Which graph partitioning algorithm can solve this problem?

Your problem is $text{NP}$-hard. To see why, consider the version of the 3-Partition problem where we’re given multiset $ X = { x_1, x_2, ldots, x_{3n}}$ of $3n$ nonnegative integers, and we need to decide whether $X$ can be partitioned into three disjoint multisets with the same sum each. Clearly, an instance $X = { x_1, x_2, ldots, x_{3n}}$ of the 3-Partition problem can be translated in polynomial time into a complete graph $G = langle V, E rangle$, where $V = { v_i}_{iin (3n)}$ and for each $v_i$, we have that the weight $w(v_i) = x_i$. That is, we view the integers as $3n$ vertices, and every two vertices are connected with an edge. Obviously, a balanced 3-clustering of $G$ corresponds to an appropriate 3-partition of the multiset $X$.

plugins – WordPress Add Media problem with adding media description in wp_editor() when used in bootstrap modal

I am working in a plugin that uses wp_editor() for the text editor and has Add Media button. In my plugin, I have used bootstrap modal to popup a form with the text editor created using wp_editor(). When I click on Add Media to upload an image, I can upload the image but cannot input descriptions like Alt Text, Title or Other description. The textbox does not even get selected and seems to be disabled. Can somebody help me?

wp_editor( $content, $editor_id, $settings);

htaccess – Problem with URL path when I applied SEO friendly URL

I was working on PHP project and making SEO friendly URL Like,

OLD : http://example.com/list_product?q=men-top-wear

New : http://example.com/list_product/men-top-wear

Here is my .htaccess file:

RewriteEngine on
Options -MultiViews

RewriteCond %{QUERY_STRING} ^q=(.*)$
RewriteRule ^list_product$ /list_product/%1? (R=301,L)

RewriteRule ^list_product/(.*)$ list_product.php?q=$1 (L)

RewriteCond %{REQUEST_FILENAME}.php -f
RewriteRule ^(.*?)/?$ /$1.php (NC,L)

It’s working well but my link path has been changed to: http://example.com/list_product/images/logo.png

But I need this to be:

It adds list_product, but it’s not working. Does anyone know why this is happening?

installation – Problem in installing Matex

I am using Mathematica 12.0, and I want to install Matex. According to this page

only writing the code ResourceFunction["MaTeXInstall"][] should work, but I get this error

enter image description here

I have downloaded “MaTeX-1.7.8.paclet” and put it in drive C, but the problem still persists.

Can someone please guide me where I am going wrong? I am not good at installing software and so on, maybe it is so simple.

algorithms – A graph theory problem that bothers me

I wonder if there is a polynomial time algorithm for this problem.

If so, what should the algorithm do? Why is it right? Has there been any discussion in the academic circle?


Given a complete graph with n vertices,The edge weight between vertex $i$ and vertex $j$ is $b[i]times b[j]$

Under the condition that the degree of point i on spanning tree is DEG [i],let the sum of all edge weights on spanning tree is maximized.


complexity theory – Decision vs Optimisation Problem in P

If a decision problem is in P, is the associated optimization problem then also efficiently solvable?

I always thought that this is the case but according to Wikipedia page on Decision Problems the complexity of a decision and function problem might differ and to me a function problem was always a special case of an optimization problem, hence I was under the impression that if the decision problem is efficiently decidable the same applies to the corresponding optimization problem.

My Hawaii “Safe Travels” COVID test is still stuck in “Verification in Process”. Is this a problem?

No, its not a problem. I’ve arrived in Hawaii with a “Verification in Process” test and was allowed to exit the airport without issues. From speaking to other people who have recently traveled to Hawaii, this is normal – they probably verify the test, but fail to update the portal with the right status.

plugins – User can ban(hide content(posts,comments)) another user.WordPress problem

I have a project with applications for android and ios, but it takes data from a site that is on WordPress. And so, they don’t want to accept my application on IOS because there is no possibility “User can ban(hide content(posts,comments)) another user”. I tried to google, I couldn’t find anything like that. No plugins, no scripts. Perhaps someone has done something similar?

Why is the common explanation to the halting problem an oversimplification?

So watching many youtube channels, the explanation to the impossibility of solving the halting problen involves assuming you can, doing the opposite, and feeding it back into itself to create a paradox.

What I don’t get is why this is an (over)simplification. The logic seems to check out. What is the flaw in this reasoning?

Problem in running Reduze-2.4 package

I installed Reduze-2.4 package for the reduction of Feynman Integrals into master integrals. I followed all the instructions given in the basic installation section of the tutorial (https://reduze.hepforge.org/download/reduze2-tutorial.pdf).
But while I am trying to run an example using command

reduze filename.yampl
I am getting this error:
reduze: command not found
Can anyone please tell why it is so?