Métodos heurísticos en problemas geométricos. visibilidad, iluminación y vigilancia

Dentro de la Geometría Computacional, uno de los campos que ha suscitado mayor interés entre la comunidad científica internacional ha sido el de la Visibilidad, es decir, el conjunto de problemas que están relacionados con los conceptos de iluminación y vigilancia de estructuras geométricas, con todas sus posibles variantes. Los resultados obtenidos en este ámbito por los investigadores, se pueden aplicar en algunos casos para solucionar problemas industriales reales relacionados con la iluminación o vigilancia,tales como iluminación de calles o de naves comerciales. Sin embargo, en muchas otras ocasiones, los elementos físicos reales que existen en la actualidad, discrepan en algún sentido de los modelos teóricos utilizados, con lo cual los resultados obtenido no son aplicables. Por ello, es necesario utilizar definiciones de visibilidad o iluminación que se acerquen cada vez más a situaciones reales. Siguiendo este objetivo, presentamos en la primera parte de esta memoria resultados combinatorios y algorítmicos utilizando dos definiciones de iluminación que añaden condiciones a los conceptos de vigilancia utilizados tradicionalmente: la primera de estas definiciones fue presentada por Ntafos en 1992, se denomina visibilidad de alcance limitado y añade una restricción a la distancia máxima de iluminación desde un determinado punto; la segunda que hemos denominado t−buena iluminación, se presenta en esta memoria por primera vez y su idea fundamental se basa en que una estructura geométrica sólo está bien iluminada si todos los puntos que la iluminan están bien distribuidos alrededor de ella. Respecto a la visibilidad de alcance limitado presentamos resultados combinatorios para polígonos escalera y polígonos pirámide, mientras para la t−buena iluminación presentamos resultados algoritmos que permiten calcular las regiones iluminadas con esta definición, por luces situadas en diferentes posiciones respecto a un polígono P. Por otra parte existen problemas en el ámbito de la Geometría Computacional que o bien son de naturaleza NP-dura, o bien no se han encontrado hasta el momento algoritmos eficientes que los solucionen. Sin embargo, en ambos casos, puede existir la necesidad real de aportar respuestas a dichos problemas, aunque dichas respuestas sean aproximadas o heurísticas. Así, en la segunda parte de esta memoria, presentamos procedimientos metaheurísticos que abordan problemas con estas características. Esquemáticamente se han abordado dos problemas.El primero de ellos es el problema de minimización del número de luces que iluminan un polígono P, cuya naturaleza NP-dura fue demostrada por Lee y Lin en 1964 y el segundo es el problema de la búsqueda de un nuevo punto en un Diagrama de Voronoi dado, tal que la región asociada a este nuevo punto tenga área máxima en el nuevo Diagrama de Voronoi construido. Para este segundo problema no se han encontrado hasta el momento soluciones algorítmicas eficientes que lo solucionen cuando los puntos se encuentran en posición general, aunque recientemene se han presentado soluciones para puntos situados en posición convexa. Para atacar heurísticamente el primero de estos problemas necesitamos solucionar previamente el problema de la búsqueda del conjunto de k luces, con k ≥ 1, cuyo área conjunta iluminada en el interior de un polígono P sea máxima. Este problema que se analiza por separado para el caso k = 1 y k > 1 constituye el contenido fundamental de la segunda parte de esta memoria

Minimum Vertex Guard problem for orthogonal polygons: a genetic approach

The problem of minimizing the number of guards placed on vertices needed to guard a given simple polygon (MINIMUM VERTEX GUARD problem) is NP-hard. This computational complexity opens two lines of investigation: the development of algorithms that determine approximate solutions and the determination of optimal solutions for special classes of simple polygons. In this paper we follow the first line of investigation proposing an approximation algorithm based on the general met heuristic Genetic Algorithms to solve the MINIMUM VERTEXGUARD problem

Estimating the Maximum Hidden Vertex Set in Polygons

It is known that the MAXIMUM HIDDEN VERTEX SET problem on a given simple polygon is NP-hard [11], therefore we focused on the development of approximation algorithms to tackle it. We propose four strategies to solve this problem, the first two (based on greedy constructive search) are designed specifically to solve it, and the other two are based on the general metaheuristics Simulated Annealing and Genetic Algorithms. We conclude, through experimentation, that our best approximate algorithm is the one based on the Simulated Annealing metaheuristic. The solutions obtained with it are very satisfactory in the sense that they are always close to optimal (with an approximation ratio of 1.7, for arbitrary polygons; and with an approximation ratio of 1.5, for orthogonal polygons). We, also, conclude, that on average the maximum number of hidden vertices in a simple polygon (arbitrary or orthogonal) with n vertices is n4

