Why maximum-matching algorithm falls into the category of fill-reducing algorithms?

My understanding is that “maximum matching” (or “maximum transversal”) are algorithms to pre-order matrix to increase the numerical stability. In Timothy Davis’ book Direct Methods for Sparse Linear Systems, 2006, however, this algorithm is put in Chapter 7 which is titled “Fill-reducing ordering”. In his more recent paper A survey of direct methods for sparse linear systems, 2016, maximum matching was also placed in section 8 which is titled “Fill-reducing orderings”.

So far, my had an impression that reordering algorithms can be categorized into 3 classes:

  • for numerical stability: maximum transversal, etc
  • for fill-reducing: AMD, etc
  • for work-reducing or parallelism-increasing: BTF, BBD, etc

I have problems in understanding putting above 3 classes into a single category called fill-reducing…

What category does questions like “Given n points on 2D plane find …” belong to

Not after a specific answer, do following questions belong to same set of problem types?

Given n points in on 2D plane, find 4 or 5 , or m subset of points with less total distant to each other than all other points.


Given n points in on 2D plane, count the number of triangles, squares etc. that they form.


Given n points in on 2D plane, find a point that is closeses to most number of points as possible.

are these optimisation questions? or is there another name for above type of questions, or there can be no category for all the questions of type

Given n points in on 2D plane, find $ \cdots$

This question did not seem to be fit for SO or Software engineering, so I am asking it here, if there is better SE to ask this question I’ll delete this question and ask it there ( in reverse order ).

Is there a way to set up an image custom field to function as a category field with a predefined photo bank?

I would like to know how can I create a predefined image bank by using Jetengine taxonomy or any other way/plugin.

My main purpose is to use Forminator plugin post create template so that the user on the front-end will be able to select an image from a predefined image bank (the same as using a category but in this case the user will see a dropbox of images and will be able to select from it).

You can see a sample of media (photo) custom field on the following link (the line with the icons and photo).




Grouping items by category

I am in the process of designing and interface where a internal user creates a programme of items. Each item can be grouped with other items in a “category”.

enter image description here

If two or items in the same category are displayed together in the list I would like duplicate information (e.g. the category name) to be removed “Category 1”

Items not in a category should be easily identifiable that they are not part of a category (second item under “Category 2”).

A category does not need to be contiguous and a category may be split up by uncategorized items and other categorized items “category 3” – It should be clear that both items with the “Category 3” heading are together.

My current concept assigns a background colour to each category – this seems to work well but I am concerned that I have a finite usable palette and it gets very busy quickly, Some other points, the category labels are unique – and user supplied, and the soloution should scale to potentially 10-20 categories over 50-60+ items.

Custom Post Type – Category Rewrite – Remove Rewrite from Sitemap

I’ve got “case_studies” post type and categories for it as “case_studies_categories” with a rewrite to include category in URL.

Everything works, but for some reason, rewrite url is in sitemap (as the first URL), for example:


and the rest is fine:

/case-studies/%case_studies_categories%/ /case-studies/category-name/post-name/ /case-studies/category-name/post-name/ /case-studies/category-name/post-name/ 

How to remove it (/case-studies/%case_studies_categories%/) from Sitemap?

