# Subset sum algorithm in O(n³ log n)?

I think that I have found an algorithm which resolve exactly the subset sum problem in $O(N^3)$ in the worst case, only for positive numbers.

After my research, I'm lost between all the algorithms for this problem.

• $O(2^N*N)$ for the naive algorithm (I understand)
• $O(2^{N/2})$ for advanced algorithm (I understand)
• $O(N * C)$ for pseudo-polynomial time algorithm (only positive numbers)

Reference : Wikipedia

• $O(N^3 * log(N))$ for an exact resolution but I don't understand the whole process

Reference : Andrea Bianchini paper

I would like to know if my resolution is in polynomial time ?

If it is, the paper of Andrea Bianchini is too. So it should proove that P=NP, but it's not the case. Why ?

• What algorithm do you propose? Why do you think it is (in)correct? Why do you give any weight to the Bianchini paper, which if it were correct would have been widely recognized by now? – Tom van der Zanden Nov 25 '14 at 19:59
• I think this paper is correct, but I think it is in a restricted area that I don't understand. My algorithm is a binary algorithm inspired by quantum physic... I don't think I have find important something, and it's for this reason I ask this question. – csblo Nov 25 '14 at 20:12

If you're not quite sure what I mean by unary encoding: Unary encoding means we encode a number by a sequence of $1$'s of appropriate length.
As an example, suppose your input consists of $10$ numbers, each between $128$ and $256$. Then your input size is, in unary, about $10 \times 256=2560$, whereas your input size is, in binary, $10 \times \log_2 (256) =80$.