Related papers: Partition Expanders
We introduce an abstract framework for the study of clustering in metric graphs: after suitably metrising the space of graph partitions, we restrict Laplacians to the clusters thus arising and use their spectral gaps to define several…
Graph separation is a central tool in parameterized algorithm design, and important separators are among its most successful ingredients. They yield small, structured families of separators that can be enumerated efficiently, and underlie…
Graph Neural Networks (GNNs) have emerged as powerful tools for learning on graph-structured data, but often struggle to balance local and global information. While graph Transformers aim to address this by enabling long-range interactions,…
In the k-partition problem (k-PP), one is given an edge-weighted undirected graph, and one must partition the node set into at most k subsets, in order to minimise (or maximise) the total weight of the edges that have their end-nodes in the…
An emerging trend in approximate counting is to show that certain `low-temperature' problems are easy on typical instances, despite worst-case hardness results. For the class of regular graphs one usually shows that expansion can be…
We consider the problem of generating uniformly random partitions of the vertex set of a graph such that every piece induces a connected subgraph. For the case where we want to have partitions with linearly many pieces of bounded size, we…
We study graph partitioning problems from a min-max perspective, in which an input graph on n vertices should be partitioned into k parts, and the objective is to minimize the maximum number of edges leaving a single part. The two main…
We study the scalability of consensus-based distributed optimization algorithms by considering two questions: How many processors should we use for a given problem, and how often should they communicate when communication is not free?…
For each positive integer $n$, let $G_n$ be the graph of integer partitions of $n$, where two partitions are adjacent if one is obtained from the other by an elementary transfer of a cell in the Ferrers diagram, followed by reordering.…
Distributed systems that manage and process graph-structured data internally solve a graph partitioning problem to minimize their communication overhead and query run-time. Besides computational complexity -- optimal graph partitioning is…
In communication field, an important issue is to group users and base stations to as many as possible subnetworks satisfying certain interference constraints. These problems are usually formulated as a graph partition problems which…
The combinatorial properties of partitions with various restrictions on their hooksets are explored. A connection with numerical semigroups extends current results on simultaneous s/t-cores. Conditions that suffice for a partition to…
In recent years, the expander decomposition method was used to develop many graph algorithms, resulting in major improvements to longstanding complexity barriers. This powerful hammer has led the community to (1) believe that most problems…
The task of finding an extension to a given partial drawing of a graph while adhering to constraints on the representation has been extensively studied in the literature, with well-known results providing efficient algorithms for…
We present a new notion of limits of weighted directed graphs of growing size based on convergence of their random quotients. These limits are specified in terms of random exchangeable measures on the unit square. We call our limits…
Time-evolving large graph has received attention due to their participation in real-world applications such as social networks and PageRank calculation. It is necessary to partition a large-scale dynamic graph in a streaming manner to…
We give a new lower bound on the expansion coefficient of an edge-vertex graph of a $d$-regular graph. As a consequence, we obtain an improvement on the lower bound on relative minimum distance of the expander codes constructed by Sipser…
Can we use machine learning to compress graph data? The absence of ordering in graphs poses a significant challenge to conventional compression algorithms, limiting their attainable gains as well as their ability to discover relevant…
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…
We introduce propagation kernels, a general graph-kernel framework for efficiently measuring the similarity of structured data. Propagation kernels are based on monitoring how information spreads through a set of given graphs. They leverage…