相关论文: An Upper Bound for Minimum True Matches in Graph I…

Counting maximum matchings in a graph is of great interest in statistical mechanics, solid-state chemistry, theoretical computer science, mathematics, among other disciplines. However, it is a challengeable problem to explicitly determine…

The graph isomorphism (GI) problem, which asks whether two graphs are structurally identical, occupies a unique position in computational complexity -- it is neither known to be solvable in polynomial time, nor proven to be NP-complete. We…

In the constrained planarity setting, we ask whether a graph admits a planar drawing that additionally satisfies a given set of constraints. These constraints are often derived from very natural problems; prominent examples are Level…

The network alignment problem asks for the best correspondence between two given graphs, so that the largest possible number of edges are matched. This problem appears in many scientific problems (like the study of protein-protein…

Graphs are fundamental objects that find widespread applications across computer science and beyond. Graph Theory has yielded deep insights about structural properties of various families of graphs, which are leveraged in the design and…

We present a method based on simulated annealing to obtain a nested split graph that approximates a real complex graph. This is used to compute a number of graph indices using very efficient algorithms that we develop, leveraging the…

The Matching Augmentation Problem (MAP) has recently received significant attention as an important step towards better approximation algorithms for finding cheap $2$-edge connected subgraphs. This has culminated in a…

Subgraph matching is the problem of determining the presence and location(s) of a given query graph in a large target graph. Despite being an NP-complete problem, the subgraph matching problem is crucial in domains ranging from network…

The Single-Source Shortest Path (SSSP) problem is well-known for the challenges in developing fast, practical, and work-efficient parallel algorithms. This work introduces a novel shortest path search method. It allows paths with different…

In this paper, we study linear programming based approaches to the maximum matching problem in the semi-streaming model. The semi-streaming model has gained attention as a model for processing massive graphs as the importance of such graphs…

Graph partitioning is a key fundamental problem in the area of big graph computation. Previous works do not consider the practical requirements when optimizing the big data analysis in real applications. In this paper, motivated by…

Graphs arising in statistical problems, signal processing, large networks, combinatorial optimization, and data analysis are often dense, which causes both computational and storage bottlenecks. One way of \textit{sparsifying} a…

A mean field feedback artificial neural network algorithm is developed and explored for the set covering problem. A convenient encoding of the inequality constraints is achieved by means of a multilinear penalty function. An approximate…

The graph similarity problem, also known as approximate graph isomorphism or graph matching problem, has been extensively studied in the machine learning community, but has not received much attention in the algorithms community: Given two…

Subgraph isomorphism, also known as subgraph matching, is typically regarded as an NP-complete problem. This complexity is further compounded in practical applications where edge weights are real-valued and may be affected by measurement…

Multilevel techniques are efficient approaches for solving the large linear systems that arise from discretized partial differential equations and other problems. While geometric multigrid requires detailed knowledge about the underlying…

Much combinatorial optimisation problems constitute a non-polynomial (NP) hard optimisation problem, i.e., they can not be solved in polynomial time. One such problem is finding the shortest route between two nodes on a graph.…

We resolve the space complexity of linear sketches for approximating the maximum matching problem in dynamic graph streams where the stream may include both edge insertion and deletion. Specifically, we show that for any $\epsilon > 0$,…

Graph clustering, an important unsupervised problem, has been shown to be more resistant to advances in Graph Neural Networks (GNNs). In addition, almost all clustering methods focus on homophilic graphs and ignore heterophily. This…

A dynamic graph algorithm is a data structure that answers queries about a property of the current graph while supporting graph modifications such as edge insertions and deletions. Prior work has shown strong conditional lower bounds for…