相关论文: Girth of the Cayley graph and Cayley hash function…

It is shown that a flat subgroup, $H$, of the totally disconnected, locally compact group $G$ decomposes into a finite number of subsemigroups on which the scale function is multiplicative. The image, $P$, of a multiplicative semigroup in…

Minwise hashing (MinHash) is a classical method for efficiently estimating the Jaccrad similarity in massive binary (0/1) data. To generate $K$ hash values for each data vector, the standard theory of MinHash requires $K$ independent…

We describe a simple and yet very scalable implementation of static functions (VFunc) and of static filters (VFilter) based on hypergraphs. We introduce the idea of {\epsilon}-cost sharding, which allows us to build structures that can…

One of the major issues of cryptography is the cryptanalysis of cipher algorithms. Cryptanalysis is the study of methods for obtaining the meaning of encrypted information, without access to the secret information that is normally required.…

Packing and covering problems for metric spaces, and graphs in particular, are of essential interest in combinatorics and coding theory. They are formulated in terms of metric balls of vertices. We consider a new problem in graph theory…

In this article we discuss a connection between two famous constructions in mathematics: a Cayley graph of a group and a (rational) billiard surface. For each rational billiard surface, there is a natural way to draw a Cayley graph of a…

Hashing methods have been widely used for efficient similarity retrieval on large scale image database. Traditional hashing methods learn hash functions to generate binary codes from hand-crafted features, which achieve limited accuracy…

This paper presents a new algorithm for calculating hash signatures of sets which can be directly used for Jaccard similarity estimation. The new approach is an improvement over the MinHash algorithm, because it has a better runtime…

Two-sort species yield differential equations for functional digraphs of Cayley permutations. From these we obtain an explicit formula for fixed-point-free Cayley permutations and prove that their proportion tends to $1/e$, as for…

We study those automatic sequences which are produced by an automaton whose underlying graph is the Cayley graph of a finite group. For $2$-automatic sequences, we find a characterization in terms of what we call homogeneity, and among…

The results of computer searches for large graphs with given (small) degree and diameter are presented. The new graphs are Cayley graphs of semidirect products of cyclic groups and related groups. One fundamental use of our ``dense graphs''…

Based on the generalized Cayley transform, a family of conservative one-step schemes of the sixth order of accuracy for the Zakharov-Shabat system is constructed. The exponential integrator is a special case. Schemes based on rational…

A binary Cayley graph is a Cayley graph based on a binary group. In 1982, Payan proved that any non-bipartite binary Cayley graph must contain a generalized Mycielski graph of an odd-cycle, implying that such a graph cannot have chromatic…

Hashing is promising for large-scale information retrieval tasks thanks to the efficiency of distance evaluation between binary codes. Generative hashing is often used to generate hashing codes in an unsupervised way. However, existing…

A graph $G$ covers a graph $H$ if there exists a locally bijective homomorphism from $G$ to $H$. We deal with regular covers where this homomorphism is prescribed by the action of a semiregular subgroup of $\textrm{Aut}(G)$. We study…

The breakthrough of achieving fully homomorphic encryption sparked enormous studies on where and how to apply homomorphic encryption schemes so that operations can be performed on encrypted data without the secret key while still obtaining…

Perfect hash functions give unique "names" to arbitrary keys requiring only a few bits per key. This is an essential building block in applications like static hash tables, databases, or bioinformatics. This paper introduces the PHast…

A new algebraic Cayley graph is constructed using finite fields. Its connectedness and diameter bound are studied via Weil's estimate for character sums. These graphs provide a new source of expander graphs, extending classical results of…

Several cryptographic systems depend upon the computational difficulty of reversing cryptographic hash functions. Robust hash functions transform inputs to outputs in such a way that the inputs cannot be later retrieved in a reasonable…

Many real world problems require fast and efficient lexical comparison of large numbers of short text strings. Search personalization is one such domain. We introduce the use of feature bit vectors using the hashing trick for improving…