2,812 research outputs found

    EPG-representations with small grid-size

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    In an EPG-representation of a graph GG each vertex is represented by a path in the rectangular grid, and (v,w)(v,w) is an edge in GG if and only if the paths representing vv an ww share a grid-edge. Requiring paths representing edges to be x-monotone or, even stronger, both x- and y-monotone gives rise to three natural variants of EPG-representations, one where edges have no monotonicity requirements and two with the aforementioned monotonicity requirements. The focus of this paper is understanding how small a grid can be achieved for such EPG-representations with respect to various graph parameters. We show that there are mm-edge graphs that require a grid of area Ω(m)\Omega(m) in any variant of EPG-representations. Similarly there are pathwidth-kk graphs that require height Ω(k)\Omega(k) and area Ω(kn)\Omega(kn) in any variant of EPG-representations. We prove a matching upper bound of O(kn)O(kn) area for all pathwidth-kk graphs in the strongest model, the one where edges are required to be both x- and y-monotone. Thus in this strongest model, the result implies, for example, O(n)O(n), O(nlogn)O(n \log n) and O(n3/2)O(n^{3/2}) area bounds for bounded pathwidth graphs, bounded treewidth graphs and all classes of graphs that exclude a fixed minor, respectively. For the model with no restrictions on the monotonicity of the edges, stronger results can be achieved for some graph classes, for example an O(n)O(n) area bound for bounded treewidth graphs and O(nlog2n)O(n \log^2 n) bound for graphs of bounded genus.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

    Low Ply Drawings of Trees

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    We consider the recently introduced model of \emph{low ply graph drawing}, in which the ply-disks of the vertices do not have many common overlaps, which results in a good distribution of the vertices in the plane. The \emph{ply-disk} of a vertex in a straight-line drawing is the disk centered at it whose radius is half the length of its longest incident edge. The largest number of ply-disks having a common overlap is called the \emph{ply-number} of the drawing. We focus on trees. We first consider drawings of trees with constant ply-number, proving that they may require exponential area, even for stars, and that they may not even exist for bounded-degree trees. Then, we turn our attention to drawings with logarithmic ply-number and show that trees with maximum degree 66 always admit such drawings in polynomial area.Comment: This is a complete access version of a paper that will appear in the proceedings of GD201

    On Upward Drawings of Trees on a Given Grid

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    Computing a minimum-area planar straight-line drawing of a graph is known to be NP-hard for planar graphs, even when restricted to outerplanar graphs. However, the complexity question is open for trees. Only a few hardness results are known for straight-line drawings of trees under various restrictions such as edge length or slope constraints. On the other hand, there exist polynomial-time algorithms for computing minimum-width (resp., minimum-height) upward drawings of trees, where the height (resp., width) is unbounded. In this paper we take a major step in understanding the complexity of the area minimization problem for strictly-upward drawings of trees, which is one of the most common styles for drawing rooted trees. We prove that given a rooted tree TT and a W×HW\times H grid, it is NP-hard to decide whether TT admits a strictly-upward (unordered) drawing in the given grid.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

    Recognizing and Drawing IC-planar Graphs

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    IC-planar graphs are those graphs that admit a drawing where no two crossed edges share an end-vertex and each edge is crossed at most once. They are a proper subfamily of the 1-planar graphs. Given an embedded IC-planar graph GG with nn vertices, we present an O(n)O(n)-time algorithm that computes a straight-line drawing of GG in quadratic area, and an O(n3)O(n^3)-time algorithm that computes a straight-line drawing of GG with right-angle crossings in exponential area. Both these area requirements are worst-case optimal. We also show that it is NP-complete to test IC-planarity both in the general case and in the case in which a rotation system is fixed for the input graph. Furthermore, we describe a polynomial-time algorithm to test whether a set of matching edges can be added to a triangulated planar graph such that the resulting graph is IC-planar

    On Smooth Orthogonal and Octilinear Drawings: Relations, Complexity and Kandinsky Drawings

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    We study two variants of the well-known orthogonal drawing model: (i) the smooth orthogonal, and (ii) the octilinear. Both models form an extension of the orthogonal, by supporting one additional type of edge segments (circular arcs and diagonal segments, respectively). For planar graphs of max-degree 4, we analyze relationships between the graph classes that can be drawn bendless in the two models and we also prove NP-hardness for a restricted version of the bendless drawing problem for both models. For planar graphs of higher degree, we present an algorithm that produces bi-monotone smooth orthogonal drawings with at most two segments per edge, which also guarantees a linear number of edges with exactly one segment.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

    Triangle-Free Penny Graphs: Degeneracy, Choosability, and Edge Count

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    We show that triangle-free penny graphs have degeneracy at most two, list coloring number (choosability) at most three, diameter D=Ω(n)D=\Omega(\sqrt n), and at most min(2nΩ(n),2nD2)\min\bigl(2n-\Omega(\sqrt n),2n-D-2\bigr) edges.Comment: 10 pages, 2 figures. To appear at the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

    Structural analysis and corrosion studies on an ISO 5832-9 biomedical alloy with TiO2 sol–gel layers

