相关论文: Hypergraph Cuts with General Splitting Functions

The perfect matching polytope, i.e. the convex hull of (incidence vectors of) perfect matchings of a graph is used in many combinatorial algorithms. Kotzig, Lov\'asz and Plummer developed a decomposition theory for graphs with perfect…

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…

Based upon the idea that network functionality is impaired if two nodes in a network are sufficiently separated in terms of a given metric, we introduce two combinatorial \emph{pseudocut} problems generalizing the classical min-cut and…

Motivated by the increasing need for fast processing of large-scale graphs, we study a number of fundamental graph problems in a message-passing model for distributed computing, called $k$-machine model, where we have $k$ machines that…

Tolerance graphs model interval relations in such a way that intervals can tolerate a certain degree of overlap without being in conflict. This subclass of perfect graphs has been extensively studied, due to both its interesting structure…

A split graph is a graph whose vertex set can be partitioned into a clique and an independent set. A connected graph $G$ is said to be $t$-admissible if admits a spanning tree in which the distance between any two adjacent vertices of $G$…

We consider deletion problems in graphs and supermodular functions where the goal is to reduce density. In Graph Density Deletion (GraphDD), we are given a graph $G=(V,E)$ with non-negative vertex costs and a non-negative parameter $\rho…

We consider the graph link prediction task, which is a classic graph analytical problem with many real-world applications. With the advances of deep learning, current link prediction methods commonly compute features from subgraphs centered…

Subgraph counting aims to count the occurrences of a subgraph template T in a given network G. The basic problem of computing structural properties such as counting triangles and other subgraphs has found applications in diverse domains.…

The computational complexity of multicut-like problems may vary significantly depending on whether the terminals are fixed or not. In this work we present a comprehensive study of this phenomenon in two types of cut problems in directed…

In this work, we resolve the query complexity of global minimum cut problem for a graph by designing a randomized algorithm for approximating the size of minimum cut in a graph, where the graph can be accessed through local queries like…

This paper aims for set-to-hypergraph prediction, where the goal is to infer the set of relations for a given set of entities. This is a common abstraction for applications in particle physics, biological systems, and combinatorial…

An important objective for analyzing real-world graphs is to achieve scalable performance on large, streaming graphs. A challenging and relevant example is the graph partition problem. As a combinatorial problem, graph partition is NP-hard,…

We study the approximability of multiway partitioning problems, examples of which include Multiway Cut, Node-weighted Multiway Cut, and Hypergraph Multiway Cut. We investigate these problems from the point of view of two possible…

The d-Cut problem is to decide if a graph has an edge cut such that each vertex has at most d neighbours at the opposite side of the cut. If $d=1$, we obtain the intensively studied Matching Cut problem. The d-Cut problem has been studied…

Removing all connections between two vertices s and z in a graph by removing a minimum number of vertices is a fundamental problem in algorithmic graph theory. This (s,z)-separation problem is well-known to be polynomial solvable and serves…

We present a parallel version of the cut-pursuit algorithm for minimizing functionals involving the graph total variation. We show that the decomposition of the iterate into constant connected components, which is at the center of this…

Many problems such as node classification and link prediction in network data can be solved using graph embeddings. However, it is difficult to use graphs to capture non-binary relations such as communities of nodes. These kinds of complex…

In this paper we study fundamental connectivity properties of hypergraphs from a graph-theoretic perspective, with the emphasis on cut edges, cut vertices, and blocks. To prepare the ground, we define various types of subhypergraphs, as…

The parametric global minimum cut problem concerns a graph $G = (V,E)$ where the cost of each edge is an affine function of a parameter $\mu \in \mathbb{R}^d$ for some fixed dimension $d$. We consider the problems of finding the next…