Related papers: Advanced Multilevel Node Separator Algorithms
The transformer-based semantic segmentation approaches, which divide the image into different regions by sliding windows and model the relation inside each window, have achieved outstanding success. However, since the relation modeling…
The current landscape of balanced graph partitioning is divided into high-quality but expensive multilevel algorithms and cheaper approaches with linear running time, such as single-level algorithms and streaming algorithms. We demonstrate…
Node counting on a graph is subject to some fundamental theoretical limitations, yet a solution to such problems is necessary in many applications of graph theory to real-world systems, such as collective robotics and distributed sensor…
We develop a multilevel algorithm for hypergraph partitioning that contracts the vertices one at a time and thus allows very high quality. This includes a rating function that avoids nonuniform vertex weights, an efficient "semi-dynamic"…
As with general graph processing systems, partitioning data over a cluster of machines improves the scalability of graph database management systems. However, these systems will incur additional network cost during the execution of a query…
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…
Flows in networks (or graphs) play a significant role in numerous computer vision tasks. The scalar-valued edges in these graphs often lead to a loss of information and thereby to limitations in terms of expressiveness. For example,…
In this paper we give a new, efficient algorithm for computing curve skeletons, based on local separators. Our efficiency stems from a multilevel approach, where we solve small problems across levels of detail and combine these in order to…
This paper presents a novel meta algorithm, Partition-Merge (PM), which takes existing centralized algorithms for graph computation and makes them distributed and faster. In a nutshell, PM divides the graph into small subgraphs using our…
In the realm of generative models for graphs, extensive research has been conducted. However, most existing methods struggle with large graphs due to the complexity of representing the entire joint distribution across all node pairs and…
Graph learning is often a necessary step in processing or representing structured data, when the underlying graph is not given explicitly. Graph learning is generally performed centrally with a full knowledge of the graph signals, namely…
Graphs are a natural representation of data from various contexts, such as social connections, the web, road networks, and many more. In the last decades, many of these networks have become enormous, requiring efficient algorithms to cut…
In the context of multi-domain network slices, multiple domains need to work together to provide a service. The problem of determining which part of the service fits within which domain is referred to as slice partitioning. The partitioning…
Community detection in graphs has many important and fundamental applications including in distributed systems, compression, image segmentation, divide-and-conquer graph algorithms such as nested dissection, document and word clustering,…
Distributed computing excels at processing large scale data, but the communication cost for synchronizing the shared parameters may slow down the overall performance. Fortunately, the interactions between parameter and data in many problems…
A {\em local graph partitioning algorithm} finds a set of vertices with small conductance (i.e. a sparse cut) by adaptively exploring part of a large graph $G$, starting from a specified vertex. For the algorithm to be local, its complexity…
The splitting-off operation in undirected graphs is a fundamental reduction operation that detaches all edges incident to a given vertex and adds new edges between the neighbors of that vertex while preserving their degrees. Lov\'asz (1974)…
Statistical analysis of large and sparse graphs is a challenging problem in data science due to the high dimensionality and nonlinearity of the problem. This paper presents a fast and scalable algorithm for partitioning such graphs into…
As networks continue to increase in size, current methods must be capable of handling large numbers of nodes and edges in order to be practically relevant. Instead of working directly with the entire (large) network, analyzing sub-networks…
Constructing a sparse spanning subgraph is a fundamental primitive in graph theory. In this paper, we study this problem in the Centralized Local model, where the goal is to decide whether an edge is part of the spanning subgraph by…