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    The aim of this study was to demonstrate the relationship between the structural and corrosion properties of an ISO 5832-9 biomedical alloy modified with titanium dioxide (TiO2) layers. These layers were obtained via the sol–gel method by acid-catalyzed hydrolysis of titanium isopropoxide in isopropanol solution. To obtain TiO2 layers with different structural properties, the coated samples were annealed at temperatures of 200, 300, 400, 450, 500, 600 and 800 C for 2 h. For all the prepared samples, accelerated corrosion measurements were performed in Tyrode’s physiological solution using electrochemical methods. The most important corrosion parameters were determined: corrosion potential, polarization resistance, corrosion rate, breakdown and repassivation potentials. Corrosion damage was analyzed using scanning electron microscopy. Structural analysis was carried out for selected TiO2 coatings annealed at 200, 400, 600 and 800 C. In addition, the morphology, chemical composition, crystallinity, thickness and density of the deposited TiO2 layers were determined using suitable electron and X-ray measurement methods. It was shown that the structure and character of interactions between substrate and deposited TiO2 layers depended on annealing temperature. All the obtained TiO2 coatings exhibit anticorrosion properties, but these properties are related to the crystalline structure and character of substrate–layer interaction. From the point of view of corrosion, the best TiO2 sol–gel coatings for stainless steel intended for biomedical applications seem to be those obtained at 400 C.This study was supported by Grant No. N N507 501339 of the National Science Centre. The authors wish to express their thanks to J. Borowski (MEDGAL, Poland) for the Rex 734 alloy

    Health promoting potential of herbal teas and tinctures from Artemisia campestris subsp maritima: from traditional remedies to prospective products

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    This work explored the biotechnological potential of the medicinal halophyte Artemisia campestris subsp. maritima (dune wormwood) as a source of health promoting commodities. For that purpose, infusions, decoctions and tinctures were prepared from roots and aerial-organs and evaluated for in vitro antioxidant, anti-diabetic and tyrosinase-inhibitory potential, and also for polyphenolic and mineral contents and toxicity. The dune wormwood extracts had high polyphenolic content and several phenolics were identified by ultra-high performance liquid chromatography-photodiode array-mass-spectrometry (UHPLC-PDA-MS). The main compounds were quinic, chlorogenic and caffeic acids, coumarin sulfates and dicaffeoylquinic acids; several of the identified phytoconstituents are here firstly reported in this A. campestris subspecies. Results obtained with this plant's extracts point to nutritional applications as mineral supplementary source, safe for human consumption, as suggested by the moderate to low toxicity of the extracts towards mammalian cell lines. The dune wormwood extracts had in general high antioxidant activity and also the capacity to inhibit a-glucosidase and tyrosinase. In summary, dune wormwood extracts are a significant source of polyphenolic and mineral constituents, antioxidants and a-glucosidase and tyrosinase inhibitors, and thus, relevant for different commercial segments like the pharmaceutical, cosmetic and/or food industries.FCT - Foundation for Science and Technology [CCMAR/Multi/04326/2013]; Portuguese National Budget; FCT [IF/00049/2012, SFRH/BD/94407/2013]; Research Foundation - Flanders (FWO) [12M8315N]info:eu-repo/semantics/publishedVersio

    Malaria mortality in Africa and Asia: evidence from INDEPTH health and demographic surveillance system sites.

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    BACKGROUND: Malaria continues to be a major cause of infectious disease mortality in tropical regions. However, deaths from malaria are most often not individually documented, and as a result overall understanding of malaria epidemiology is inadequate. INDEPTH Network members maintain population surveillance in Health and Demographic Surveillance System sites across Africa and Asia, in which individual deaths are followed up with verbal autopsies. OBJECTIVE: To present patterns of malaria mortality determined by verbal autopsy from INDEPTH sites across Africa and Asia, comparing these findings with other relevant information on malaria in the same regions. DESIGN: From a database covering 111,910 deaths over 12,204,043 person-years in 22 sites, in which verbal autopsy data were handled according to the WHO 2012 standard and processed using the InterVA-4 model, over 6,000 deaths were attributed to malaria. The overall period covered was 1992-2012, but two-thirds of the observations related to 2006-2012. These deaths were analysed by site, time period, age group and sex to investigate epidemiological differences in malaria mortality. RESULTS: Rates of malaria mortality varied by 1:10,000 across the sites, with generally low rates in Asia (one site recording no malaria deaths over 0.5 million person-years) and some of the highest rates in West Africa (Nouna, Burkina Faso: 2.47 per 1,000 person-years). Childhood malaria mortality rates were strongly correlated with Malaria Atlas Project estimates of Plasmodium falciparum parasite rates for the same locations. Adult malaria mortality rates, while lower than corresponding childhood rates, were strongly correlated with childhood rates at the site level. CONCLUSIONS: The wide variations observed in malaria mortality, which were nevertheless consistent with various other estimates, suggest that population-based registration of deaths using verbal autopsy is a useful approach to understanding the details of malaria epidemiology
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