Pole Dancing: 3D Morphs for Tree Drawings

We study the question whether a crossing-free 3D morph between two straight-line drawings of an $n$-vertex tree can be constructed consisting of a small number of linear morphing steps. We look both at the case in which the two given drawings are two-dimensional and at the one in which they are three-dimensional. In the former setting we prove that a crossing-free 3D morph always exists with $O(\log n)$ steps, while for the latter $\Theta(n)$ steps are always sufficient and sometimes necessary.Comment: Appears in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018

Euclidean Greedy Drawings of Trees

Greedy embedding (or drawing) is a simple and efficient strategy to route messages in wireless sensor networks. For each source-destination pair of nodes s, t in a greedy embedding there is always a neighbor u of s that is closer to t according to some distance metric. The existence of greedy embeddings in the Euclidean plane R^2 is known for certain graph classes such as 3-connected planar graphs. We completely characterize the trees that admit a greedy embedding in R^2. This answers a question by Angelini et al. (Graph Drawing 2009) and is a further step in characterizing the graphs that admit Euclidean greedy embeddings.Comment: Expanded version of a paper to appear in the 21st European Symposium on Algorithms (ESA 2013). 24 pages, 20 figure

Application of Queuing Analytic Theory to Decrease Waiting Times in Emergency Department: Does it Make Sense?

Background: Patients who receive care in an emergency department (ED), are usually unattended while waiting in queues. Objectives: This study was done to determine, whether the application of queuing theory analysis might shorten the waiting times of patients admitted to emergency wards. Patients and Methods: This was an operational study to use queuing theory analysis in the ED. In the first phase, a field study was conducted to delineate the performance of the ED and enter the data obtained into simulator software. In the second phase, "ARENA" software was used for modeling, analysis, creating a simulation and improving the movement of patients in the ED. Validity of the model was confirmed through comparison of the results with the real data using the same instrument. The third phase of the study concerned modeling in order to assess the effect of various operational strategies, on the queue waiting time of patients who were receiving care in the ED. Results: In the first phase, it was shown that 47.7% of the 3000 patient records were cases referred for trauma treatment, and the remaining 52.3% were referred for non-trauma services. A total of 56% of the cases were male and 44% female. Maximum input was 4.5 patients per hour and the minimum input was 0.5 per hour. The average length of stay for patients in the trauma section was three hours, while for the non-trauma section it was four hours. In the second phase, modeling was tested with common scenarios. In the third phase, the scenario with the addition of one or more senior emergency resident(s) on each shift resulted in a decreased length of stay from 4 to 3.75 hours. Moreover, the addition of one bed to the Intensive Care Unit (ICU) and/or Critical Care Unit (CCU) in the study hospital, reduced the occupancy rate of the nursing service from 76% to 67%. By adding another clerk to take electrocardiograms (ECG) in the ED, the average time from a request to performing the procedure is reduced from 26 to 18 minutes. Furthermore, the addition of 50% more staff to the laboratory and specialist consultations led to a 90 minute reduction in the length of stay. It was also shown that earlier consultations had no effect on the length of stay. Conclusions: Application of queuing theory analysis can improve movement and reduce the waiting times of patients in bottlenecks within the ED throughput

Gabriel Triangulations and Angle-Monotone Graphs: Local Routing and Recognition

A geometric graph is angle-monotone if every pair of vertices has a path between them that---after some rotation---is $x$- and $y$-monotone. Angle-monotone graphs are $\sqrt 2$-spanners and they are increasing-chord graphs. Dehkordi, Frati, and Gudmundsson introduced angle-monotone graphs in 2014 and proved that Gabriel triangulations are angle-monotone graphs. We give a polynomial time algorithm to recognize angle-monotone geometric graphs. We prove that every point set has a plane geometric graph that is generalized angle-monotone---specifically, we prove that the half-$\theta_6$-graph is generalized angle-monotone. We give a local routing algorithm for Gabriel triangulations that finds a path from any vertex $s$ to any vertex $t$ whose length is within $1 + \sqrt 2$ times the Euclidean distance from $s$ to $t$. Finally, we prove some lower bounds and limits on local routing algorithms on Gabriel triangulations.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

Convexity-Increasing Morphs of Planar Graphs

We study the problem of convexifying drawings of planar graphs. Given any planar straight-line drawing of an internally 3-connected graph, we show how to morph the drawing to one with strictly convex faces while maintaining planarity at all times. Our morph is convexity-increasing, meaning that once an angle is convex, it remains convex. We give an efficient algorithm that constructs such a morph as a composition of a linear number of steps where each step either moves vertices along horizontal lines or moves vertices along vertical lines. Moreover, we show that a linear number of steps is worst-case optimal. To obtain our result, we use a well-known technique by Hong and Nagamochi for finding redrawings with convex faces while preserving y-coordinates. Using a variant of Tutte's graph drawing algorithm, we obtain a new proof of Hong and Nagamochi's result which comes with a better running time. This is of independent interest, as Hong and Nagamochi's technique serves as a building block in existing morphing algorithms.Comment: Preliminary version in Proc. WG 201