Solving the minimum vertex floodlight problem with hybrid metaheuristics

In this paper we propose four approximation algorithms (metaheuristic based), for the Minimum Vertex Floodlight Set problem. Urrutia et al. [9] solved the combinatorial problem, although it is strongly believed that the algorithmic problem is NP-hard. We conclude that, on average, the minimum number of vertex floodlights needed to illuminate a orthogonal polygon with n vertices is n/4,29

Escondiendo puntos en espirales e histogramas

El problema de maximizar el número de vértices que no son visibles dos a dos en un polígono simple P, (MAXIMUN HIDDEN VERTEX SET) es un problema NP-duro [6]. En este trabajo se resuelve el problema para dos tipos de polígonos: espirales e histogramas. Para los primeros se obtiene un algoritmo lineal que resuelve el problema MHVS y cotas para el máximo número h de vértices ocultos, [r2 ]+ 1 ≤ h ≤ r + 1, siendo r el número de vértices cóncavos del polígono espiral. Para polígonos histograma se demuestra que h = r − (p − 1), siendo p el número de lados fondo

Connecting red cells in a bichromatic Voronoi diagram

Let S be a set of n + m sites, of which n are red and have weight wR, and m are blue and weigh wB. The objective of this paper is to calculate the minimum value of wR such that the union of the red Voronoi cells in the weighted Voronoi diagram of S is a connected set. The problem is solved for the multiplicatively-weighted Voronoi diagram in O((n+m)^2 log(nm)) time and for the additively-weighted Voronoi diagram in O(nmlog(nm)) time

Distance domination, guarding and vertex cover for maximal outerplanar graphs

In this paper we de ne a distance guarding concept on plane graphs and associate this concept with distance domination and distance vertex cover concepts on triangulation graphs. Furthermore, for any n-vertex maximal outerplanar graph, we provide tight upper bounds for g2d(n) (2d-guarding number), γ2d(n) (2d-domination number) and β2d(n) (2d-vertex cover number).European Science FoundationMinisterio de Ciencia e InnovaciónFundação para a Ciência e a TecnologiaFondo Europeo de Desarrollo Regiona

Some results on open edge guarding of polygons

This paper focuses on a variation of the Art Gallery problem that considers open edge guards. The “open” prefix means the endpoints of an edge where a guard is are not taken into account for visibility purposes. This paper studies the number of open edge guards that are sufficient and sometimes necessary to guard some classes of simple polygons.Fondo Europeo de Desarrollo RegionalEuropean Science FoundationMinisterio de Ciencia e InnovaciónFundação para a Ciência e a Tecnologi

Effects of hospital facilities on patient outcomes after cancer surgery: an international, prospective, observational study

Background Early death after cancer surgery is higher in low-income and middle-income countries (LMICs) compared with in high-income countries, yet the impact of facility characteristics on early postoperative outcomes is unknown. The aim of this study was to examine the association between hospital infrastructure, resource availability, and processes on early outcomes after cancer surgery worldwide.Methods A multimethods analysis was performed as part of the GlobalSurg 3 study-a multicentre, international, prospective cohort study of patients who had surgery for breast, colorectal, or gastric cancer. The primary outcomes were 30-day mortality and 30-day major complication rates. Potentially beneficial hospital facilities were identified by variable selection to select those associated with 30-day mortality. Adjusted outcomes were determined using generalised estimating equations to account for patient characteristics and country-income group, with population stratification by hospital.Findings Between April 1, 2018, and April 23, 2019, facility-level data were collected for 9685 patients across 238 hospitals in 66 countries (91 hospitals in 20 high-income countries; 57 hospitals in 19 upper-middle-income countries; and 90 hospitals in 27 low-income to lower-middle-income countries). The availability of five hospital facilities was inversely associated with mortality: ultrasound, CT scanner, critical care unit, opioid analgesia, and oncologist. After adjustment for case-mix and country income group, hospitals with three or fewer of these facilities (62 hospitals, 1294 patients) had higher mortality compared with those with four or five (adjusted odds ratio [OR] 3.85 [95% CI 2.58-5.75]; p<0.0001), with excess mortality predominantly explained by a limited capacity to rescue following the development of major complications (63.0% vs 82.7%; OR 0.35 [0.23-0.53]; p<0.0001). Across LMICs, improvements in hospital facilities would prevent one to three deaths for every 100 patients undergoing surgery for cancer.Interpretation Hospitals with higher levels of infrastructure and resources have better outcomes after cancer surgery, independent of country income. Without urgent strengthening of hospital infrastructure and resources, the reductions in cancer-associated mortality associated with improved access will not be realised

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