Abstract
A rectilinear dual of a plane graph refers to a partition of a rectangular area into nonoverlapping rectilinear polygonal modules, where each module corresponds to a vertex such that two modules have side-contact iff their corresponding vertices are adjacent. It is known that 8-sided rectilinear polygons are sufficient and necessary to construct rectilinear duals of maximal plane graphs. The result stands even if modules are restricted to T-shape polygons. We show that the optimum polygonal complexity of T-free rectilinear duals is exactly 12. It justifies the intuition that T-shape is more powerful than other 8-sided modules. Our construction of 12-sided T-free rectilinear duals only requires monotone staircase modules. We also consider the issue of area-universality, and show that monotone staircase modules are not sufficient to construct area-universal rectilinear duals in general even when an unbounded polygonal complexity is allowed; however, eight sides are sufficient for Hamiltonian plane graphs. This line of research regarding monotone staircase modules is also motivated by the so-called monotone staircase cuts in VLSI floorplanning. We feel that our results provide a new insight towards a comprehensive understanding of modules in rectilinear duals.
Research supported in part by National Science Council of Taiwan under Grants NSC-100-2221-E-002-132-MY3 and NSC-100-2923-E-002-001-MY3.
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Chang, YJ., Yen, HC. (2014). Rectilinear Duals Using Monotone Staircase Polygons. In: Zhang, Z., Wu, L., Xu, W., Du, DZ. (eds) Combinatorial Optimization and Applications. COCOA 2014. Lecture Notes in Computer Science(), vol 8881. Springer, Cham. https://doi.org/10.1007/978-3-319-12691-3_8
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DOI: https://doi.org/10.1007/978-3-319-12691-3_8
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