Greedy Rectilinear Drawings

A drawing of a graph is greedy if for each ordered pair of vertices u and v, there is a path from u to v such that the Euclidean distance to v decreases monotonically at every vertex of the path. The existence of greedy drawings has been widely studied under different topological and geometric constraints, such as planarity, face convexity, and drawing succinctness. We introduce greedy rectilinear drawings, in which each edge is either a horizontal or a vertical segment. These drawings have several properties that improve human readability and support network routing. We address the problem of testing whether a planar rectilinear representation, i.e., a plane graph with specified vertex angles, admits vertex coordinates that define a greedy drawing. We provide a characterization, a linear-time testing algorithm, and a full generative scheme for universal greedy rectilinear representations, i.e., those for which every drawing is greedy. For general greedy rectilinear representations, we give a combinatorial characterization and, based on it, a polynomial-time testing and drawing algorithm for a meaningful subset of instances.Comment: Appears in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018

Upward Planar Morphs

We prove that, given two topologically-equivalent upward planar straight-line drawings of an $n$-vertex directed graph $G$, there always exists a morph between them such that all the intermediate drawings of the morph are upward planar and straight-line. Such a morph consists of $O(1)$ morphing steps if $G$ is a reduced planar $st$-graph, $O(n)$ morphing steps if $G$ is a planar $st$-graph, $O(n)$ morphing steps if $G$ is a reduced upward planar graph, and $O(n^2)$ morphing steps if $G$ is a general upward planar graph. Further, we show that $\Omega(n)$ morphing steps might be necessary for an upward planar morph between two topologically-equivalent upward planar straight-line drawings of an $n$-vertex path.Comment: Appears in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018) The current version is the extended on

Oxidative stress and its association with ST resolution and clinical outcome measures in patients with ST-segment elevation myocardial infarction (STEMI) undergoing primary percutaneous coronary intervention

Objective: Reperfusion of ischemic myocardium generates oxidative stress, which itself can mediate myocardial injury. So, in this study, we investigated the level of oxidative stress markers and its association with clinical outcomes in patients with ST-segment elevation myocardial infarction (STEMI) undergoing primary percutaneous coronary intervention. Results: As indicated in the results, Post MI (Myocardial Infarction) heart failure was significantly higher in the group A (11 vs 4, p = 0.047). Complete STR (ST-segment resolution) was observed to be significantly higher in the group B (36 vs 17, p = 0.006). The SOD (Superoxide dismutase) and GPX (Glutathione peroxidase) levels were significantly higher in the group B compared to the other group (1547.51 ± 328.29 vs. 1449.97 ± 246.06, p = 0.019 and 60.62 ± 11.95 vs 57.41 ± 10.14, p = 0.042). The levels of GPX and SOD were shown to be directly related with complete STR and post PCI (Percutaneous coronary intervention)TIMI(Thrombolysis in Myocardial Infarction) flow 3 in the group A (p = 0.002 and p < 0.01, p = 0.005 and p < 0.02, respectively). © 2020, The Author(s)

An analytic network process model to prioritize supply chain risks in green residential megaprojects

Megaprojects and specifically ‘green’ construction of residential megaprojects can contain significant risks of failure. To design proper risk mitigation strategies, after identifying key risk factors, the next step is to conduct assessments that would facilitate the process of risk element prioritization. Risk assessment comprises the establishment of factor interrelation and discerning the indicators of importance. This research proposes a novel version of an integrated prioritization method and analyzes twelve all-inclusive key supply chain oriented risk factors identified in a previous study. Through a comprehensive literature review three criteria, impact, probability, and manageability are selected. Also, a fourth criterion namely influence rate is included in the model, based on the driving powers that can also be derived from the Interpretive Structural Modeling’s (ISM) assessment. Fundamentally, the calculations hinge on the Analytic Network Process (ANP) method which provides an assessment of the alternatives’ weights based on pairwise comparisons concerning the criteria specified. To enhance the accuracy of the perceptive judgments of the expert panelists, a bell-shaped fuzzy function is used to convert the verbal statements to crisp values. In addition, Row Sensitivity Analysis is administered to check the stability of the results and provide predictive scenarios. To validate the model, a case study, located in Iran, was conducted, where an expert panel consisting of four individuals made the pair-wise comparisons through an ANP questionnaire. Results indicate priority and sensitivity of the alternatives concerning criteria, for the case under study