> \pJava Excel API v2.6 Ba==h\:#8X@"1Arial1Arial1Arial1Arial + ) , * `WDC,S4#titletitle[alternative]title[translated]author[google(nobreakline)] contributor[author(nobreakline)]"contributor[scopusid(nobreakline)]date[issued]relation[journaltitle]identifier[issn] citationsidentifier[major]subject(nobreakline) publisheridentifier[thesisdegree]contributor[advisor]relation[ispartofseries]relation[index(nobreakline)]typeabstractidentifier[govdoc]identifier[uri]identifier[doi(doi)]identifier[isbn]identifier[ismn]
identifier( 6tXx tX ܴ Ǡ) Lବ<Algorithsm for Embedding 6-Planar Graphs in Triangular grids1995
Y ȐĬYtTŐYP YMasterMaster's Thesis1 Ǡ)tǀ ȴ GX | x HX \\ || Q¤Д t. ܴ Ǡ)@ ȴ G| ܴ <\ Q¤Д <\ GX @ ܴX <\ ɔ ܴ X \\ Q. ܴ Ǡ)@ VLSI \ $Ĭ \ tǩp 1 t, tᬀX /, \ͥ X 8t, X P( D tǔ } ptD p, t\ pt iXt ų1t \ | ܴ\XՔ t ܴ Ǡ)X t.
|8 ( 6tXx t | \֕(visibility representation)D tǩX ܴ Ǡ)XՔ ) t l\. \ $Ĭ@ ų1D t0 t |8 XՔ } pt@ tᬀ@ t<\ tǔ \ 1t ǔ ptt. l tD $\ Ǡ) Lବ tᬀ| $\ Ǡ) LବD H\.
tᬀ| $\ Lବ@ |8 H\ tᬀ p X ܭYD ȩX Ǡ) X tᬀX / 4n8tX D Xp, tD $\ Lବ@ Ǡ) X tt (3n-5)*(2n-2)tX D \. , n@ ȴ GX X /t. P Lବ P t O(n)t.;The graph embedding is one-to-one mapping from the source graph G to the target graph H for its objectives. The grid embedding for a graph G maps vertices to distinct grid points and edges to nonintersecting grid paths.
Some constraints of grid embedding applying to VLSI circuit design are minimizing the area, the longest edge length and the number of bends. So, the goal of this kind of a grid embedding is the drawing a graph in 2-dimensional plane with satisfying these constraints and high readability.
In this thesis, the methods for embedding 6-planar graphs in triangular grids using the visibility representations are studied. Because there is a trade-off between minimizing the number of bends and minimizing the total areas, this thesis presents two algorithms for reducing the number of bends and the areas, respectively. The first algorithm reduces the number of bends by applying a sequence of bend-stretching transformations and then the embedding graph has at most 4n+8 bends, where n is the number of vertices of a graph G. Also, the result of the second algorithm has at most (3n-5)*(2n-2) areas. These algorithms run in linear time.~http://dspace.ewha.ac.kr/handle/2015.oak/198236;
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