    add_action('init','case_studies_init');  function case_studies_init(){      $  labels = array(         'name'               => _x( 'Case Studies', 'Case Studies' ),         'singular_name'      => _x( 'Case Study', 'Case Study' ),         'add_new'            => _x( 'Add Case Study', 'Case Study' ),         'add_new_item'       => __( 'Add Case Study' ),         'edit_item'          => __( 'Edit Case Study' ),         'new_item'           => __( 'New Case Study' ),         'all_items'          => __( 'All Case Study' ),         'view_item'          => __( 'View Case Study' ),         'search_items'       => __( 'Search Case Study' ),         'not_found'          => __( 'No Case Studies Found' ),         'not_found_in_trash' => __( 'No Case Studies in Trash' ),         'parent_item_colon'  => '',         'menu_name'          => 'Case Studies'     );     $  args = array(         'labels'                => $  labels,         'description'           => 'Holds case studies post data',         'public'                => true,         'menu_position'         => 7,         'hierarchical'          => true,         'menu_icon'             => 'dashicons-admin-comments',         'rewrite'               => array('slug' => 'case-studies/%case_studies_categories%', 'with_front' => false),         'supports'              => array( 'title', 'revisions', 'thumbnail'),         'has_archive'           => true,         'show_ui'               => true,         'show_in_nav_menus'     => true,         'show_in_menu'          => true,         'show_in_admin_bar'     => true,         'taxonomies'            => array("case_study_categories"),     );      register_post_type('case_studies',$  args);   //  flush_rewrite_rules( false ); }  // register a custom category taxonomy type // so that the categories are not connected to the 'post' type taxonomies  add_action( 'init', 'register_case_study_tax' );  function register_case_study_tax(){      $  labels = array(     'name'              => _x( 'Case Study Categories', 'case-studies'),     'singular_name'     => _x( 'Case Study Category', 'testimonials'),     'search_items'      => __( 'Search Case Study Categories'),     'all_items'         => __( 'All Case Study Categories'),     'parent_item'       => __( 'Parent Case Study Category'),     'parent_item_colon' => __( 'Parent Case Study Category:'),     'edit_item'         => __( 'Edit Case Study Category'),     'update_item'       => __( 'Update Case Study Category'),     'add_new_item'      => __( 'Add Case Study Category'),     'new_item_name'     => __( 'New Case Study Category'),     'menu_name'         => __( 'Case Study Categories'),     );      $  args = array(     'labels'                => $  labels,     'taxonomy'              => 'case_study_categories',     'object_type'           => 'case_studies',     'hierarchical'          => true,     'show_ui'               => true,     'show_admin_column'     => true,     'query_var'             => false,     );      register_taxonomy('case_studies_categories', 'case_studies', $  args); }   /** filter URL link for post type url **/ add_filter('post_type_link', 'case_studies_permalink_structure', 10, 4);  function case_studies_permalink_structure($  post_link, $  post, $  leavename, $  sample) {   if ( false !== strpos( $  post_link, '%case_studies_categories%' ) ) {     $  event_type_term = get_the_terms( $  post->ID, 'case_studies_categories' );     if($  event_type_term)     $  post_link = str_replace( '%case_studies_categories%', array_pop( $  event_type_term )->slug, $  post_link );    }  return $  post_link; } 

I’m sure I’ve done something stupid, please assist if possible.


WordPress search not able to find the category

I have 3 to 4 categories on my website. I am using WordPress search but when I am searching my category then I am getting

Nothing Found

also, I tried to search the subcategory then also I am getting the same message.

Would you help me out with this issue?


 <section id="primary" class="content-area mainSearch">     <main id="main" class="site-main">       <div class="equalPadding">         <div class="cp-seeWrapper">     <?php if ( have_posts() ) :            get_search_form();//search form           ?>           <div class="resultCount"><?php           global $  wp_query;           echo $  wp_query->found_posts.' RESULTS';             ?></div>          <div class="row">       <?php          while (have_posts()){the_post();?>         //displaying result here         <?php } ?>        <?php      else :       get_template_part( 'template-parts/content', 'none' );      endif;     ?>           </div>     </div>     </div>     </main><!-- #main -->   </section><!-- #primary --> 

Is, beta reduction in type theory being considered as counit for hom-tensor adjunction in category theory, a denotational or operational semantic?

In the article at nlab about the relation between type theory and category theory, it is said that “beta reduction” in type theory corresponds to “counit for hom-tensor adjunction” in category theory and also “substitution” corresponds to “composition of classifying morphisms / pullback of display maps” correspondingly.

Are these considered denotational or operational semantics?

What is the adjunct of the evaluation morphism in a closed monodical category?

According to the nlab article about evaluation map if $ X, Y \in C$ , a closed monodical category then the adjunct to evaluation morphism $ [X, Y]\otimes X \rightarrow Y$ is the identity morphism $ [X, Y] \rightarrow [X, Y]$ .

Is that correct and if yes why?
Because it seems to me that the adjunct of such has to be $ X \rightarrow [Y, (X \otimes Y)]$