In facility layouts—the designing of floorplans with certain rooms adjacent to each other—there are often area constraints for the rooms. Robinson and Janjic showed that, if areas are specified for rooms with a given maximal outerplanar adjacency graph, then any convex polygon with the correct area can be divided into convex rooms to satisfy both area and adjacency requirements. If the perimeter and rooms must be rectangular, undimensioned floorplans can be found to fit any maximal outerplanar adjacency graph with at most four vertices of degree 2. It is shown that in some cases it is not always possible to satisfy the area constraints.
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References
1.
EarlC FMarchL J, 1979, “Architectural applications of graph theory” in Applications of Graph Theory Eds WilsonR JBeinekeL W (Academic Press, London) pp 327–355
2.
HararyF, 1969Graph Theory (Addison-Wesley, Reading, MA)
3.
LynesJ A, 1977, “Windows and floorplans”Environment and Planning B451–55
4.
RobinsonD FJanjicI, 1985, “The constructability of floorplans with certain given outerplanar adjacency graph and room areas” Proceedings Xth British Combinatorics Conference July 1985 Ars Combinatoria20B133–142
