New Algorithm for Drawings of 3-Planar Graphs

Graphs arise in a natural way in many applications, together with the need to be drawn. Except for very small instances, drawing a graph by hand becomes a very complex task, which must be performed by automatic tools. The field of graph drawing is concerned with finding algorithms to draw graph in an aesthetically pleasant way, based upon a certain number of aesthetic criteria that define what a good drawing, (synonyms: diagrams, pictures, layouts), of a graph should be. This problem can be found in many such as in the computer networks, data networks, class inter-relationship diagrams in object oriented databases and object oriented programs, visual programming interfaces, database design systems, software engineering…etc. Given a plane graph G, we wish to find a drawing of G in the plane such that the vertices of G are represented as grid points, and the edges are represented as straight-line segments between their endpoints without any edge-intersection. Such drawings are called planar straight-line drawings of G. An additional objective is to minimize the area of the rectangular grid in which G is drawn. In this paper we introduce a new algorithms that finds an embedding of 3-planar graph. Keywords: 3- Planar Graph; Graph Drawing; drawing on grid

CONSORT 2010 checklist of information to include when reporting a randomised trial*.

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List of interventions.

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Change of daily process measures over the study period among the whole cohort and in subgroups of ICUs with baseline spontaneous trial (SAT) compliance of >50% and ≤50.

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List of participating sites and ethics committee approvals.

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Data measures definitions.

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Characteristics of participating sites.

IQR: interquartile range. (PDF)</p

Map of Saudi Arabia with distribution of participating ICUs.

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Distribution of compliance, non-compliance and contraindications (with reasons) to the interventions.

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