Mixed Linear Layouts of Planar Graphs

A $k$-stack (respectively, $k$-queue) layout of a graph consists of a total order of the vertices, and a partition of the edges into $k$ sets of non-crossing (non-nested) edges with respect to the vertex ordering. In 1992, Heath and Rosenberg conjectured that every planar graph admits a mixed $1$-stack $1$-queue layout in which every edge is assigned to a stack or to a queue that use a common vertex ordering. We disprove this conjecture by providing a planar graph that does not have such a mixed layout. In addition, we study mixed layouts of graph subdivisions, and show that every planar graph has a mixed subdivision with one division vertex per edge.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Compact Drawings of 1-Planar Graphs with Right-Angle Crossings and Few Bends

We study the following classes of beyond-planar graphs: 1-planar, IC-planar, and NIC-planar graphs. These are the graphs that admit a 1-planar, IC-planar, and NIC-planar drawing, respectively. A drawing of a graph is 1-planar if every edge is crossed at most once. A 1-planar drawing is IC-planar if no two pairs of crossing edges share a vertex. A 1-planar drawing is NIC-planar if no two pairs of crossing edges share two vertices. We study the relations of these beyond-planar graph classes (beyond-planar graphs is a collective term for the primary attempts to generalize the planar graphs) to right-angle crossing (RAC) graphs that admit compact drawings on the grid with few bends. We present four drawing algorithms that preserve the given embeddings. First, we show that every $n$-vertex NIC-planar graph admits a NIC-planar RAC drawing with at most one bend per edge on a grid of size $O(n) \times O(n)$. Then, we show that every $n$-vertex 1-planar graph admits a 1-planar RAC drawing with at most two bends per edge on a grid of size $O(n^3) \times O(n^3)$. Finally, we make two known algorithms embedding-preserving; for drawing 1-planar RAC graphs with at most one bend per edge and for drawing IC-planar RAC graphs straight-line

Simultaneous Embeddings with Few Bends and Crossings

A simultaneous embedding with fixed edges (SEFE) of two planar graphs $R$ and $B$ is a pair of plane drawings of $R$ and $B$ that coincide when restricted to the common vertices and edges of $R$ and $B$. We show that whenever $R$ and $B$ admit a SEFE, they also admit a SEFE in which every edge is a polygonal curve with few bends and every pair of edges has few crossings. Specifically: (1) if $R$ and $B$ are trees then one bend per edge and four crossings per edge pair suffice (and one bend per edge is sometimes necessary), (2) if $R$ is a planar graph and $B$ is a tree then six bends per edge and eight crossings per edge pair suffice, and (3) if $R$ and $B$ are planar graphs then six bends per edge and sixteen crossings per edge pair suffice. Our results improve on a paper by Grilli et al. (GD'14), which proves that nine bends per edge suffice, and on a paper by Chan et al. (GD'14), which proves that twenty-four crossings per edge pair suffice.Comment: Full version of the paper "Simultaneous Embeddings with Few Bends and Crossings" accepted at GD '1

Hierarchical Partial Planarity

In this paper we consider graphs whose edges are associated with a degree of {\em importance}, which may depend on the type of connections they represent or on how recently they appeared in the scene, in a streaming setting. The goal is to construct layouts of these graphs in which the readability of an edge is proportional to its importance, that is, more important edges have fewer crossings. We formalize this problem and study the case in which there exist three different degrees of importance. We give a polynomial-time testing algorithm when the graph induced by the two most important sets of edges is biconnected. We also discuss interesting relationships with other constrained-planarity problems.Comment: Conference version appeared in WG201

Recognizing and Drawing IC-planar Graphs

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 $G$ with $n$ vertices, we present an $O(n)$-time algorithm that computes a straight-line drawing of $G$ in quadratic area, and an $O(n^3)$-time algorithm that computes a straight-line drawing of $G$ 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 Embeddability of Buses in Point Sets

Set membership of points in the plane can be visualized by connecting corresponding points via graphical features, like paths, trees, polygons, ellipses. In this paper we study the \emph{bus embeddability problem} (BEP): given a set of colored points we ask whether there exists a planar realization with one horizontal straight-line segment per color, called bus, such that all points with the same color are connected with vertical line segments to their bus. We present an ILP and an FPT algorithm for the general problem. For restricted versions of this problem, such as when the relative order of buses is predefined, or when a bus must be placed above all its points, we provide efficient algorithms. We show that another restricted version of the problem can be solved using 2-stack pushall sorting. On the negative side we prove the NP-completeness of a special case of BEP.Comment: 19 pages, 9 figures, conference version at GD 201

