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In this paper we investigate the parameterized complexity of the task of counting and detecting occurrences of small patterns in unit disk graphs: Given an $n$-vertex unit disk graph $G$ with an embedding of ply $p$ (that is, the graph is…
Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…
Edge computing enables data processing closer to the source, significantly reducing latency, an essential requirement for real-time vision-based analytics such as object detection in surveillance and smart city environments. However, these…
A great variety of complex systems ranging from user interactions in communication networks to transactions in financial markets can be modeled as temporal graphs, which consist of a set of vertices and a series of timestamped and directed…
Graph embedding is a popular algorithmic approach for creating vector representations for individual vertices in networks. Training these algorithms at scale is important for creating embeddings that can be used for classification, ranking,…
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…
Problems on repeated geometric patterns in finite point sets in Euclidean space are extensively studied in the literature of combinatorial and computational geometry. Such problems trace their inspiration to Erd\H{o}s' original work on that…
We study deterministic algorithms for computing graph cuts, with focus on two fundamental problems: balanced sparse cut and $k$-vertex connectivity for small $k$ ($k=O(\polylog n)$). Both problems can be solved in near-linear time with…
In this paper, we introduce a generalization of graphlets to heterogeneous networks called typed graphlets. Informally, typed graphlets are small typed induced subgraphs. Typed graphlets generalize graphlets to rich heterogeneous networks…
Motif counting plays a crucial role in understanding the structural properties of networks. By computing motif frequencies, researchers can draw key insights into the structural properties of the underlying network. As networks become…
Bipartite graphs are a prevalent modeling tool for real-world networks, capturing interactions between vertices of two different types. Within this framework, bicliques emerge as crucial structures when studying dense subgraphs: they are…
Dense subgraph discovery is an important graph-mining primitive with a variety of real-world applications. One of the most well-studied optimization problems for dense subgraph discovery is the densest subgraph problem, where given an…
Pattern matching is a fundamental tool for answering complex graph queries. Unfortunately, existing solutions have limited capabilities: they do not scale to process large graphs and/or support only a restricted set of search templates or…
Let $W(G)$ be the Wiener index of a graph $G$. We say that a vertex $v \in V(G)$ is a \v{S}olt\'es vertex in $G$ if $W(G - v) = W(G)$, i.e. the Wiener index does not change if the vertex $v$ is removed. In 1991, \v{S}olt\'es posed the…
Given a graph $G = (V, E)$ and an integer $k$, we study $k$-Vertex Seperator (resp. $k$-Edge Separator), where the goal is to remove the minimum number of vertices (resp. edges) such that each connected component in the resulting graph has…
Let $H$ be a fixed $k$-vertex graph with $m$ edges and minimum degree $d >0$. We use the learning graph framework of Belovs to show that the bounded-error quantum query complexity of determining if an $n$-vertex graph contains $H$ as a…
Counting instances of specific subgraphs in a larger graph is an important problem in graph mining. Finding cliques of size k (k-cliques) is one example of this NP-hard problem. Different algorithms for clique counting avoid counting the…
In this paper, we propose a fully distributed algorithm for frequency offsets estimation in decentralized systems. With the proposed algorithm, each node estimates its frequency offsets by local computations and limited exchange of…
Many real-world applications give rise to large heterogeneous networks where nodes and edges can be of any arbitrary type (e.g., user, web page, location). Special cases of such heterogeneous graphs include homogeneous graphs, bipartite,…
Finding the dense regions of a graph and relations among them is a fundamental problem in network analysis. Core and truss decompositions reveal dense subgraphs with hierarchical relations. The incremental nature of algorithms for computing…