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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 techniques are useful to characterize spectral signature relations for hyperspectral images. However, such images consists of disjoint classes due to spatial details that are often ignored by existing graph computing tools.…

Graph representation learning (also called graph embeddings) is a popular technique for incorporating network structure into machine learning models. Unsupervised graph embedding methods aim to capture graph structure by learning a…

The rise of graph-structured data has driven major advances in Graph Machine Learning (GML), where graph embeddings (GEs) map features from Knowledge Graphs (KGs) into vector spaces, enabling tasks like node classification and link…

Graph representation learning aims to effectively encode high-dimensional sparse graph-structured data into low-dimensional dense vectors, which is a fundamental task that has been widely studied in a range of fields, including machine…

Performing link prediction using knowledge graph embedding models has become a popular approach for knowledge graph completion. Such models employ a transformation function that maps nodes via edges into a vector space in order to measure…

Many of the classic graph problems cannot be solved in the Massively Parallel Computation setting (MPC) with strongly sublinear space per machine and $o(\log n)$ rounds, unless the 1-vs-2 cycles conjecture is false. This is true even on…

We resolve in the affirmative conjectures of Repovs and A. Skopenkov (1998), and M. Skopenkov (2003) generalizing the classical Hanani-Tutte theorem to the setting of approximating maps of graphs on 2-dimensional surfaces by embeddings. Our…

In the graph stream model of computation, an algorithm processes the edges of an input graph in one or more sequential passes while using a memory sublinear in the input size. This model poses significant challenges for constructing long…

In a finite undirected simple graph, a {\it chordless cycle} is an induced subgraph which is a cycle. We propose two algorithms to enumerate all chordless cycles of such a graph. Compared to other similar algorithms, the proposed algorithms…

This paper studies the problem of embedding very large information networks into low-dimensional vector spaces, which is useful in many tasks such as visualization, node classification, and link prediction. Most existing graph embedding…

Graph embedding is an important approach for graph analysis tasks such as node classification and link prediction. The goal of graph embedding is to find a low dimensional representation of graph nodes that preserves the graph information.…

Mapping complex input data into suitable lower dimensional manifolds is a common procedure in machine learning. This step is beneficial mainly for two reasons: (1) it reduces the data dimensionality and (2) it provides a new data…

Graph Neural Networks (GNNs) are widely used for learning on graph-structured data, but scaling GNN training to massive graphs remains challenging. To enable scalable distributed training, graphs are divided into smaller partitions that are…

A unit cube in $k$ dimensional space (or \emph{$k$-cube} in short) is defined as the Cartesian product $R_1\times R_2\times...\times R_k$ where $R_i$(for $1\leq i\leq k$) is a closed interval of the form $[a_i,a_i+1]$ on the real line. A…

An important question in the study of quasi-perfect codes is whether such codes can be constructed for all possible lengths $n$. In this paper, we address this question for specific values of $n$. First, we investigate the existence of…

Graphs with bounded highway dimension were introduced by Abraham et al. [SODA 2010] as a model of transportation networks. We show that any such graph can be embedded into a distribution over bounded treewidth graphs with arbitrarily small…

The complexity of a reasoning task over a graphical model is tied to the induced width of the underlying graph. It is well-known that the conditioning (assigning values) on a subset of variables yields a subproblem of the reduced complexity…

Cutwidth is one of the classic layout parameters for graphs. It measures how well one can order the vertices of a graph in a linear manner, so that the maximum number of edges between any prefix and its complement suffix is minimized. As…

Graphs are ubiquitous, and they can model unique characteristics and complex relations of real-life systems. Although using machine learning (ML) on graphs is promising, their raw representation is not suitable for ML algorithms. Graph…