PENGARUH PENAMBAHAN LENSA NOZZLE DAN JUMLAH BLADE AIRFOIL TIPE NACA 4415 TERHADAP HASIL DAYA LISTRIK TURBIN ANGIN SUMBU HORISONTAL

Danur Lambang Pristiandaru. PENGARUH PENAMBAHAN LENSA NOZZLE TURBIN ANGIN DAN JUMLAH BLADE AIRFOIL TIPE NACA 4415 TERHADAP HASIL DAYA LISTRIK. Skripsi, Fakultas Keguruan dan Ilmu Pendidikan Universitas Sebelas Maret Surakarta. Januari 2016 Tujuan penelitian ini adalah: (1) Menyelidiki pengaruh jumlah blade pada turbin angin non-twisted blade tipe airfoil NACA 4415 terhadap daya listrik yang dihasilkan. (2) Menyelidiki pengaruh penambahan lensa nozzle pada turbin angin non-twisted blade tipe airfoil NACA 4415 terhadap daya listrik yang dihasilkan turbin angin. (3) Menyelidiki pengaruh bersama (interaksi) antara penambahan lensa nozzle dan jumlah blade terhadap daya listrik yang dihasilkan turbin angin. Penelitian ini menggunakan metode deskriptif kuantitatif. Sampel dalam penelitian ini adalah Turbin Angin Sumbu Horisontal (TASH) dengan desain blade airfoil NACA 4415 non-twisted. 3 desain lensa nozzle digunakan untuk mengetahui pengaruhnya terhadap peningkatan daya listrik TASH. Terdapat 3 variasi jumlah blade yaitu jumlah blade 2, jumlah blade 3, dan jumlah blade 4. Variasi kecepatan angin yang digunakan dalam penelitian ini adalah 2,5 m/s, 3,5 m/s, dan 4,5 m/s. Data diperoleh dengan melakukan pengujian TASH menggunakan angin rekayasa, daya listrik yang dihasilkan dibaca dan direkam oleh data logger. Data yang diperoleh dari hasil penelitian dimasukkan ke dalam tabel dan ditampilkan dalam bentuk grafik, kemudian dianalisis. Berdasarkan hasil penelitian dapat disimpulkan bahwa: (1) Adanya pengaruh variasi jumlah blade terhadap daya listrik turbin angin. TASH 3 blade menghasilkan daya listrik yang paling besar yaitu 0,7222 W pada kecepatan angin 4,5 m/s. (2) Adanya pengaruh penambahan lensa nozzle terhadap turbin angin. Lensa nozzle mampu meningkatkan hasil daya listrik turbin angin semua jenis variasi jumlah blade dibandingkan turbin angin tanpa lensa nozzle. (3) Ada pengaruh bersama yang signifikan antara variasi jumlah blade dan variasi jenis lensa terhadap daya listrik turbin angin. TASH 3 blade dengan lensa C pada kecepatan angin 4,5 m/s memiliki daya listrik tertinggi yaitu sebesar 0,82041 W. Daya listrik tersebut meningkat 13,60% dibanding TASH 3 blade tanpa penambahan lensa, yaitu 0,7222 W. Kata kunci: Turbin Angin, Lensa Nozzle, Daya Listrik, Data Logge

Improved Approximation Algorithms for Box Contact Representations

We study the following geometric representation problem: Given a graph whose vertices correspond to axis-aligned rectangles with fixed dimensions, arrange the rectangles without overlaps in the plane such that two rectangles touch if the graph contains an edge between them. This problem is called Contact Representation of Word Networks (Crown) since it formalizes the geometric problem behind drawing word clouds in which semantically related words are close to each other. Crown is known to be NP-hard, and there are approximation algorithms for certain graph classes for the optimization version, Max-Crown, in which realizing each desired adjacency yields a certain profit. We present the first O(1)-approximation algorithm for the general case, when the input is a complete weighted graph, and for the bipartite case. Since the subgraph of realized adjacencies is necessarily planar, we also consider several planar graph classes (namely stars, trees, outerplanar, and planar graphs), improving upon the known results. For some graph classes, we also describe improvements in the unweighted case, where each adjacency yields the same profit. Finally, we show that the problem is APX-complete on bipartite graphs of bounded maximum degree. © 2016, Springer Science+Business Media New York

