Related papers: Automorphism Shuffles for Graphs and Hypergraphs a…

A circulant (di)graph is a (di)graph on n vertices that admits a cyclic automorphism of order n. This paper provides a survey of the work that has been done on finding the automorphism groups of circulant (di)graphs, including the…

This article introduces an algorithm, MergeShuffle, which is an extremely efficient algorithm to generate random permutations (or to randomly permute an existing array). It is easy to implement, runs in $n\log_2 n + O(1)$ time, is in-place,…

Cryptography is always very important in data origin authentications, entity authentication, data integrity and confidentiality. In recent years, a variety of chaotic cryptographic schemes have been proposed. These schemes have typical…

This letter discusses the problem of testing the degree of randomness within an image, particularly for a shuffled or encrypted image. Its key contributions are: 1) a mathematical model of perfectly shuffled images; 2) the derivation of the…

Spectral clustering is a widely used algorithm to find clusters in networks. Several researchers have studied the stability of spectral clustering under local differential privacy with the additional assumption that the underlying networks…

As graph analytics often involves compute-intensive operations, GPUs have been extensively used to accelerate the processing. However, in many applications such as social networks, cyber security, and fraud detection, their representative…

We study how many riffle shuffles are required to mix n cards if only certain features of the deck are of interest, e.g. suits disregarded or only the colors of interest. For these features, the number of shuffles drops from 3/2 log_2(n) to…

This paper characterizes hierarchical clustering methods that abide by two previously introduced axioms -- thus, denominated admissible methods -- and proposes tractable algorithms for their implementation. We leverage the fact that, for…

Deep recommender systems rely heavily on large embedding tables to handle high-cardinality categorical features such as user/item identifiers, and face significant memory constraints at scale. To tackle this challenge, hashing techniques…

`Double edge swaps' transform one graph into another while preserving the graph's degree sequence, and have thus been used in a number of popular Markov chain Monte Carlo (MCMC) sampling techniques. However, while double edge-swaps can…

A new family of strongly regular graphs, called the general symplectic graphs $Sp(2\nu, q)$, associated with nonsingular alternate matrices is introduced. Their parameters as strongly regular graphs, their chromatic numbers as well as their…

Cut-based directed graph (digraph) clustering often focuses on finding dense within-cluster or sparse between-cluster connections, similar to cut-based undirected graph clustering methods. In contrast, for flow-based clusterings the edges…

We investigate the $k$-cycle shuffle on repeated cards, namely on a deck consisting of $l$ identical copies of each of $m$ card types, with total size $n=ml$. We establish asymptotic results for the total variation mixing of this shuffle,…

Graph clustering has many important applications in computing, but due to growing sizes of graphs, even traditionally fast clustering methods such as spectral partitioning can be computationally expensive for real-world graphs of interest.…

Inspired by a common technique for shuffling a deck of cards on a table without riffling, we continue the study of a prequel paper on the pile shuffle and its capabilities as a sorting device. We study two sort feasibility problems of…

We introduce and analyze the $S_k$ shuffle on $N$ cards, a natural generalization of the celebrated random adjacent transposition shuffle. In the $S_k$ shuffle, we choose uniformly at random a block of $k$ consecutive cards, and shuffle…

Consider the following one player game. A deck containing $m$ copies of $n$ different card types is shuffled uniformly at random. Each round the player tries to guess the next card in the deck, and then the card is revealed and discarded.…

Persistence diagrams (PDs), often characterized as sets of death and birth of homology class, have been known for providing a topological representation of a graph structure, which is often useful in machine learning tasks. Prior works rely…

Consider a card guessing game with complete feedback in which a deck of $n$ cards ordered $1,\dots, n$ is riffle-shuffled once. With the goal to maximize the number of correct guesses, a player guesses cards from the top of the deck one at…

Many complex systems show non-pairwise interactions, which can be captured by hypergraphs. In this work, we propose an edge-swapping method to sample random directed hypergraphs with fixed vertex and hyperarc degrees, which can be applied…