Related papers: Preimages for Z\'emor's Cayley hash function
Randomized algorithms are often enjoyed for their simplicity, but the hash functions used to yield the desired theoretical guarantees are often neither simple nor practical. Here we show that the simplest possible tabulation hashing…
Given a set $S$ of $n$ keys, a perfect hash function for $S$ maps the keys in $S$ to the first $m \geq n$ integers without collisions. It may return an arbitrary result for any key not in $S$ and is called minimal if $m = n$. The most…
The Euclidean algorithm is one of the oldest algorithms known to mankind. Given two integral numbers $a_1$ and $a_2$, it computes the greatest common divisor (gcd) of $a_1$ and $a_2$ in a very elegant way. From a lattice perspective, it…
Integer factorization has been one of the cornerstone applications of the field of quantum computing since the discovery of an efficient algorithm for factoring by Peter Shor. Unfortunately, factoring via Shor's algorithm is well beyond the…
LU-factorization of matrices is one of the fundamental algorithms of linear algebra. The widespread use of supercomputers with distributed memory requires a review of traditional algorithms, which were based on the common memory of a…
Recently, a family of tractable NMF algorithms have been proposed under the assumption that the data matrix satisfies a separability condition Donoho & Stodden (2003); Arora et al. (2012). Geometrically, this condition reformulates the NMF…
Finding meaningful clusters in drive-by-download malware data is a particularly difficult task. Malware data tends to contain overlapping clusters with wide variations of cardinality. This happens because there can be considerable…
Mining and exploring databases should provide users with knowledge and new insights. Tiles of data strive to unveil true underlying structure and distinguish valuable information from various kinds of noise. We propose a novel Boolean…
We propose a two-step algorithm for the construction of a Hidden Markov Model (HMM) of assigned size, i.e. cardinality of the state space of the underlying Markov chain, whose $n$-dimensional distribution is closest in divergence to a given…
The paper introduces a novel, hierarchical preconditioner based on nested dissection and hierarchical matrix compression. The preconditioner is intended for continuous and discontinuous Galerkin formulations of elliptic problems. We exploit…
Motivated by the problem of testing planarity and related properties, we study the problem of designing efficient {\em partition oracles}. A {\em partition oracle} is a procedure that, given access to the incidence lists representation of a…
Efficient matrix determinant calculations have been studied since the 19th century. Computers expand the range of determinants that are practically calculable to include matrices with symbolic entries. However, the fastest determinant…
The Boolean matrix factorization problem consists in approximating a matrix by the Boolean product of two smaller Boolean matrices. To obtain optimal solutions when the matrices to be factorized are small, we propose SAT and MaxSAT…
The task of factoring integers poses a significant challenge in modern cryptography, and quantum computing holds the potential to efficiently address this problem compared to classical algorithms. Thus, it is crucial to develop quantum…
Factor models are widely used for dimension reduction. Bayesian approaches to these models often place a prior on the factor loadings that allows for infinitely many factors, with loadings increasingly shrunk toward zero as the column index…
Network intrusion detection systems are an active area of research to identify threats that face computer networks. Network packets comprise of high dimensions which require huge effort to be examined effectively. As these dimensions…
Aiming to provide weak as possible axiomatic assumptions in which one can develop basic linear algebra, we give a uniform and integral version of the short propositional proofs for the determinant identities demonstrated over $GF(2)$ in…
We study the time complexity of induced subgraph isomorphism problems where the pattern graph is fixed. The earliest known example of an improvement over trivial algorithms is by Itai and Rodeh (1978) who sped up triangle detection in…
Quantum computers are able to outperform classical algorithms. This was long recognized by the visionary Richard Feynman who pointed out in the 1980s that quantum mechanical problems were better solved with quantum machines. It was only in…
In 1985, Janko and Tran Van Trung published an algorithm for constructing symmetric designs with prescribed automorphisms. This algorithm is based on the equations by Dembowski (1958) for tactical decompositions of point-block incidence…