Hierarchical planar graph embedding (sometimes called level planar graphs) is widely recognized as a very important task in diverse fields of research and development. Given a proper hierarchical planar graph, we want to find a geometric position of every vertex (layout) in a straight-line grid drawing without any edge-intersection. An additional objective is to minimize the area of the rectangular grid in which G is drawn with more aesthetic embedding. In this paper we propose several ideas to find an embedding of G in a rectangular grid with area, ( -1) &\#215; (k-1), where is the number of vertices in the longest level and k is the number of levels in G.)
%0 Journal Article
%1 IJACSA.2012.031216
%A Mohamed A. El Sayed Ahmed A. A. Radwan, Nahla F Omran
%D 2012
%J International Journal of Advanced Computer Science and Applications(IJACSA)
%K algorithms; drawing. graph graphs; hierarchical level
%N 12
%T Study of Proper Hierarchical Graphs on a Grid
%U http://ijacsa.thesai.org/
%V 3
%X Hierarchical planar graph embedding (sometimes called level planar graphs) is widely recognized as a very important task in diverse fields of research and development. Given a proper hierarchical planar graph, we want to find a geometric position of every vertex (layout) in a straight-line grid drawing without any edge-intersection. An additional objective is to minimize the area of the rectangular grid in which G is drawn with more aesthetic embedding. In this paper we propose several ideas to find an embedding of G in a rectangular grid with area, ( -1) &\#215; (k-1), where is the number of vertices in the longest level and k is the number of levels in G.)
@article{IJACSA.2012.031216,
abstract = {Hierarchical planar graph embedding (sometimes called level planar graphs) is widely recognized as a very important task in diverse fields of research and development. Given a proper hierarchical planar graph, we want to find a geometric position of every vertex (layout) in a straight-line grid drawing without any edge-intersection. An additional objective is to minimize the area of the rectangular grid in which G is drawn with more aesthetic embedding. In this paper we propose several ideas to find an embedding of G in a rectangular grid with area, ( -1) \&\#215; (k-1), where is the number of vertices in the longest level and k is the number of levels in G.)},
added-at = {2014-02-21T08:00:08.000+0100},
author = {{Mohamed A. El Sayed Ahmed A. A. Radwan}, Nahla F Omran},
biburl = {https://www.bibsonomy.org/bibtex/29f9847911d14cb58f8dce2417f344f20/thesaiorg},
interhash = {6ae05f40822062be75a9b19ac72bb8aa},
intrahash = {9f9847911d14cb58f8dce2417f344f20},
journal = {International Journal of Advanced Computer Science and Applications(IJACSA)},
keywords = {algorithms; drawing. graph graphs; hierarchical level},
number = 12,
timestamp = {2014-02-21T08:00:08.000+0100},
title = {{Study of Proper Hierarchical Graphs on a Grid}},
url = {http://ijacsa.thesai.org/},
volume = 3,
year = 2012
}