Aplicaciones de la Teoría de Grafos a la Vida Real (I)

Brought by: edX

Overview

Este curso trata la Teoría de Grafos desde el punto de vista de la modelización, lo que nos permitirá con posterioridad resolver muchos problemas de diversa índole. Presentaremos ejemplos de los distintos problemas en un contexto real, analizaremos la representación de éstos mediante grafos y veremos los algoritmos necesarios para resolverlos.

Resolveremos problemas que aparecen en la logística, la robótica, la genética, la sociología, el diseño de redes y el cálculo de rutas óptimas, mediante el uso de la Teoría de Grafos. Nuestro objetivo será presentar tanto los contenidos de la misma como la modelización de los casos planteados.

En cada tema comenzaremos presentando el problema a resolver. Posteriormente introduciremos la teoría y los algoritmos correspondientes, modelizaremos el problema propuesto y finalmente hallaremos su solución. En general explicaremos en qué consiste y cómo se deduce cada algoritmo, haciendo para ello una traza a modo de ejemplo.

Las unidades del curso son:

Unidad 1: Conceptos básicos de la Teoría de Grafos

Unidad 2: Accesibilidad

Unidad 3: Grafos ponderados

Unidad 4: Árboles

Los contenidos de este curso fueron reconocidos con una Mención Especial del I Premio Ministerio de Educación, Cultura y Deportes (España) – Telefónica L.S. - Universia a la iniciativa de MOOC's en MiríadaX.

Taught by

Dra. Cristina Jordán Lluch and Dr. José Alberto Conejero Casares

Aplicaciones de la Teoría de Grafos a la Vida Real (I)
Go to course

Aplicaciones de la Teoría de Grafos a la Vida Real (I)

