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In order to find the outcome probabilities of quantum mechanical systems like the optical networks underlying Boson sampling, it is necessary to be able to compute the permanents of unitary matrices, a computationally hard task. Here we…
Given two input graphs, finding the largest subgraph that occurs in both, i.e., finding the maximum common subgraph, is a fundamental operator for evaluating the similarity between two graphs in graph data analysis. Existing works for…
Graph signal sampling is the problem of selecting a subset of representative graph vertices whose values can be used to interpolate missing values on the remaining graph vertices. Optimizing the choice of sampling set using concepts from…
This paper proposes a novel method of algorithmic subsampling (data sketching) for multiway cluster dependent data. We establish a new uniform weak law of large numbers and a new central limit theorem for the multiway algorithmic subsample…
Since the work of Kaligosi and Sanders (2006), it is well-known that Quicksort -- which is commonly considered as one of the fastest in-place sorting algorithms -- suffers in an essential way from branch mispredictions. We present a novel…
Given a graph $G$, a vertex switch of $v \in V(G)$ results in a new graph where neighbors of $v$ become nonneighbors and vice versa. This operation gives rise to an equivalence relation over the set of labeled digraphs on $n$ vertices. The…
This paper presents a new distributed-memory algorithm called FastSV for finding connected components in an undirected graph. Our algorithm simplifies the classic Shiloach-Vishkin algorithm and employs several novel and efficient hooking…
Since its introduction Boson Sampling has been the subject of intense study in the world of quantum computing. The task is to sample independently from the set of all $n \times n$ submatrices built from possibly repeated rows of a larger $m…
Counting the frequency of small subgraphs is a fundamental technique in network analysis across various domains, most notably in bioinformatics and social networks. The special case of triangle counting has received much attention. Getting…
A general rate estimation method is proposed that is based on studying the in-sample evolution of appropriately chosen diverging/converging statistics. The proposed rate estimators are based on simple least squares arguments, and are shown…
Finding dense subgraphs is a fundamental algorithmic tool in data mining, community detection, and clustering. In this problem, one aims to find an induced subgraph whose edge-to-vertex ratio is maximized. We study the directed case of this…
A fast algorithm for B-splines in mixed models is presented. B-splines have local support and are computational attractive, because the corresponding matrices are sparse. A key element of the new algorithm is that the local character of…
The Bayesian network structure learning (BNSL) problem asks for a directed acyclic graph that maximizes a given score function. For networks with $n$ nodes, the fastest known algorithms run in time $O(2^n n^2)$ in the worst case, with no…
Generative network models play an important role in algorithm development, scaling studies, network analysis, and realistic system benchmarks for graph data sets. The commonly used graph-based benchmark model R-MAT has some drawbacks…
Partite, $3$-uniform hypergraphs are $3$-uniform hypergraphs in which each hyperedge contains exactly one point from each of the $3$ disjoint vertex classes. We consider the degree sequence problem of partite, $3$-uniform hypergraphs, that…
We introduce and study randomized sequential importance sampling algorithms for estimating the number of perfect matchings in bipartite graphs. In analyzing their performance, we establish various non-standard central limit theorems. We…
Graph isomorphism is an important computer science problem. The problem for the general case is unknown to be in polynomial time. The base algorithm for the general case works in quasi-polynomial time. The solutions in polynomial time for…
We introduce FastGraph, a novel GPU-optimized k-nearest neighbor algorithm specifically designed to accelerate graph construction in low-dimensional spaces (2-10 dimensions), critical for high-performance graph neural networks. Our method…
We propose a novel algorithm for efficiently computing a sparse directed adjacency matrix from a group of time series following a causal graph process. Our solution is scalable for both dense and sparse graphs and automatically selects the…
We present an accurate, real-time approach to robotic grasp detection based on convolutional neural networks. Our network performs single-stage regression to graspable bounding boxes without using standard sliding window or region proposal…