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The graph matching optimization problem is an essential component for many tasks in computer vision, such as bringing two deformable objects in correspondence. Naturally, a wide range of applicable algorithms have been proposed in the last…
The graph isomorphism is to determine whether two graphs are isomorphic. A closely related problem is automorphism detection, where an isomorphism between two graphs is a bijection between their vertex sets that preserves adjacency, and an…
The Subgraph Isomorphism problem asks, given a host graph G on n vertices and a pattern graph P on k vertices, whether G contains a subgraph isomorphic to P. The restriction of this problem to planar graphs has often been considered. After…
Graph partition is a key component to achieve workload balance and reduce job completion time in parallel graph processing systems. Among the various partition strategies, edge partition has demonstrated more promising performance in…
Graph machine learning has enjoyed a meteoric rise in popularity since the introduction of deep learning in graph contexts. This is no surprise due to the ubiquity of graph data in large scale industrial settings. Tacitly assumed in all…
Node-link diagrams are a popular method for representing graphs that capture relationships between individuals, businesses, proteins, and telecommunication endpoints. However, node-link diagrams may fail to convey insights regarding graph…
The role of polymorphisms in determining the complexity of constraint satisfaction problems is well established. In this context we study the stability of CSP complexity and polymorphism properties under some basic graph theoretic…
Covering problems are fundamental classical problems in optimization, computer science and complexity theory. Typically an input to these problems is a family of sets over a finite universe and the goal is to cover the elements of the…
The graph partitioning problem is widely used and studied in many practical and theoretical applications. The multilevel strategies represent today one of the most effective and efficient generic frameworks for solving this problem on…
Verifying the veracity of claims requires reasoning over a large knowledge base, often in the form of corpora of trustworthy sources. A common approach consists in retrieving short portions of relevant text from the reference documents and…
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…
We study the complexity of counting (weighted) planar graph homomorphism problem $\tt{Pl\text{-}GH}(M)$ parametrized by an arbitrary symmetric non-negative real valued matrix $M$. For matrices with pairwise distinct diagonal values, we…
An important objective for analyzing real-world graphs is to achieve scalable performance on large, streaming graphs. A challenging and relevant example is the graph partition problem. As a combinatorial problem, graph partition is NP-hard,…
Graph sampling allows mining a small representative subgraph from a big graph. Sampling algorithms deploy different strategies to replicate the properties of a given graph in the sampled graph. In this study, we provide a comprehensive…
We prove that there exists an algorithm for determining whether two piecewise-linear spatial graphs are isomorphic. In its most general form, our theorem applies to spatial graphs furnished with vertex colorings, edge colorings and/or edge…
We derive rigorous bounds for well-defined community structure in complex networks for a stochastic block model (SBM) benchmark. In particular, we analyze the effect of inter-community "noise" (inter-community edges) on any "community…
It is confirmed in this work that the graph isomorphism can be tested in polynomial time, which resolves a longstanding problem in the theory of computation. The contributions are in three phases as follows. 1. A description graph…
Community identification is a long-standing challenge in the modern network science, especially for very large scale networks containing millions of nodes. In this paper, we propose a new metric to quantify the structural similarity between…
Computing maximum independent sets in graphs is an important problem in computer science. In this paper, we develop an evolutionary algorithm to tackle the problem. The core innovations of the algorithm are very natural combine operations…
Given graphs $H$ and $G$, possibly with vertex-colors, a homomorphism is a function $f:V(H)\to V(G)$ that preserves colors and edges. Many interesting counting problems (e.g., subgraph and induced subgraph counts) are finite linear…