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Rectilinear Duals Using Monotone Staircase Polygons

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Combinatorial Optimization and Applications (COCOA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8881))

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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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Authors and Affiliations

  1. Department of Electrical Engineering, National Taiwan University, Taipei, 106, Taiwan, Republic of China

    Yi-Jun Chang & Hsu-Chun Yen

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  1. Yi-Jun Chang
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  2. Hsu-Chun Yen
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Correspondence to Hsu-Chun Yen .

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Editors and Affiliations

  1. Zhejiang Normal University, Jinhua, Zhejiang, China

    Zhao Zhang

  2. University of Texas, Tyler, Texas, USA

    Lidong Wu

  3. University of Texas, Dallas, Texas, USA

    Wen Xu

  4. University of Texas, Dallas, USA

    Ding-Zhu Du

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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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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12690-6

  • Online ISBN: 978-3-319-12691-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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