Stable matching with dynamic preference lists

I have a set $ F$ of $ n_1$ families, a set $ C$ of $ n_2$ children ($ n_1<n_2$ ) and a set $ M$ of feasible one-to-one matchings of the families with the children. All the children have the same preference list over the families, but the families have different preference lists.

Our objective is to select from the set $ M$ a stable matching. It is clear that the family with rank 1 will be matched with the child she ranks the best among those that is matched with them in $ M$ , the family with rank 2 will be matched with the child she ranks the best among those that is matched with them in the matchings selected for family 1 and so on.

When the preference lists are fixed, the constraint can be modeled as follows:

$ 1 \leq \sum\limits_{j’\in J^{\leq}_{C_j^i}(i)}x_{ij’} + \sum\limits_{i’\in F^{\leq}_{i}}x_{i’C_j^i} $ ; $ i \in F$ , $ j=1,\ldots,i$


  • $ x_{ij}$ equals one if family $ i$ is matched with rank $ j$ .
  • $ C_j^i$ is the child with rank $ j$ for family $ i$ .
  • $ J^{\leq}_{s}(i)$ is the set of children that family $ i$ ranks at the same level or better than child $ s$ .
  • $ C^{\leq}_{i}$ is the set of families that are at the same level or better than family $ i$ .

How to modify this constraint to take into account the changes in the preference lists?

Algorithm for efficiently sorting large lists based on user preference

I’ll preface this question by saying I’m having a difficult time even formulating the problem, so my explanation might be fuzzy and/or I might be missing obvious solutions.

I have a list of 479 books which I would like to sort based on a “Fuzzy” criterion such as “which books would I like to read before the others in this list?”.

I took a stab at solving this by storing a record for each book in a database, and pre-populating a rank column with a unique sequential number from 1 to 479. For any particular rank, I’d like to read the corresponding book more than a book with a higher rank number. If the rank number is closer to 1, the corresponding book is one I wish to read earlier.

I created an interface that presents me with a choice between two books selected randomly from the database. After I click the book I would rather read first, the following happens:

  • If the rank of the selected book is already lower (more interesting) than the other, I don’t change the rank of either book;
  • If the selected book has a rank that’s higher (less interesting) than the other, I change the selected book’s rank to be the same as the other book, and add 1 to the rank of all the other books where the rank is more than or equal (including the other book, which would now be ranked directly below the selected book).

Finally, for each book I also store a counter of the times it has been evaluated. After I make a selection between two books, this counter increases for both the books that were presented to me. This allows me to avoid presenting books that have already been evaluated a certain number of times until all other books have been evaluated the same number of times.

I found the algorithm to be utterly ineffective: after going through all 479 of the books once, I looked at the list sorted by rank and noticed the list does not reflect at all my own perception of how I’d prioritize these books.

I’m looking for an algorithm that:

  • Allows me to organize the list in an order that I would perceive to be accurate based on my personal notion of which books I’d like to read first;
  • Can prioritize the aforementioned list with as little effort required as possible (i.e. an algorithm that requires the user to compare every book with every other book in the list in order to come to a valid sorting order isn’t ideal).

Purge Guake with config files: Preference files survive somewhere

I need to completely remove Guake. It seems to have some bug that I triggered while setting keybindings. Now the “close tab” keybinding does not work anymore. I tried

$   sudo apt-get purge guake $   sudo apt-get purge --auto-remove guake 

and different variantions of these. When I reinstall Guake, my old preferences are still there: Keybindings, color scheme etc. I can’t locate where the preference files are located though. How can I remove Guake entirely together with the somehow broken preference files?

Ubuntu 18.04 Can’t change preference order of languages in language menu

I want to add English and Japanese to the languages on my computer so I can use an input method editor to switch from one keyboard to the other. I want to keep English as the main system language for work but still be able to keep a Japanese keyboard handy, but all methods on the internet require me to reorder ‘Japanese’ between ‘English (United Kingdom)’ and ‘English’. However, whenever I drag Japanese between these two languages, it either does not move to the space in between them or jumps up to the top. Attempting to displace it from the top will result in it being placed below English and thus not be considered. Is there any way I can edit this information from the terminal perhaps? This laptop is a bit of a potato since I need it to be expendable, so perhaps I might just be having problems with the incredibly computationally demanding tasks of dragging items in a dropdown menu? Please advise.

I’ve looked at This post which says basically “oh you can’t do it, it doesn’t make any sense’. I’ve tried putting it between United States and normal english, between united states and UK english, but none of it works…

How to customize default enabled EC curves or the curves preference in Azul Zulu JDK

We use Zulu JDK and want to customize the default enabled EC curves. Oracle JRE provides this using jdk.tls.namedGroups system property in

section “Improve the default strength of EC in JDK” describe this for Oracle JDK

Any suggestion?


How to make laptop use external monitors in preference to its own

So I have a Lenovo Thinkpad P51, and its graphic card (Nvidia Quadro M2200) can only support up to 4 displays. I have connected 4 monitors via its dock thus making a total of 5 displays (one being the built in monitor in the laptop). Is there a way to make it so that, maybe if I close the lid, it can utilize the 4 monitors in Ubuntu 18.04? Right now, when I close it, only the three first monitors remain. Is there a procedure to do this in Windows as well?

Thank you very much!

Should you put a Notification preference into your Inapp preferences (Android)

Our Android app is featuring push-notifications, and we want the user to be able to activate/deavtivate them. Should we make an option for this in our inapp-preferences or is it just confusing because the user is able to configure this for every app in the android preferences?

Is there a best practice?

beach ball in bluetooth in System Preference when trying to connect to Anne Pro 2 keyboard

I have trouble connecting to my Anne Pro 2 keyboard recently after the latest firmware update (see screenshot)

enter image description here

Therefore I have tried to deregister the device and register it again.

The issue is: when I tried to connect to 28-ec-9a-9b-73-53 (presumably the AP2 keyboard), the bluetooth pane was frozen and a beach ball appeared and kept spinning.

enter image description here

I have tried the ‘Clean bind’ in the AP2 utility,

enter image description here

then retry the connection but it does not work.

What can I try in this case?

Magento 2-Override FinalPriceBox using Preference or Plugin class of Configurable Product module

Anyone has idea how to make preference or plugin on Magento\ConfigurableProduct\Pricing\Render\FinalPriceBox class of Magento\ConfigurableProduct.

Basically, new function i wanted to add in the FinalPriceBox class and to use new function in final_price.phtml file.

I see code in the di.xml of module-configurableproduct module. But do not know how to use in new custom module?

<type name="Magento\ConfigurableProduct\Pricing\Price\FinalPrice">         <arguments>             <argument name="priceResolver" xsi:type="object">ConfigurableFinalPriceResolver</argument>         </arguments>     </type> 

Keto Fit Pro Reviews is an powerful weight reduction preference

Keto Fit Pro Reviews is a clearly produced complement and supplies you fast-appearing effects and not using an aspect effect in any respect. This is accomplished via the enormous studies that's done before the formulation of the product. You are able to get a low priced choice for yourself which is going to present you lower starvation ranges, together with a high metabolism. The keto weight loss plan may put positive threat in your fitness in a…

Keto Fit Pro Reviews is an powerful weight reduction preference