A Graph Theoretical Approach for Creating Building Floor Plans

  • Krishnendra ShekhawatEmail author
  • Pinki
  • José P. Duarte
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 1028)


Existing floor planning algorithms are mostly limited to rectangular room geometries. This restriction is a significant reason why they are not used much in design practice. To address this issue, we propose an algorithm (based on graph theoretic tools) that generates rectangular and, if required, orthogonal floor plans while satisfying the given adjacency requirements. If a floor plan does not exist for the given adjacency requirements, we introduce circulations within a floor plan to have a required floor plan.


Adjacency Algorithm Graph theory Rectangular floor plan Orthogonal floor plan 



The research described in this paper evolved as part of the research project Mathematics-aided Architectural Design Layouts (File Number: ECR/2017/000356) funded by the Science and Engineering Research Board, India.


  1. 1.
    Levin, P.H.: Use of graphs to decide the optimum layout of buildings. Archit. J. 7, 809–817 (1964)Google Scholar
  2. 2.
    Cousin, J.: Topological organization of architectural spaces. Architectural Des. 40, 491–493 (1970)Google Scholar
  3. 3.
    Grason, J.: A dual linear representation for space filling location problems of the floorplan type. In: Moore, G.T. (ed.) Emerg. Methods Environ. Des. Plann., pp. 170–178. MIT Press, Cambridge (1970)Google Scholar
  4. 4.
    Steadman, J.P.: Graph theoretic representation of architectural arrangement. Architect. Res. Teach. 2(3), 161–172 (1973)Google Scholar
  5. 5.
    Sauda, E.J.: Computer program for the generation of dwelling unit floor plans. March thesis, University of California, Los Angeles-Architecture (1975)Google Scholar
  6. 6.
    Lynes, J.A.: Windows and floor plans. Environ. Plan. B. 4, 51–55 (1977)CrossRefGoogle Scholar
  7. 7.
    Baybars, I., Eastman, C.M.: Enumerating architectural arrangements by generating their underlying graphs. Environ. Plan. B. 7, 289–310 (1980)CrossRefGoogle Scholar
  8. 8.
    Roth, J., Hashimshony, R., Wachman, A.: Turning a graph into a rectangular floor plan. Build. Environ. 17(3), 163–173 (1982)CrossRefGoogle Scholar
  9. 9.
    Radcliffe, P.E., Kawal, D.E., Stephenson, R.J.: Critical Path Method, vol. III. Cahner, Chicago (1967)Google Scholar
  10. 10.
    Robinson, D.F., Janjic, I.: The constructability of floorplans with certain given outerplanar adjacency graph and room areas. In: Proceedings Xth British Combinatorics Conference, Ars Combinatoria, vol. 20B, pp. 133–142 (1985)Google Scholar
  11. 11.
    Bhasker, J., Sahni, S.: A linear time algorithm to check for the existence of a rectangular dual of a planar triangulated graph. Networks 17(3), 307–317 (1987)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Rinsma, I.: Rectangular and orthogonal floorplans with required room areas and tree adjacency. Environ. Plan. B: Plan. Des. 15, 111–118 (1988)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Rinsma, I., Giffin, J.W., Robinson, D.F.: Orthogonal floorplans from maximal planar graphs. Environ. Plan. B: Plan. Des. 174, 67–71 (1990)Google Scholar
  14. 14.
    Yeap, K.-H., Sarrafzadeh, M.: Floor-planning by graph dualization: 2-concave rectilinear modules. SIAM J. Comput. 22(3), 500–526 (1993)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Giffin, J.W., Watson, K., Foulds, L.R.: Orthogonal layouts using the deltahedron heuristic. Australas. J. Comb. 12, 127–144 (1995)MathSciNetzbMATHGoogle Scholar
  16. 16.
    He, X.: On floor-plan of plane graphs. SIAM J. Comput. 28(6), 2150–2167 (1999)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Recuero, A., Río, O., Alvarez, M.: Heuristic method to check the realisability of a graph into a rectangular plan. Adv. Eng. Soft. 31, 223–231 (2000)Google Scholar
  18. 18.
    Liao, C.-C., Lu, H.-I., Yen, H.-C.: Compact floor-planning via orderly spanning trees. J. Algorithm 48, 441–451 (2003)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Jokar, M.R.A., Sangchooli, A.S.: Constructing a block layout by face area. Int. J. Manuf. Technol. 54, 801–809 (2011)CrossRefGoogle Scholar
  20. 20.
    Zhang, H., Sadasivam, S.: Improved floor-planning of graphs via adjacency-preserving transformations. J. Comb. Optim. 22, 726–746 (2011)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Regateiro, F., Bento, J., Dias, J.: Floor plan design using block algebra and constraint satisfaction. Adv. Eng. Inf. 26, 361–382 (2012)CrossRefGoogle Scholar
  22. 22.
    Shekhawat, K.: Algorithm for constructing an optimally connected rectangular floor plan. Front. Archit. Res. 3(3), 324–330 (2014)CrossRefGoogle Scholar
  23. 23.
    Shekhawat, K., Duarte, J.P.: Rectilinear floor plans. Commun. Comput. Inf. Sci. 724, 395–411 (2017)Google Scholar
  24. 24.
    Slusarczyk, G.: Graph-based representation of design properties in creating building floorplans. Comput. Aid. Des. 95, 24–39 (2018)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Shekhawat, K.: Enumerating generic rectangular floor plans. Autom. Constr. 92, 151–165 (2018)CrossRefGoogle Scholar
  26. 26.
    He, X.: On finding the rectangular duals of planar triangular graphs. SIAM J. Comput. 22, 1218–1226 (1993)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Shekhawat, K., Duarte, J.P.: Automated best connected rectangular floorplans. In: Gero, J.S. (ed.) Design Computing and Cognition ’16, pp. 495–511. Springer, Cham (2017). Scholar
  28. 28.
    Steadman, P.: Why are most buildings rectangular? ARQ Mag. 10(2), 119–130 (2006)CrossRefGoogle Scholar

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© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of MathematicsBITS PilaniPilaniIndia
  2. 2.SCDC, School of Architecture and Landscape ArchitectureThe Pennsylvania State UniversityUniversity ParkUSA

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