相关论文: Girth of the Cayley graph and Cayley hash function…
A symmetric encryption method based on properties of quasicrystals is proposed. The advantages of the cipher are strict aperiodicity and everywhere discontinuous property as well as the speed of computation, simplicity of implementation and…
We introduce shortcut graphs and groups. Shortcut graphs are graphs in which cycles cannot embed without metric distortion. Shortcut groups are groups which act properly and cocompactly on shortcut graphs. These notions unify a surprisingly…
A function $f : U \to \{0,\ldots,n-1\}$ is a minimal perfect hash function for a set $S \subseteq U$ of size $n$, if $f$ bijectively maps $S$ into the first $n$ natural numbers. These functions are important for many practical applications…
We propose a flexible procedure for large-scale image search by hash functions with kernels. Our method treats binary codes and pairwise semantic similarity as latent and observed variables, respectively, in a probabilistic model based on…
This paper first reviews some basic properties of cryptographic hash function, secret sharing scheme, and Latin square. Then we discuss why Latin square or its critical set is a good choice for secret representation and its relationship…
Stark and Terras introduced the edge zeta function of a finite graph in 1996. The edge zeta function is the reciprocal of a polynomial in twice as many variables as edges in the graph and can be computed in polynomial time. We look at graph…
In this paper, firstly, we provide some necessary and sufficient conditions for generalized Cayley graphs on abelian groups to be bipartite. Secondly, we deduce several necessary and sufficient conditions for generalized Cayley graphs on…
Searching on bipartite graphs serves as a fundamental task for various real-world applications, such as recommendation systems, database retrieval, and document querying. Conventional approaches rely on similarity matching in continuous…
We consider a refinement of the partition function of graph homomorphisms and present a quasi-polynomial algorithm to compute it in a certain domain. As a corollary, we obtain quasi-polynomial algorithms for computing partition functions…
We prove that random d-regular Cayley graphs of the symmetric group asymptotically almost surely have girth at least (log_{d-1}|G|)^{1/2}/2 and that random d-regular Cayley graphs of simple algebraic groups over F_q asymptotically almost…
We describe a consistent hashing algorithm which performs multiple lookups per key in a hash table of nodes. It requires no additional storage beyond the hash table, and achieves a peak-to-average load ratio of 1 + epsilon with just 1 +…
A minimal perfect hash function (MPHF) bijectively maps a set S of objects to the first |S| integers. It can be used as a building block in databases and data compression. RecSplit [Esposito et al., ALENEX'20] is currently the most space…
An attractive approach for fast search in image databases is binary hashing, where each high-dimensional, real-valued image is mapped onto a low-dimensional, binary vector and the search is done in this binary space. Finding the optimal…
Consider the Cayley graph of $S_n$ generated by a random pair of elements $x,y$. Conjecturally, the girth of this graph is $\Omega(n \log n)$ with probability tending to $1$ as $n\to\infty$. We show that it is at least $\Omega(n^{1/3})$.
In most state-of-the-art hashing-based visual search systems, local image descriptors of an image are first aggregated as a single feature vector. This feature vector is then subjected to a hashing function that produces a binary hash code.…
Semantic Hashing is a popular family of methods for efficient similarity search in large-scale datasets. In Semantic Hashing, documents are encoded as short binary vectors (i.e., hash codes), such that semantic similarity can be efficiently…
Control Flow Graph (CFG) similarity analysis is an essential technique for a variety of security analysis tasks, including malware detection and malware clustering. Even though various algorithms have been developed, existing CFG similarity…
We consider the hash function $h(x) = ((ax+b) \bmod p) \bmod n$ where $a,b$ are chosen uniformly at random from $\{0,1,\ldots,p-1\}$. We prove that when we use $h(x)$ in hashing with chaining to insert $n$ elements into a table of size $n$…
Graph classification aims to categorise graphs based on their structure and node attributes. In this work, we propose to tackle this task using tools from graph signal processing by deriving spectral features, which we then use to design…
String matching is the problem of finding all the occurrences of a pattern in a text. We propose improved versions of the fast family of string matching algorithms based on hashing $q$-grams. The improvement consists of considering minimal…