Abstract
Arectangular graph is a plane graph where all regions are four-sided and all edges are oriented in either the vertical or the horizontal direction. In addition the graph enclosure must also be rectangular. Given a plane graph representing a desired component connectivity, itsrectangular dual can be used to build afloorplan. This indicates that a system implementation can allocate rectangular floorplan regions to components that can be pairwise connected through common borders.
This paper proves that constructing a rectangular dual graph is equivalent to a matching problem in a bipartite graph derived from the given plane graph. A simple existence theorem in terms of the graph structure is obtained as a corollary.
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Communicated by D. T. Lee.
This work was supported by the National Science Council, Taiwan, Republic of China, under Contract NSC 78-0404-E006-14.
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Lai, YT., Leinwand, S.M. A theory of rectangular dual graphs. Algorithmica 5, 467–483 (1990). https://doi.org/10.1007/BF01840399
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DOI: https://doi.org/10.1007/BF01840399