Examples of Analysis of Branch and Bound Method

I am solving a graph problem, which can be formulated as an integer programme. Based on computer experiments, it seems that the branch and bound method works well. I would like to analyse the running time, and wonder whether there have been other problems where branch and bound method was used and the theoretical bounds on the running time has been established?

On another note, if anyone knows any examples of problems where the range of possible values that a variable in a linear programme can take, I’d also be interested in.

Can someone explain me the Credit-Debit proof method for calculating operations?

I’ve started taking a data structure course and we are currently learning about different data structures. We also learned when to increase the capacity of an array by creating another array with double the size of the original one.

The proof used to demonstrate this was a credit-debit proof where each operations has a cost. ex: doubling an array cost 2 dollars reducing an array by half cost 1 dollar.

I simply don’t understand how proof of that type works. Doing a quick online search I haven’t find the term credit-debit used to refer to this. Maybe It’s not its name? Would be nice if someone could give me some links that explain those proofs.

Pseudo code of recursive method of printing all permutations of $n$ given integers

I really don’t understand this pseudo code. The function prints all permutations of $ n$ given integers, assuming that all numbers are different.

Is there a way to explain this code more easily as I really don’t get the purpose of the swapping.

PERMUTATE(A, start, end)    if start == end return A    else       PERMUTATE(A,start+1,end)       for i = start+1 to end          SWAP(A[i],A[start])          PERMUTATE(A,start+1,end)          SWAP(A[start],A[i]) 

Petrick’s Méthod With Maxterms

I recently learnt about Quine-McCluskey and Petrick’s methods and they are all okay by me using minterms the procedure is as follows :

1- Reduce the prime implicant chart by eliminating the essential prime implicant rows and the corresponding columns.

2- Label the rows of the reduced prime implicant chart $ P0,P1,P2,…Pn$

3- Form a logical function $ P$  which is true when all the columns are covered. P consists of a product of sums where each sum term has the form $ P_{i_0}+P_{i_1}+…+P_{i_n}$ where each $ P_{i_j}$ represents a row covering column $ i$

4- Reduce $ P$  to a minimum sum of products by multiplying out and applying $ X+XY=X$

5- Each term in the result represents a solution, that is, a set of rows which covers all of the minterms in the table. To determine the minimum solutions, first find those terms which contain a minimum number of prime implicants.

6- Next, for each of the terms found in step five, count the number of literals in each prime implicant and find the total number of literals.

7- Choose the term or terms composed of the minimum total number of literals, and write out the corresponding sums of prime implicants.

I have a problem I want to apply this same method but with essential prime implicants as Maxterms (POS expressions) I really need someone to indicate the difference that will occur in each step

Thanks

How can ideas like Lagrange Multipliers and Penalty Method be applied for solving algorithms?

I have a programming assignment which I was told that is solvable with some DP algorithm. The question involves some $ k$ which is essentially a constraint. In particular the question is a variant of LIS problem where at most $ k$ exceptions (restarts) are allowed.

But I know that there is a better solution. My professor mentioned Lagrange Multipliers and giving a penalty for each restart. But after googling these terms I wasn’t able to find out something related to algorithms. I read about them on Wikipedia but I can’t figure out how to use them. Also every article is related to Calculus and function optimization.

Is there a keyword that can describe better what I want to read about?

OpenID Authentication Method Reference Name for a code sent via email

Introduction:

I am currently implementing acr_values, acr & amr principles on a Open ID Provider server.

The claim amr (described in the OpenID RFC 1.0) has no standard clearly defined in this same RFC, but I would like to base the system on the RFC 8176 mentioned by IANA.

One of the server authentication method is about sending a confirmation code via email.

About the authentication method:

The server uses a cryptographically secure pseudo-random number generator and store a hash of it using argon2. It is sent to an email, then hash are compared on another request. There is a short expiration time for each code. This method is indeed not considered by the server as a secure method to prove an identity, but is still selectable when no access to any resource is required.

The question is:

What Authentication Method Reference Name would you use in this case ?

Most descriptions are quite strict so I only see mca as a possibility today. It is not an otp to me since it is not implementing https://tools.ietf.org/html/rfc4226.

Thanks for sharing.

[ Law Enforcement & Police ] Open Question : In real life, could a burglar use the Home Alone method to rob houses?

In the original movie, Joe Pesci played a burglar who disguised himself as a police officer, and had the following conversation with Macaulay Culkin’s on screen father: Joe Pesci: “I’d like a word with you sir.” Mr. McCallister: “Am I under arrest or something?” Joe Pesci: “Oh no not at all sir, it’s Christmas time, there are always a lot of burglars around the holidays, and we’re just making sure everyones taking the proper precautions, that’s all.” Mr. McCallister: “Oh yes, well we have automatic timers for our lights, dead bolts for our doors, we can’t be too careful if we’re spending the holidays in Paris.” Joe Pesci: “Ah, you’re taking a trip to Paris?” Mr. McCallister: “Yes, we plan to leave tomarrow morning.” Joe Pesci: “Well don’t worry about your home, it’s in good hands.” *Flashes his shady gold tooth smile* Then he knew exactly when the house would be vacant, he knew exactly what they’d be up against when they enter the house, and he knew that none of the neighbors would spot him, because he already had the same conversation with those neighbors who told him of their own holiday travel plans. As long as the burglars don’t run into a crafty kid with a tarantula, could burglars use this method in real life? Dress up as a police officer and get all the information right from the horses mouth?

Is there a spell, magical item, or any other method to accurately calculate how long ago an object/construct was created?

I’m interested in D&D 5e but I will also accept answers from previous D&D versions as well as similar systems (e.g., Pathfinder 1e/2e).


Janathiel II, famous historian, cartographer, and the Grand Wizard of Whitescar is studying the ancient structures of Ær-Toril known as Rhas.

These are gigantic and ancient structures/areas that cannot possibly have been created by nature. For example, Rhas Nolh is an almost perfect mountain pass that spans more than 100 kilometres, Rhas Aldhaen is an ancient forest that does not age (i.e., each tree is forever the same), etc.

Janathiel II has a theory: All of the Rhas constructs were created approximately during the same time period/era possibly by a technologically/magically advanced civilization.

To test this theory, however, he needs an accurate way of measuring how old an object is. Even worse, this method should be accurate even when counting thousands of years (if not hundreds of thousands).

If Janathiel II was living on Earth during the 21st century he could have used radiocarbon dating, but unfortunately for him, he lives in Ær-Toril.

Is there a spell, magical item, or any other method Janathiel II can use to accurately calculate how long ago an object/construct was created?