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The big graph database model provides strong modeling for complex applications and efficient querying. However, it is still a big challenge to find all exact matches of a query graph in a big graph database, which is known as the subgraph…

We present a near-linear-time algorithm that, given a bridgeless cubic graph, finds a perfect matching intersecting every 3-edge-cut in exactly one edge. This improves over a cubic algorithm of Boyd et al. for the same problem, and over our…

Pure exploration in multi-armed bandits has emerged as an important framework for modeling decision-making and search under uncertainty. In modern applications, however, one is often faced with a tremendously large number of options. Even…

We initiate the algorithmic study of retracting a graph into a cycle in the graph, which seeks a mapping of the graph vertices to the cycle vertices, so as to minimize the maximum stretch of any edge, subject to the constraint that the…

This paper initiates the study of online algorithms for the maximum weight $b$-matching problem, a generalization of maximum weight matching where each node has at most $b \geq 1$ adjacent matching edges. The problem is motivated by…

We develop a novel distributed algorithm for the minimum cut problem. We primarily aim at solving large sparse problems. Assuming vertices of the graph are partitioned into several regions, the algorithm performs path augmentations inside…

In several online prediction problems of recent interest the comparison class is composed of matrices with bounded entries. For example, in the online max-cut problem, the comparison class is matrices which represent cuts of a given graph…

Community search over large graphs is a fundamental problem in graph analysis. Recent studies propose to compute top-k influential communities, where each reported community not only is a cohesive subgraph but also has a high influence…

We introduce a novel quantum algorithm for similar subgraph identification in form of an NP-hard cardinality-constrained binary quadratic optimization problem. Given a weighted reference graph with Laplacian $\boldsymbol{B}$, our algorithm…

This paper initiates the study of the classic balanced graph partitioning problem from an online perspective: Given an arbitrary sequence of pairwise communication requests between $n$ nodes, with patterns that may change over time, the…

To solve the combinatorial optimization problems especially the minimal Vertex-cover problem with high efficiency, is a significant task in theoretical computer science and many other subjects. Aiming at detecting the solution space of…

This paper studies a distributed online convex optimization problem, where agents in an unbalanced network cooperatively minimize the sum of their time-varying local cost functions subject to a coupled inequality constraint. To solve this…

Dense subgraph extraction is a fundamental problem in graph analysis and data mining, aimed at identifying cohesive and densely connected substructures within a given graph. It plays a crucial role in various domains, including social…

Inference on vertex-aligned graphs is of wide theoretical and practical importance.There are, however, few flexible and tractable statistical models for correlated graphs, and even fewer comprehensive approaches to parametric inference on…

We study two variants of \textsc{Maximum Cut}, which we call \textsc{Connected Maximum Cut} and \textsc{Maximum Minimal Cut}, in this paper. In these problems, given an unweighted graph, the goal is to compute a maximum cut satisfying some…

The notions of dominating sets of graphs began almost 400 years ago with the game of chess, which sparked the analysis of dominating sets of graphs, at first relatively loosely until the beginnings of the 1960s, when the issue was given…

The graph alignment problem aims to identify the vertex correspondence between two correlated graphs. Most existing studies focus on the scenario in which the two graphs share the same vertex set. However, in many real-world applications,…

Densest Subgraph Problem (DSP) is an important primitive problem with a wide range of applications, including fraud detection, community detection and DNA motif discovery. Edge-based density is one of the most common metrics in DSP.…

Graph-level anomaly detection has become a critical topic in diverse areas, such as financial fraud detection and detecting anomalous activities in social networks. While most research has focused on anomaly detection for visual data such…

Spectral Clustering as a relaxation of the normalized/ratio cut has become one of the standard graph-based clustering methods. Existing methods for the computation of multiple clusters, corresponding to a balanced $k$-cut of the graph, are…