Related papers: In-database connected component analysis
Optimizing the parallel training of large models requires exploring intra-operator parallelism plans for a computation graph that typically contains tens of thousands of primitive operators. While the optimization of parallel data…
Many applications collect a large number of time series, for example, the financial data of companies quoted in a stock exchange, the health care data of all patients that visit the emergency room of a hospital, or the temperature sequences…
Most of the machine learning algorithms are limited to learn from flat data: a recordset with prefixed structure. When learning from a record, these types of algorithms don't take into account other objects even though they are directly…
Maximal Clique Enumeration (MCE) is a fundamental graph mining problem, and is useful as a primitive in identifying dense structures in a graph. Due to the high computational cost of MCE, parallel methods are imperative for dealing with…
Node counting on a graph is subject to some fundamental theoretical limitations, yet a solution to such problems is necessary in many applications of graph theory to real-world systems, such as collective robotics and distributed sensor…
We present the first linear-time algorithm that computes the $4$-edge-connected components of an undirected graph. Hence, we also obtain the first linear-time algorithm for testing $4$-edge connectivity. Our results are based on a…
We present a new application for keyword search within relational databases, which uses a novel algorithm to solve the join discovery problem by finding Memex-like trails through the graph of foreign key dependencies. It differs from…
We present an $O(\log d + \log\log_{m/n} n)$-time randomized PRAM algorithm for computing the connected components of an $n$-vertex, $m$-edge undirected graph with maximum component diameter $d$. The algorithm runs on an ARBITRARY CRCW…
Graphs are a highly expressive data structure, but it is often difficult for humans to find patterns from a complex graph. Hence, generating human-interpretable sequences from graphs have gained interest, called graph2seq learning. It is…
We study the reverse mathematics and computability of countable graph theory, obtaining the following results. The principle that every countable graph has a connected component is equivalent to $\mathsf{ACA}_0$ over $\mathsf{RCA}_0$. The…
The construction of Mapper has emerged in the last decade as a powerful and effective topological data analysis tool that approximates and generalizes other topological summaries, such as the Reeb graph, the contour tree, split, and joint…
Much algorithmic research in NLP aims to efficiently manipulate rich formal structures. An algorithm designer typically seeks to provide guarantees about their proposed algorithm -- for example, that its running time or space complexity is…
The Massive Parallel Computing (MPC) model gained popularity during the last decade and it is now seen as the standard model for processing large scale data. One significant shortcoming of the model is that it assumes to work on static…
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…
We study the deterministic dynamics of networks N composed by m non identical, mutually pulse-coupled cells. We assume weighted, asymmetric and positive (cooperative) interactions among the cells, and arbitrarily large values of m. We…
A connected component labeling algorithm is developed for implicitly-defined domains specified by multivariate polynomials. The algorithm operates by recursively subdividing the constraint domain into hyperrectangular subcells until the…
The majority of data scientists and machine learning practitioners use relational data in their work [State of ML and Data Science 2017, Kaggle, Inc.]. But training machine learning models on data stored in relational databases requires…
The number of triangles in a graph is a fundamental metric, used in social network analysis, link classification and recommendation, and more. Driven by these applications and the trend that modern graph datasets are both large and dynamic,…
Principal component analysis (PCA) is a well-established tool in machine learning and data processing. The principal axes in PCA were shown to be equivalent to the maximum marginal likelihood estimator of the factor loading matrix in a…
Graph-based representations underlie a wide range of scientific problems. Graph connectivity is typically represented as a sparse matrix in the Compressed Sparse Row format. Large-scale graphs rely on distributed storage, allocating…