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Construction of floorplans for plane graphs over polygonal boundaries

Author

Listed:
  • Rohit Lohani

    (Department of Mathematics, BITS Pilani)

  • Krishnendra Shekhawat

    (Department of Mathematics, BITS Pilani)

Abstract

A floorplan (F) is a partition of a polygonal boundary (P) into n-regions satisfying the adjacencies given by an n-vertex graph. Here, it is assumed that the sides of the polygonal boundary are either parallel to the x-axis or y-axis or have slopes $$-1$$ - 1 or 1. For a given polygonal boundary P (having m line segments) and a plane triangulated graph G, this paper presents a linear-time algorithm for constructing a floorplan with the required polygonal boundary satisfying all given adjacencies. Further, it has been proved that the number of sides of each region in the obtained floorplan (F) is at most m + 1 (except one region, which can have at most m + 5 sides) for the given polygonal boundary P of length m.

Suggested Citation

  • Rohit Lohani & Krishnendra Shekhawat, 2024. "Construction of floorplans for plane graphs over polygonal boundaries," Journal of Combinatorial Optimization, Springer, vol. 48(3), pages 1-25, October.
    • Handle: RePEc:spr:jcomop:v:48:y:2024:i:3:d:10.1007_s10878-024-01217-8
    DOI: 10.1007/s10878-024-01217-8
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