Factoring a Graph in Polynomial Time

Factoring a Graph in Polynomial Time

The Cartesian product G x H of graphs G and H has as vertices the pairs (g, h) with g a vertex of G and h a vertex of H; (gl, hI) is connected by an edge to (g2' h2) in G x H just when {gl' g2} is an edge of G and hI = h2' or when g, = g2 and {h" h2} is an edge of H. The Cartesian product admits unique factorization (Sabidussi [4]) but until recently no efficient algorithm was known for produci...

Polynomial time factoring algorithm using Bayesian arithmetic

In a previous paper, we have shown that any Boolean formula can be encoded as a linear programming problem in the framework of Bayesian probability theory. When applied to NP-complete algorithms, this leads to the fundamental conclusion that P = NP. Now, we implement this concept in elementary arithmetic and especially in multiplication. This provides a polynomial time deterministic factoring a...

On Szeged Polynomial of a Graph

Further results on implicit factoring in polynomial time

In PKC 2009, May and Ritzenhofen presented interesting problems related to factoring large integers with some implicit hints. One of the problems is as follows. Consider N1 = p1q1 and N2 = p2q2, where p1, p2, q1, q2 are large primes. The primes p1, p2 are of same bit-size with the constraint that certain amount of Least Significant Bits (LSBs) of p1, p2 are same. Further the primes q1, q2 are o...

Nondeterministic polynomial time factoring in the tile assembly model

Formalized study of self-assembly has led to the definition of the tile assembly model, Previously I presented ways to compute arithmetic functions, such as addition and multiplication, in the tile assembly model: a highly distributed parallel model of computation that may be implemented using molecules or a large computer network such as the Internet. Here, I present tile assembly model system...