Brought by: edX

  • edX
  • Free
  • English
  • Certificate Available
  • Certain days
  • intermediate
  • Spanish
8.1.2PHP Version411msRequest Duration2MBMemory UsageGET en/courses/{slug}Route
    • Booting (260ms)
    • Application (150ms)
    • 1 x Booting (63.23%)
      260.08ms
      1 x Application (36.54%)
      150.30ms
      14 templates were rendered
      • public.courses.show (resources/views/public/courses/show.blade.php)3bladefile
        Params
        0
        course
        1
        links
        2
        config
      • public.courses.partials.breadcrumbs (resources/views/public/courses/partials/breadcrumbs.blade.php)6bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
      • public.courses.partials.heading (resources/views/public/courses/partials/heading.blade.php)7bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
        6
        classes
      • public.courses.partials.details (resources/views/public/courses/partials/details.blade.php)6bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
      • public.courses.partials.breadcrumbs (resources/views/public/courses/partials/breadcrumbs.blade.php)6bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
      • public.courses.partials.heading (resources/views/public/courses/partials/heading.blade.php)7bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
        6
        classes
      • public.layouts.main (resources/views/public/layouts/main.blade.php)6bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
      • public.layouts.partials.meta (resources/views/public/layouts/partials/meta.blade.php)6bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
      • public.layouts.partials.navbar (resources/views/public/layouts/partials/navbar.blade.php)6bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
      • public.auth.profile.partials.links (resources/views/public/auth/profile/partials/links.blade.php)6bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
      • public.auth.profile.partials.link (resources/views/public/auth/profile/partials/link.blade.php)8bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
        6
        route
        7
        title
      • public.auth.profile.partials.link (resources/views/public/auth/profile/partials/link.blade.php)8bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
        6
        route
        7
        title
      • public.auth.profile.partials.link (resources/views/public/auth/profile/partials/link.blade.php)8bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
        6
        route
        7
        title
      • public.layouts.partials.flash-session (resources/views/public/layouts/partials/flash-session.blade.php)6bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
      uri
      GET en/courses/{slug}
      middleware
      web, localize:en
      controller
      App\Http\Controllers\CourseController@show
      as
      en.courses.show
      namespace
      prefix
      /en
      where
      file
      app/Http/Controllers/CourseController.php:17-35
      7 statements were executed5.41ms
      • select * from `courses` where `slug_en` = 'aplicaciones-de-la-teoría-de-grafos-a-la-vida-real-(i)' limit 1
        4.04ms/app/Http/Controllers/CourseController.php:20corspedia
        Metadata
        Bindings
        • 0. aplicaciones-de-la-teoría-de-grafos-a-la-vida-real-(i)
        Backtrace
        • 17. /app/Http/Controllers/CourseController.php:20
        • 18. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 19. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 20. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 21. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • update `courses` set `visitors` = `visitors` + 1, `courses`.`updated_at` = '2025-02-15 16:38:08' where `id` = 202
        250μs/app/Http/Controllers/CourseController.php:21corspedia
        Metadata
        Bindings
        • 0. 2025-02-15 16:38:08
        • 1. 202
        Backtrace
        • 17. /app/Http/Controllers/CourseController.php:21
        • 18. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 19. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 20. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 21. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select `id`, `name_en`, `name_ar`, `topic_id`, `slug_en`, `slug_ar` from `subjects` where `subjects`.`id` in (6)
        220μs/app/Http/Controllers/CourseController.php:23corspedia
        Metadata
        Backtrace
        • 20. /app/Http/Controllers/CourseController.php:23
        • 21. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 22. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 23. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 24. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select `id`, `name_en`, `name_ar`, `slug_en`, `slug_ar` from `topics` where `topics`.`id` in (1)
        200μs/app/Http/Controllers/CourseController.php:23corspedia
        Metadata
        Backtrace
        • 25. /app/Http/Controllers/CourseController.php:23
        • 26. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 27. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 28. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 29. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `institutions` where `institutions`.`id` in (44) and `institutions`.`deleted_at` is null
        240μs/app/Http/Controllers/CourseController.php:23corspedia
        Metadata
        Backtrace
        • 20. /app/Http/Controllers/CourseController.php:23
        • 21. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 22. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 23. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 24. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `providers` where `providers`.`id` in (1) and `providers`.`deleted_at` is null
        200μs/app/Http/Controllers/CourseController.php:23corspedia
        Metadata
        Backtrace
        • 20. /app/Http/Controllers/CourseController.php:23
        • 21. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 22. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 23. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 24. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `html_files` where `html_files`.`id` = 199 limit 1
        260μs/app/Models/Course.php:84corspedia
        Metadata
        Bindings
        • 0. 199
        Backtrace
        • 21. /app/Models/Course.php:84
        • 28. view::public.courses.show:29
        • 30. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:125
        • 31. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 32. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
      App\Models\HtmlFile
      1
      App\Models\Provider
      1
      App\Models\Institution
      1
      App\Models\Topic
      1
      App\Models\Subject
      1
      App\Models\Course
      1
        _token
        2hNu9iJgeLMjjEuktlONlF9UvvmQQqKwvsTZlhXq
        locale
        en
        _previous
        array:1 [ "url" => "https://www.corspedia.com/en/courses/aplicaciones-de-la-teor%C3%ADa-de-grafos-...
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /en/courses/aplicaciones-de-la-teor%C3%ADa-de-grafos-a-la-vida-real-%28i%29
        status_code
        200
        
        status_text
        OK
        format
        html
        content_type
        text/html; charset=UTF-8
        request_query
        []
        
        request_request
        []
        
