Nonlocal differential equations with (p,q)$ {(p,q)}$ growth

Factoring N = pq

We discuss the problem of factoring N = pq and survey some approaches. We then present a specialized factoring algorithm that runs in time Õ(q0.31), which is comparable to the runtime Õ(p) of the factoring algorithm for integers of the form N = pq presented in [1]. We then survey the factoring algorithm of [1] and discuss the number of advice bits needed for it to run in polynomial time. Furthe...

The Dwarf Nova Pq Andromedae

Texture Classification with the PQ Kernel

Computer vision researchers have developed various learning methods based on the bag of words model for image related tasks, including image categorization, image retrieval and texture classification. In this model, images are represented as histograms of visual words (or textons) from a vocabulary that is obtained by clustering local image descriptors. Next, a classifier is trained on the data...

Factoring pq with Quadratic Forms: Nice Cryptanalyses

We present a new algorithm based on binary quadratic forms to factor integers of the form N = pq. Its heuristic running time is exponential in the general case, but becomes polynomial when special (arithmetic) hints are available, which is exactly the case for the so-called NICE family of public-key cryptosystems based on quadratic fields introduced in the late 90s. Such cryptosystems come in t...

Planarity Algorithms via PQ-Trees

We give a linear-time planarity test that unifies and simplifies the algorithms of Shih and Hsu and Boyer and Myrvold; in our view, these algorithms are really one algorithm with different implementations. This leads to a short and direct proof of correctness without the use of Kuratowski’s theorem. Our planarity test extends to give a uniform random embedding, to count embeddings, to represent...