Factoring cardinal product graphs in polynomial time
نویسندگان
چکیده
منابع مشابه
Factoring directed graphs with respect to the cardinal product in polynomial time II
By a result of McKenzie [7] all finite directed graphs that satisfy certain connectivity conditions have unique prime factorizations with respect to the cardinal product. McKenzie does not provide an algorithm, and even up to now no polynomial algorithm that factors all graphs satisfying McKenzie’s conditions is known. Only partial results [1, 3, 5] have been published, all of which depend on c...
متن کاملFactoring directed graphs with respect to the cardinal product in polynomial time
By a result of McKenzie [4] finite directed graphs that satisfy certain connectivity and thinness conditions have the unique prime factorization property with respect to the cardinal product. We show that this property still holds under weaker connectivity and stronger thinness conditions. Furthermore, for such graphs the factorization can be determined in polynomial time.
متن کاملFactoring 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...
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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...
متن کاملFurther 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...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1998
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(98)00069-7