        request_headers
        0 of 0
        array:24 [ "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] "cdn-loop" => array:1 [ 0 => "cloudflare; loops=1" ] "priority" => array:1 [ 0 => "u=0, i" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "cf-connecting-ip" => array:1 [ 0 => "18.217.145.147" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "cf-visitor" => array:1 [ 0 => "{"scheme":"https"}" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "x-forwarded-proto" => array:1 [ 0 => "https" ] "cf-ipcountry" => array:1 [ 0 => "US" ] "accept-encoding" => array:1 [ 0 => "gzip, br" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "x-forwarded-for" => array:1 [ 0 => "18.217.145.147" ] "cf-ray" => array:1 [ 0 => "9126b9f87d2afa1d-ORD" ] "host" => array:1 [ 0 => "www.corspedia.com" ] "content-length" => array:1 [ 0 => "" ] "content-type" => array:1 [ 0 => "" ] ]
        request_server
        0 of 0
        array:50 [ "USER" => "www-data" "HOME" => "/var/www" "HTTP_SEC_CH_UA_MOBILE" => "?0" "HTTP_SEC_CH_UA" => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129"" "HTTP_CACHE_CONTROL" => "no-cache" "HTTP_PRAGMA" => "no-cache" "HTTP_CDN_LOOP" => "cloudflare; loops=1" "HTTP_PRIORITY" => "u=0, i" "HTTP_UPGRADE_INSECURE_REQUESTS" => "1" "HTTP_USER_AGENT" => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" "HTTP_CF_CONNECTING_IP" => "18.217.145.147" "HTTP_ACCEPT" => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" "HTTP_SEC_FETCH_SITE" => "none" "HTTP_CF_VISITOR" => "{"scheme":"https"}" "HTTP_SEC_FETCH_MODE" => "navigate" "HTTP_SEC_FETCH_USER" => "?1" "HTTP_X_FORWARDED_PROTO" => "https" "HTTP_CF_IPCOUNTRY" => "US" "HTTP_ACCEPT_ENCODING" => "gzip, br" "HTTP_SEC_FETCH_DEST" => "document" "HTTP_SEC_CH_UA_PLATFORM" => ""Windows"" "HTTP_X_FORWARDED_FOR" => "18.217.145.147" "HTTP_CF_RAY" => "9126b9f87d2afa1d-ORD" "HTTP_HOST" => "www.corspedia.com" "REDIRECT_STATUS" => "200" "SERVER_NAME" => "corspedia.com" "SERVER_PORT" => "443" "SERVER_ADDR" => "141.95.147.152" "REMOTE_USER" => "" "REMOTE_PORT" => "14352" "REMOTE_ADDR" => "172.70.130.198" "SERVER_SOFTWARE" => "nginx/1.18.0" "GATEWAY_INTERFACE" => "CGI/1.1" "HTTPS" => "on" "REQUEST_SCHEME" => "https" "SERVER_PROTOCOL" => "HTTP/2.0" "DOCUMENT_ROOT" => "/var/www/corspedia/public" "DOCUMENT_URI" => "/index.php" "REQUEST_URI" => "/en/courses/aplicaciones-de-la-teor%C3%ADa-de-grafos-a-la-vida-real-%28i%29" "SCRIPT_NAME" => "/index.php" "CONTENT_LENGTH" => "" "CONTENT_TYPE" => "" "REQUEST_METHOD" => "GET" "QUERY_STRING" => "" "SCRIPT_FILENAME" => "/var/www/corspedia/public/index.php" "PATH_INFO" => "" "FCGI_ROLE" => "RESPONDER" "PHP_SELF" => "/index.php" "REQUEST_TIME_FLOAT" => 1739637487.6846 "REQUEST_TIME" => 1739637487 ]
        request_cookies
        []
        
