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This paper studies real-world road networks from an algorithmic perspective, focusing on empirical studies that yield useful properties of road networks that can be exploited in the design of fast algorithms that deal with geographic data.…
In this paper, we propose GPSP, a novel Graph Partition and Space Projection based approach, to learn the representation of a heterogeneous network that consists of multiple types of nodes and links. Concretely, we first partition the…
Motivated by performance optimization of large-scale graph processing systems that distribute the graph across multiple machines, we consider the balanced graph partitioning problem. Compared to the previous work, we study the…
Graph-based models require aggregating information in the graph from neighbourhoods of different sizes. In particular, when the data exhibit varying levels of smoothness on the graph, a multi-scale approach is required to capture the…
Consider a plane graph G, drawn with straight lines. For every pair a,b of vertices of G, we compare the shortest-path distance between a and b in G (with Euclidean edge lengths) to their actual distance in the plane. The worst-case ratio…
Embedding networks into a fixed dimensional feature space, while preserving its essential structural properties is a fundamental task in graph analytics. These feature vectors (graph descriptors) are used to measure the pairwise similarity…
In this work, we study the computability of topological graphs, which are obtained by gluing arcs and rays together at their endpoints. We prove that every semicomputable graph in a computable metric space can be approximated, with…
In geographic information systems and in the production of digital maps for small devices with restricted computational resources one often wants to round coordinates to a rougher grid. This removes unnecessary detail and reduces space…
Consider the following problem: given a graph with edge costs and a subset Q of vertices, find a minimum-cost subgraph in which there are two edge-disjoint paths connecting every pair of vertices in Q. The problem is a failure-resilient…
Edge connectivity and vertex connectivity are two fundamental concepts in graph theory. Although by now there is a good understanding of the structure of graphs based on their edge connectivity, our knowledge in the case of vertex…
The construction of large-scale, low-latency networks becomes difficult as the number of nodes increases. In general, the way to construct a theoretically optimal solution is unknown. However, it is known that some methods can construct…
Graph neural networks (GNNs) have emerged as powerful tools for learning protein structures by capturing spatial relationships at the residue level. However, existing GNN-based methods often face challenges in learning multiscale…
Graphs have been utilized as a powerful tool to model pairwise relationships between people or objects. Such structure is a special type of a broader concept referred to as hypergraph, in which each hyperedge may consist of an arbitrary…
A GraphMaps is a system that visualizes a graph using zoom levels, which is similar to a geographic map visualization. GraphMaps reveals the structural properties of the graph and enables users to explore the graph in a natural way by using…
Network sampling is integral to the analysis of social, information, and biological networks. Since many real-world networks are massive in size, continuously evolving, and/or distributed in nature, the network structure is often sampled in…
Graph connectivity is a fundamental combinatorial optimization problem that arises in many practical applications, where usually a spanning subgraph of a network is used for its operation. However, in the real world, links may fail…
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…
Subgraphs reveal information about the geometry and functionalities of complex networks. For scale-free networks with unbounded degree fluctuations, we obtain the asymptotics of the number of times a small connected graph occurs as a…
Graph drawings are useful tools for exploring the structure and dynamics of data that can be represented by pair-wise relationships among a set of objects. Typical real-world social, biological or technological networks exhibit high…
Graph matching aims to establish correspondences between vertices of graphs such that both the node and edge attributes agree. Various learning-based methods were recently proposed for finding correspondences between image key points based…