Elsevier, 2015-09) Shekhawat, Krishnendra
    This paper presents a systematic pathway for the floor plan design when given the shape of required floor plan, the list of spaces, the dimensions of each space and the weighted matrix of required adjacencies between the spaces. The first step is to partition the given shape into say k possible rectangles. Then using the given adjacencies, divide the given spaces into k groups. Next is to construct a rectangular block for each group and at last adjoin all rectangular blocks to have the required floor plan. The obtained rectangular blocks are one of the best arrangement of spaces inside a rectangle from the point of view of connectivity.
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    Best connected rectangular arrangements Author links open overlay panel
    (Elsevier, 2016-03) Shekhawat, Krishnendra
    It can be found quite often in the literature that many well-known architects have employed either the golden rectangle or the Fibonacci rectangle in their works. On contrary, it is rare to find any specific reason for using them so often. Recently, Shekhawat (2015) proved that the golden rectangle and the Fibonacci rectangle are one of the best connected rectangular arrangements and this may be one of the reasons for their high presence in architectural designs. In this work we present an algorithm that generates best connected rectangular arrangements so that the proposed solutions can be further used by architects for their designs.
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    A computer-generated plus-shaped arrangement and its architectural applications
    (Elsevier, 2017-10) Shekhawat, Krishnendra
    This work consider the problem of rectilinear arrangement which is about arranging given rectangular objects of different sizes in the frame of a given rectilinear polygon while considering dimension and position of each rectangle and adjacency relations among the rectangles. The current work is part of a larger work aimed at automated generation of rectilinear arrangements while satisfying given dimensional and topological constraints. In this paper, we present a set of algorithms for obtaining a plus-shaped arrangement. In addition, we present some heuristic techniques for reducing the size of extra spaces present inside the obtained arrangement. At the end, we demonstrate architectural application of the presented work.
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    Introduction to generic rectangular floor plans
    (CUP, 2018-05) Shekhawat, Krishnendra
    An important task in the initial stages of most architectural design processes is the design of planar floor plans, that are composed of non-overlapping rooms divided from each other by walls while satisfying given topological and dimensional constraints. The work described in this paper is part of a larger research aimed at developing the mathematical theory for examining the feasibility of given topological constraints and providing a generic floor plan solution for all possible design briefs. In this paper, we mathematically describe universal (or generic) rectangular floor plans with n rooms, that is, the floor plans that topologically contain all possible rectangular floor plans with n rooms. Then, we present a graph-theoretical approach for enumerating generic rectangular floor plans upto nine rooms. At the end, we demonstrate the transformation of generic floor plans into a floor plan corresponding to a given graph.
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    Enumerating generic rectangular floor plans
    (Elsevier, 2018-08) Shekhawat, Krishnendra
    A rectangular floor plan (RFP) is a floor plan in which plan's boundary and each room is a rectangle. The problem is to construct a RFP for the given adjacency requirements, if it exists. In this paper, we aim to present a generic solution to the above problem by enumerating a set of RFP that topologically contain all possible RFP. This set of RFP is called generic rectangular floor plans (GRFP). Furthermore, the construction of GRFP leads us to the necessary condition for the existence of a RFP corresponding to a given graph.
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    A theory of L-shaped floor-plans
    (Elsevier, 2023-01) Shekhawat, Krishnendra
    Existing graph-theoretic approaches to construct floor-plans for a given plane graph are mainly restricted to floor-plans with rectangular boundary. This paper introduces 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. Further, we present necessary and sufficient conditions for the existence of a non-trivial L-shaped floor-plan corresponding to a properly triangulated plane graph (PTPG) G. Also, we develop an algorithm for its construction, if it exists.