        response_headers
        0 of 0
        array:5 [ "content-type" => array:1 [ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [ 0 => "no-cache, private" ] "date" => array:1 [ 0 => "Sat, 15 Feb 2025 16:38:08 GMT" ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6InFNdU9qT0pDdG8zUWdINW1RS2pGcWc9PSIsInZhbHVlIjoiWEIyZlcvZStOSkE1N0xIV3VOZmQzNzd3WjVyZWRLME8wdUxhRnMxY0RucU1JNkVGMkVvdlhQcW0zMVdvdmkxcU5HTEF0RnVmN2NHTWNuWGZLVGR6b0pmUTRod1ZBNlNWc21RQUNWc1dSdHVMUDFUTENtWWFZbzd5eDUwNUtlQ0siLCJtYWMiOiI2ZWNjZDZjZWY2NTYwNWRiNzI2NTRhZGQyMjk2MjUxODdmN2EyZjgxZmU1NTMxMzM3ZDI0ZTU1ODY4ZTdjZmRlIiwidGFnIjoiIn0%3D; expires=Sat, 15 Feb 2025 18:38:08 GMT; Max-Age=7200; path=/; samesite=laxXSRF-TOKEN=eyJpdiI6InFNdU9qT0pDdG8zUWdINW1RS2pGcWc9PSIsInZhbHVlIjoiWEIyZlcvZStOSkE1N0xIV3VOZmQzNzd3WjVyZWRLME8wdUxhRnMxY0RucU1JNkVGMkVvdlhQcW0zMVdvdmkxcU5HTEF0R" 1 => "laravel_session=eyJpdiI6Ik1abzFLSVNpOXFVa1YydU00U2FRZEE9PSIsInZhbHVlIjoiYVJLaGRrNkNJRVVaWDhuaDhMRStyN3hkQS9FZVpRS2thTTZ0dUlCdFNIdDNLRkwzdlJ4WVlsczNBVlVxTS85eFh3Mnh6WmZQL1A1Z2ltZUgwWUFrZlQxaHFaSzZiLzNKWU5CLzNBa3p3K21tUzZCYTUvdk1lMzlWVzB6dEZjdm4iLCJtYWMiOiIwOWQxMDE0NzZhY2I2ZjhjNjc4MjZlNWJiMjZlNWY0YjYzM2Y0NDI5NGQ3MGJlZDgxNTA4MWU1N2JhYjFiM2JhIiwidGFnIjoiIn0%3D; expires=Sat, 15 Feb 2025 18:38:08 GMT; Max-Age=7200; path=/; httponly; samesite=laxlaravel_session=eyJpdiI6Ik1abzFLSVNpOXFVa1YydU00U2FRZEE9PSIsInZhbHVlIjoiYVJLaGRrNkNJRVVaWDhuaDhMRStyN3hkQS9FZVpRS2thTTZ0dUlCdFNIdDNLRkwzdlJ4WVlsczNBVlVxTS85eFh3" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6InFNdU9qT0pDdG8zUWdINW1RS2pGcWc9PSIsInZhbHVlIjoiWEIyZlcvZStOSkE1N0xIV3VOZmQzNzd3WjVyZWRLME8wdUxhRnMxY0RucU1JNkVGMkVvdlhQcW0zMVdvdmkxcU5HTEF0RnVmN2NHTWNuWGZLVGR6b0pmUTRod1ZBNlNWc21RQUNWc1dSdHVMUDFUTENtWWFZbzd5eDUwNUtlQ0siLCJtYWMiOiI2ZWNjZDZjZWY2NTYwNWRiNzI2NTRhZGQyMjk2MjUxODdmN2EyZjgxZmU1NTMxMzM3ZDI0ZTU1ODY4ZTdjZmRlIiwidGFnIjoiIn0%3D; expires=Sat, 15-Feb-2025 18:38:08 GMT; path=/XSRF-TOKEN=eyJpdiI6InFNdU9qT0pDdG8zUWdINW1RS2pGcWc9PSIsInZhbHVlIjoiWEIyZlcvZStOSkE1N0xIV3VOZmQzNzd3WjVyZWRLME8wdUxhRnMxY0RucU1JNkVGMkVvdlhQcW0zMVdvdmkxcU5HTEF0R" 1 => "laravel_session=eyJpdiI6Ik1abzFLSVNpOXFVa1YydU00U2FRZEE9PSIsInZhbHVlIjoiYVJLaGRrNkNJRVVaWDhuaDhMRStyN3hkQS9FZVpRS2thTTZ0dUlCdFNIdDNLRkwzdlJ4WVlsczNBVlVxTS85eFh3Mnh6WmZQL1A1Z2ltZUgwWUFrZlQxaHFaSzZiLzNKWU5CLzNBa3p3K21tUzZCYTUvdk1lMzlWVzB6dEZjdm4iLCJtYWMiOiIwOWQxMDE0NzZhY2I2ZjhjNjc4MjZlNWJiMjZlNWY0YjYzM2Y0NDI5NGQ3MGJlZDgxNTA4MWU1N2JhYjFiM2JhIiwidGFnIjoiIn0%3D; expires=Sat, 15-Feb-2025 18:38:08 GMT; path=/; httponlylaravel_session=eyJpdiI6Ik1abzFLSVNpOXFVa1YydU00U2FRZEE9PSIsInZhbHVlIjoiYVJLaGRrNkNJRVVaWDhuaDhMRStyN3hkQS9FZVpRS2thTTZ0dUlCdFNIdDNLRkwzdlJ4WVlsczNBVlVxTS85eFh3" ] ]
        session_attributes
        0 of 0
        array:5 [ "_token" => "2hNu9iJgeLMjjEuktlONlF9UvvmQQqKwvsTZlhXq" "locale" => "en" "_previous" => array:1 [ "url" => "https://www.corspedia.com/en/courses/aplicaciones-de-la-teor%C3%ADa-de-grafos-a-la-vida-real-%28i%29" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]