NDLI: Improved floor-planning of graphs via adjacency-preserving transformations

Content Provider	Springer Nature Link
Author	Zhang, Huaming Sadasivam, Sadish
Copyright Year	2010
Abstract	Let G=(V,E) and G′=(V′,E′) be two graphs, an adjacency-preserving transformation from G to G′ is a one-to-many and onto mapping from V to V′ satisfying the following: (1) Each vertex v∈V in G is mapped to a non-empty subset $\mathcal{A}(v)\subset V'$ in G′. The subgraph induced by $\mathcal{A}(v)$ is a connected subgraph of G′; (2) if u≠v∈V, then $\mathcal{A}(u)\cap\mathcal{A}(v)=\emptyset$ ; and (3) two vertices u and v are adjacent to each other in G if and only if subgraphs induced by $\mathcal{A}(u)$ and $\mathcal{A}(v)$ are connected in G′.In this paper, we study adjacency-preserving transformations from plane triangulations to irreducible triangulations (which are internally triangulated, with four exterior vertices and no separating triangles). As one shall see, our transformations not only preserve adjacency well, but also preserve the endowed realizers of plane triangulations well in the endowed transversal structures of the image irreducible triangulations, which may be desirable in some applications.We then present such an application in floor-planning of plane graphs. The expected grid size of the floor-plan of our linear time algorithm is improved to $(\frac{5n}{8}+O(1))\times (\frac{23n}{24}+O(1))$ , though the worst case grid size bound of the algorithm remains $\lfloor\frac{2n+1}{3}\rfloor\times(n-1)$ , which is the same as the algorithm presented in Liao et al. (J. Algorithms 48:441–451, 2003).
Starting Page	726
Ending Page	746
Page Count	21
File Format	PDF
ISSN	13826905
Journal	Journal of Combinatorial Optimization
Volume Number	22
Issue Number	4
e-ISSN	15732886
Language	English
Publisher	Springer US
Publisher Date	2010-04-24
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Floor-plan Rectangular dual Plane triangulation Irreducible triangulation Optimization Combinatorics Theory of Computation Mathematical Modeling and Industrial Mathematics Convex and Discrete Geometry Operations Research/Decision Theory
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Control and Optimization Discrete Mathematics and Combinatorics Computational Theory and Mathematics Computer Science Applications

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