## Set cover problem satisfying half constraints

Consider a variation of the set cover problem in which we only have to cover some certain amount of elements. Is this problem still NP-hard? I guess yes? Is there a good reference?

## problem with a CDF

I’ve just started using mathematica, I should import a .txt file and run an experimental CDF and compare it with Kolmogorov Smirnov tests to see if to analyze the disparity of points with a Gauss curve or with a Logarithmic. Could someone help me to make these graphs and compare them? Thank you all

## Problem while debugging services with WinDBG using GFLAGS

Please i have a little problem when i try to debug services using WinDBG and GFLAGS. Here’s some screeenshots resuming my problem, so, here’s what i did. First, i configured GFLAGS like this :

Then, i lunched the service, and used the following command line :

And finally, i had this error :

If someone can help, it would be very great, Thanks a lot !

## Flip Output of SAT problem

Why cant I Just create a TM A that runs a NTM B with a formula to compute the SAT Problem and Just Flip its Output. So when the Input NTM B Returns true (formula is satisfyable) the TM A Return false.

## NP-Complete problem whose corresponding optimization problem is not NP-Hard

For this question I will refer to$$\ NP-hard$$ problems as those that are at least as hard as$$\ NP-complete$$ problems. That is, a problem$$\ H$$ is$$\ NP-hard$$ if there is an$$\ NP-complete$$ problem$$\ G$$, such that$$\ G$$ is reducible to$$\ H$$ in polynomial time.$$\ NP-hard$$ problems are not restricted to decision problems and are not necessarily in$$\ NP$$.

Considering the above, is there any optimization problem$$\ L$$ such that$$\ L \notin NP-hard$$ and whose corresponding decision problem is$$\ NP-complete$$?

For example, consider the case for the travelling salesman problem. (TSP)

Optimization problem: Given a list of cities and the distances between each pair, what is the shortest path that visits each city and returns to the original city?

Decision problem: Given a list of cities, the distances between each pair and a length$$\ L$$, does there exist a path that visits each city and returns to the original city of length at most$$\ L$$.

It is well known that the decision problem of TSP is$$\ NP-complete$$ and its corresponding optimization problem is$$\ NP-hard$$.

To sum up, what is an example of a$$\ NP-complete$$ problem whose corresponding optimization problem lies outside the class$$\ NP-hard$$? Perhaps, it is$$\ EXPTIME$$.

## Problem with simplification in mathematica

I have an expression that I think should be simplified to zero but mathematica gives me a weird result, I have

Simplify[-2*Sqrt[2*a] + Sqrt[(2^3)*a]] 

The result given by mathematica is

-2 Sqrt[2] (-1 + ) Sqrt[a] 

When I first copied from the notebook and pasted here the term (-1 + ) it pasted the following line:

(-1 + \.08) 

Is this of any help to solve the issue? I’d simply like mathematica to simplify in a smart way.

EDIT: FullSimplify returns the same output

## Time and Space Complexity for Brute Force Knapsack Problem

I was wondering if someone could confirm my working for the complexity for 0/1 Knapsack Brute Force and Dynamic Programming solutions,

For the Brute force I reasoned its $$O(N.2^N)$$

This is because to work out all possible subsets (The way I did brute force was to compute power set then calc weight/values for each set), takes $$2^N$$ and then we calculate the sum of each subset of size from 1-N, that takes $$N.2^N$$

Space complexity would be $$O(P)$$ where p is the total number of subsets

But from my notes the Brute Force 0/1 Knapsack is $$O(2^N)$$ with space $$O(N)$$

I think that is for the recursive solution but my brute force is not recursive.

## Soundcloud Player Problem. Is There A Solution?

Hi everybody. I am working on a website and trying to incorporate soundcloud into the design. The Flash version of the soundcloud mp3 player is absolutely perfect for the design of my site. Unfortunately, people on ipods/pads can't see/play the music on that player…

The HTML5 player is nice, but is almost double the size of the Flash player. It's way too big for the design of my site. It moves the products "below the fold" on the page.

Is there any way to cut off a bottom portion…

Soundcloud Player Problem. Is There A Solution?

## Constraint satisfaction in a resource allocation problem optimized using evolutionary algorithms

I am working on an allocation problem where a resource $$R$$ needs to be allocated to $$n$$ users each with demand $$d_i$$. The problem has two objectives: objective 1 – maximize user utility given by $$f_1(e_i)=log(1+e_i/d_i)$$ and objective 2 – minimize $$f_2(e_i) = {e_i}^2/c_i$$ where $$e_i$$ is the allocation to the $$ith$$ user $$d_i$$ and $$c_i$$ are constants. The problem has two constraints i.e., $$e_i \le d_i$$ (allocation is ≤ demand) and $$\sum_i^{n} e_i = R$$ (sum of all allocations equals total available resource). I am using an evolutionary algorithm for this problem. But, after the evolution is complete, the algorithm leaves unallocated resource while there is still unmet user demand. I am curious if it is an expected outcome or it is due to some algorithmic or implementation flaw. I would appreciate any guidance

## i have this problem since i created the site, it gives me error 500 and 400 every time i publish a post!

Ho un grave problema sul mio sito Web ospitato su WordPress, ricevo l’errore 500 server e l’errore 404 invio un post e poi ricarico la pagina molte volte che l’errore scompare, e tutto torna alla normalità, ho guardato il registro di accesso e ho notato che al referar manca una lettera del mio sito che sarebbe sconti-coupon.it invece dice conti-coupon.it, dammi una mano per risolverlo per favore ..