<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>1692-3324</journal-id>
<journal-title><![CDATA[Revista Ingenierías Universidad de Medellín]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. ing. univ. Medellín]]></abbrev-journal-title>
<issn>1692-3324</issn>
<publisher>
<publisher-name><![CDATA[Universidad de Medellín]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1692-33242021000200115</article-id>
<article-id pub-id-type="doi">10.22395/rium.v20n39a7</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[A Look at Algorithm BEPtoPNST]]></article-title>
<article-title xml:lang="es"><![CDATA[Una mirada al algoritmo BEPtoPNST]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[García-Ojeda]]></surname>
<given-names><![CDATA[Juan C.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de Cartagena Facultad de Ingeniería ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2021</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2021</year>
</pub-date>
<volume>20</volume>
<numero>39</numero>
<fpage>115</fpage>
<lpage>128</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S1692-33242021000200115&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S1692-33242021000200115&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S1692-33242021000200115&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract This work analyzes the computational complexity of algorithm BEPtoPNS  T which transforms a building-evacuation problem (BEP) into a time-expanded, process-network synthesis (PNS  T ) problem. The solution of the latter is achieved by resorting to the P-graph method which exploits the combinatorial nature of a BEP. Unlike other approaches, the P-graph method provides not only the optimal solution (best evacuation route as a function of egress time), but also the best n sub-optimal solutions. For the complexity analysis, a generic processor, and a Random-access machine (RAM) model were deployed as well as a mathematical model to calculate the number and cost of the operations performed. It was observed that algorithm BEPtoPNS  T exhibits an asymptotic complexity of order O ( T | A | (| N | -k)). When solving a BEP, however, the total complexity grows exponentially with order O (T | A | (| N | -k)) + O (2 h )) in the worst case; where h represents the total number of operating units specified in the corresponding PNS  T problem. Nevertheless, the computational complexity can be reduced significantly when the P-graph method is deployed.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen El presente trabajo estudia y analiza la complejidad computacional, en el peor de los casos, del algoritmo BEPtoPNS  T . El objetivo de BEPtoPNS  T es transformar problemas de rutas de evacuación en edificios (Building- -Evacuation Problems, BEP) en problemas de síntesis de redes procesos de tiempo extendido (Time-Extended, Process-Network Synthesis, PNS T ), los cuales se solucionan por medio del método P-graph. La relevancia de analizar el algoritmo BEPtoPNS  T se sustenta en el hecho que el método P-graph explota la naturaleza combinatoria de un BEP luego de ser transformado en un PNS  T . El método P-graph no sólo provee la solución óptima (mejor ruta de evacuación en función del tiempo de egreso), sino que también provee las mejores n soluciones subóptimas; característica que a la fecha no ofrecen otros métodos de optimización. Para el análisis del algoritmo BEPtoNPS  T , se consideró un procesador genérico, el modelo Random-access machine, RAM, así como un modelo matemático para calcular el número de operaciones ejecutadas y sus costos, resultando en una complejidad asintótica de orden O ( T | A | (| N | -k)). Sin embargo, la complejidad total del proceso, incluyendo el método P-graph, crece de manera exponencial, es decir, O (T | A | (| N | -k)) + O (2 N )), en el peor de los casos.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[building-evacuation routes]]></kwd>
<kwd lng="en"><![CDATA[process-network synthesis]]></kwd>
<kwd lng="en"><![CDATA[rigorous structures]]></kwd>
<kwd lng="en"><![CDATA[combinatorial optimization]]></kwd>
<kwd lng="en"><![CDATA[P-graph]]></kwd>
<kwd lng="en"><![CDATA[pseudocode]]></kwd>
<kwd lng="en"><![CDATA[RAM model]]></kwd>
<kwd lng="en"><![CDATA[algorithm complexity]]></kwd>
<kwd lng="en"><![CDATA[asymptotic notation]]></kwd>
<kwd lng="en"><![CDATA[Big-O]]></kwd>
<kwd lng="es"><![CDATA[rutas de evacuación en edificios]]></kwd>
<kwd lng="es"><![CDATA[síntesis de redes de procesos]]></kwd>
<kwd lng="es"><![CDATA[estructuras rigurosas]]></kwd>
<kwd lng="es"><![CDATA[optimización combinatoria]]></kwd>
<kwd lng="es"><![CDATA[P-graph]]></kwd>
<kwd lng="es"><![CDATA[pseudocódigo]]></kwd>
<kwd lng="es"><![CDATA[modelo RAM]]></kwd>
<kwd lng="es"><![CDATA[complejidad de algoritmos]]></kwd>
<kwd lng="es"><![CDATA[notación asintótica]]></kwd>
<kwd lng="es"><![CDATA[O grande]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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