Either find a perfect matching, or prove that none exist

I am looking for a polynomial-time algorithm that takes as input a bipartite graph, and returns one of two options:

  1. If a perfect matching exists, it returns the matching;

  2. Otherwise, it returns an “evidence” that a perfect matching does not exist, based on Hall’s theorem, i.e., it returns a set $ X$ such that the number of neighbors of $ X$ is smaller than $ |X|$ .

I found in wikipedia various algorithms for finding a maximum matching in an unweighted bipartite graph. Such algorithms can be used to determine if a perfect matching exists. But does any of these algorithms also return an evidence in case of failure?

Asymmetric public-key cryptography: can either key be used to encrypt or decrypt?

Key exchange describes a public key encrypting plaintext and the private key decrypting, while in digital signatures the reverse is true where the private key is used to encrypt a hash that the companion public key decrypts.

Should I think of asymmetric keys along the lines of one key encrypts and the other decrypts or can either in a pair be used to encrypt or decrypt?

What I’m getting at is, are the public and private key names just logical in that in a key exchange, the public key is shared on an unsecured medium making it “public” yet the private key needs to remain a secret in order to protect the shared key?

I hope this question makes sense and I’ll try to clarify if needed but this the best way I could word it at the moment.

Intuitive method for users to select either of 2 destinations in a search results interface

I am trying to design an interface where users are navigate to a modules (from a list of 2 or 3 modules) from a search results page.

Notes: 1. Every user will have a default module: example ModX 2. Every user will have more than 1 module: example ModX (default) & ModY & ModZ 3. Each module talks about CUSTOMERS or ACCOUNTs. 4. Each module is a menu item

Problem Upon searching for a Customer name… example Disney Limited. User will see “disney limited” in search results. User should now be able to navigate to ModX by default, but incase he wishes to navigate to ModY of Disney Limited…how would he do it?

Ubuntu 18.04 either stuck on Ubuntu screen OR bad resolution?

I am a complete newbie at this, so forgive me if this is a silly question.

  1. Installed Ubuntu 18.04 on a Toshiba netbook from a trial I was running from a USB stick (overwrote Windows 10 OS while I was at it).

  2. After the reboot, wound up stuck on the Ubuntu splash screen, and followed these instructions: Black screen after installation of Ubuntu 18.04

It seemed to work! Was able to load OS. However….

  1. My screen resolution now seems to be stuck on 800×600, whereas running the “trial” version from the USB there were other (better) options. Then I found this instruction: unable to change screen resolution

which seems to contradict the instruction I mention in 2, above?

Could someone please give me some direction around how to make the windows (particularly in ‘settings’) fit onto my monitor? (They currently extend past the edges, apparently no matter what I do.) Also, the refresh rate seems to be awful now, whereas it wasn’t before. Is that a related issue?

Sorry if I’m just an idiot, but I gotta start learning stuff somewhere…


Can I say the two cases of Recursion Tree are always either $\theta{(n)}$ or $\theta({n\log{n}})$

Given positive constants: $ c_1, c_2, …, c_k, c^\prime$ , assume that
$ T(n) = T(c_1n) + T(c_2n) + …+ T(c_kn) + c^\prime n$

There are two cases:

  1. $ c_1 + c_2 + …+ c_k < 1$
  2. $ c_1 + c_2 + …+ c_k = 1$

As I observed (from some problems), in case 1 $ T(n) = \theta{(n)}$ , in case 2 $ T(n) = \theta{(n\log{n})}$ But I didn’t find the theory says this always true, so I’m wondering, generally is this true or a theorem or is there any counterexample?

For example, of Case 1 : $ T(n) = T(\frac{n}{2}) + T(\frac{n}{4}) + T(\frac{n}{8}) + n = \theta{(n)}$
and of Case 2 : $ T(n) = T(\frac{n}{3}) + T(\frac{2n}{3}) + n = \theta{(n\log{n})}$

Few Websites are either Copying or crawling my content what Should I do? [duplicate]

This question already has an answer here:

  • Our website was copied 100% and mirrored on a different domain 6 answers
  • Another website is mirroring and ranks above my site in search results 6 answers
  • How much of your content needs to be copied before you can file a DMCA complaint? 1 answer

I have noticed quite a change in my SERP over the months and came to know few sites have copied my content. How Should I Complain this to Google?

Is there a General Criteria for this?

There are Google provisions that I understand. But are their any clear policies regarding this?

The URL could not be validated. Either the page does not exist or the server cound no

When submitting my sites to free web directories I got this error

The URL could not be validated. Either the page does not exist or the server cound not be contacted.

I tried to submit to 40 different directories but same error I got.

Anyone who could help me?

Is submitting site starting https:// is an issue?

Is there is any way either in Obj c or swift, to alter the background so nicely that one could feel the person must be in the image

I just want to know is it possible..to alter the background image so nicely that one could feel the person must be in the picture..if yes then please let me know any tutorial regarding this..or any kind of help. both obj c or swift language code will be helpfull..thanks in advance