Is prolonged infusion of piperacillin/tazobactam and meropenem in critically ill patients associated with improved pharmacokinetic/pharmacodynamic and patient outcomes? An observation from the Defining Antibiotic Levels in Intensive care unit patients (DALI) cohort

Objectives:We utilized the database of the Defining Antibiotic Levels in Intensive care unit patients (DALI) study to statistically compare the pharmacokinetic/pharmacodynamic and clinical outcomes between prolonged-infusion and intermittent-bolus dosing of piperacillin/tazobactam and meropenem in critically ill patients using inclusion criteria similar to those used in previous prospective studies.Methods: This was a post hoc analysis of a prospective, multicentre pharmacokinetic point-prevalence study (DALI), which recruited a large cohort of critically ill patients from 68 ICUs across 10 countries.Results: Of the 211 patients receiving piperacillin/tazobactam and meropenem in the DALI study, 182 met inclusion criteria. Overall, 89.0% (162/182) of patients achieved the most conservative target of 50% fT(> MIC) (time over which unbound or free drug concentration remains above the MIC). Decreasing creatinine clearance and the use of prolonged infusion significantly increased the PTA for most pharmacokinetic/pharmacodynamic targets. In the subgroup of patients who had respiratory infection, patients receiving beta-lactams via prolonged infusion demonstrated significantly better 30 day survival when compared with intermittent-bolus patients [86.2% (25/29) versus 56.7% (17/30); P=0.012]. Additionally, in patients with a SOFA score of >= 9, administration by prolonged infusion compared with intermittent-bolus dosing demonstrated significantly better clinical cure [73.3% (11/15) versus 35.0% (7/20); P=0.035] and survival rates [73.3% (11/15) versus 25.0% (5/20); P=0.025].Conclusions: Analysis of this large dataset has provided additional data on the niche benefits of administration of piperacillin/tazobactam and meropenem by prolonged infusion in critically ill patients, particularly for patients with respiratory infections

Prevalence, associated factors and outcomes of pressure injuries in adult intensive care unit patients: the DecubICUs study

Funder: European Society of Intensive Care Medicine; doi: http://dx.doi.org/10.13039/501100013347Funder: Flemish Society for Critical Care NursesAbstract: Purpose: Intensive care unit (ICU) patients are particularly susceptible to developing pressure injuries. Epidemiologic data is however unavailable. We aimed to provide an international picture of the extent of pressure injuries and factors associated with ICU-acquired pressure injuries in adult ICU patients. Methods: International 1-day point-prevalence study; follow-up for outcome assessment until hospital discharge (maximum 12 weeks). Factors associated with ICU-acquired pressure injury and hospital mortality were assessed by generalised linear mixed-effects regression analysis. Results: Data from 13,254 patients in 1117 ICUs (90 countries) revealed 6747 pressure injuries; 3997 (59.2%) were ICU-acquired. Overall prevalence was 26.6% (95% confidence interval [CI] 25.9–27.3). ICU-acquired prevalence was 16.2% (95% CI 15.6–16.8). Sacrum (37%) and heels (19.5%) were most affected. Factors independently associated with ICU-acquired pressure injuries were older age, male sex, being underweight, emergency surgery, higher Simplified Acute Physiology Score II, Braden score 3 days, comorbidities (chronic obstructive pulmonary disease, immunodeficiency), organ support (renal replacement, mechanical ventilation on ICU admission), and being in a low or lower-middle income-economy. Gradually increasing associations with mortality were identified for increasing severity of pressure injury: stage I (odds ratio [OR] 1.5; 95% CI 1.2–1.8), stage II (OR 1.6; 95% CI 1.4–1.9), and stage III or worse (OR 2.8; 95% CI 2.3–3.3). Conclusion: Pressure injuries are common in adult ICU patients. ICU-acquired pressure injuries are associated with mainly intrinsic factors and mortality. Optimal care standards, increased awareness, appropriate resource allocation, and further research into optimal prevention are pivotal to tackle this important patient safety threat