Related papers: Speeding Up Graph Algorithms via Switching Classes

This paper presents a general graph representation learning framework called DeepGL for learning deep node and edge representations from large (attributed) graphs. In particular, DeepGL begins by deriving a set of base features (e.g.,…

A powerful framework for studying graphs is to consider them as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius.…

In this paper, we investigate the problem of finding {\it bisections} (i.e., balanced bipartitions) in graphs. We prove the following two results for {\it all} graphs $G$: (1). $G$ has a bisection where each vertex $v$ has at least $(1/4 -…

This paper deals with the problem of finding a collection of vertex-disjoint paths in a given graph G=(V,E) such that each path has at least four vertices and the total number of vertices in these paths is maximized. The problem is NP-hard…

Graph Neural Networks (GNNs) have attracted considerable attention and have emerged as a new promising paradigm to process graph-structured data. GNNs are usually stacked to multiple layers and the node representations in each layer are…

Determining whether two graphs are structurally identical is a fundamental problem with applications spanning mathematics, computer science, chemistry, and network science. Despite decades of study, graph isomorphism remains a challenging…

Recent work on Graph Neural Networks has demonstrated that self-supervised pretraining can further enhance performance on downstream graph, link, and node classification tasks. However, the efficacy of pretraining tasks has not been fully…

We present a graph theoretic upper bound on speedup needed to achieve 100% throughput in a multicast switch using network coding. By bounding speedup, we show the equivalence between network coding and speedup in multicast switches - i.e.…

After a somewhat rocky start, geometry and topology have established a foothold in machine learning. Message passing, either on graphs or higher-order complexes, is one of the main drivers of geometric deep learning, and paradigms that were…

We propose a fast approximate algorithm for large graph matching. A new projected fixed-point method is defined and a new doubly stochastic projection is adopted to derive the algorithm. Previous graph matching algorithms suffer from high…

With growing emphasis on privacy regulations, machine unlearning has become increasingly critical in real-world applications such as social networks and recommender systems, many of which are naturally represented as graphs. However,…

Graph matching aims to find correspondences between two graphs. This paper integrates several well-known graph matching algorithms into a framework: the constrained gradient method. The primary difference among these algorithms lies in…

Quantum computers can sometimes exponentially outperform classical ones, but only for problems with sufficient structure. While it is well known that query problems with full permutation symmetry can have at most polynomial quantum speedup…

Predicting node labels on a given graph is a widely studied problem with many applications, including community detection and molecular graph prediction. This paper considers predicting multiple node labeling functions on graphs…

This article deals with homomorphisms of oriented graphs with respect to push equivalence. Here homomorphisms refer to arc preserving vertex mappings, and push equivalence refers to the equivalence class of orientations of a graph $G$ those…

Graph neural networks (GNNs) are emerging for machine learning research on graph-structured data. GNNs achieve state-of-the-art performance on many tasks, but they face scalability challenges when it comes to real-world applications that…

We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…

Consider two graphs G_1 and G_2 on the same vertex set V and suppose that G_i has m_i edges. Then there is a bipartition of V into two classes A and B so that for both i=1,2 the number of edges between A and B in G_i is (1+o(1))m_i/2. This…

Graph classification is an important area in both modern research and industry. Multiple applications, especially in chemistry and novel drug discovery, encourage rapid development of machine learning models in this area. To keep up with…

Graphs can model real-world, complex systems by representing entities and their interactions in terms of nodes and edges. To better exploit the graph structure, graph neural networks have been developed, which learn entity and edge…