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Graph embedding has become a key component of many data mining and analysis systems. Current graph embedding approaches either sample a large number of node pairs from a graph to learn node embeddings via stochastic optimization or…

A matching in a graph is induced if no two of its edges are joined by an edge, and finding a large induced matching is a very hard problem. Lin et al. (Approximating weighted induced matchings, Discrete Applied Mathematics 243 (2018)…

A geometric graph is a combinatorial graph, endowed with a geometry that is inherited from its embedding in a Euclidean space. Formulation of a meaningful measure of (dis-)similarity in both the combinatorial and geometric structures of two…

Similarity graphs are an active research direction for the nearest neighbor search (NNS) problem. New algorithms for similarity graph construction are continuously being proposed and analyzed by both theoreticians and practitioners.…

In this article, we propose tree edit distance with variables, which is an extension of the tree edit distance to handle trees with variables and has a potential application to measuring the similarity between mathematical formulas,…

The tree-depth problem can be seen as finding an elimination tree of minimum height for a given input graph $G$. We introduce a bicriteria generalization in which additionally the width of the elimination tree needs to be bounded by some…

Graph embedding, representing local and global neighborhood information by numerical vectors, is a crucial part of the mathematical modeling of a wide range of real-world systems. Among the embedding algorithms, random walk-based algorithms…

Betweenness is a well-known centrality measure that ranks the nodes of a network according to their participation in shortest paths. Since an exact computation is prohibitive in large networks, several approximation algorithms have been…

In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…

Model-based methods for recommender systems have been studied extensively for years. Modern recommender systems usually resort to 1) representation learning models which define user-item preference as the distance between their embedding…

The edit distance is a basic string similarity measure used in many applications such as text mining, signal processing, bioinformatics, and so on. However, the computational cost can be a problem when we repeat many distance calculations…

Network embedding has been intensively studied in the literature and widely used in various applications, such as link prediction and node classification. While previous work focus on the design of new algorithms or are tailored for various…

Graph sparsification is a well-established technique for accelerating graph-based learning algorithms, which uses edge sampling to approximate dense graphs with sparse ones. Because the sparsification error is random and unknown, users must…

Problems in scientific computing, such as distributing large sparse matrix operations, have analogous formulations as hypergraph partitioning problems. A hypergraph is a generalization of a traditional graph wherein "hyperedges" may connect…

In this paper, we develop deterministic fully dynamic algorithms for computing approximate distances in a graph with worst-case update time guarantees. In particular, we obtain improved dynamic algorithms that, given an unweighted and…

We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…

In this paper, we consider two fundamental cut approximation problems on large graphs. We prove new lower bounds for both problems that are optimal up to logarithmic factors. The first problem is to approximate cuts in balanced directed…

The distance of a graph from being triangle-free is a fundamental graph parameter, counting the number of edges that need to be removed from a graph in order for it to become triangle-free. Its corresponding computational problem is the…

Low-dimensional representations, or embeddings, of a graph's nodes facilitate several practical data science and data engineering tasks. As such embeddings rely, explicitly or implicitly, on a similarity measure among nodes, they require…

Graph embedding is a transformation of nodes of a graph into a set of vectors. A~good embedding should capture the graph topology, node-to-node relationship, and other relevant information about the graph, its subgraphs, and nodes. If these…