Related papers: Balanced Districting on Grid Graphs with Provable …
Fair graph partition of social networks is a crucial step toward ensuring fair and non-discriminatory treatments in unsupervised user analysis. Current fair partition methods typically consider node balance, a notion pursuing a…
Let $G=(V,E)$ be a simple undirected graph with $n$ vertices then a set partition $\pi=\{V_1, ..., V_k\}$ of the vertex set of $G$ is a connected set partition if each subgraph $G[V_j]$ induced by the blocks $V_j$ of $\pi$ is connected for…
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…
A common way of partitioning graphs is through minimum cuts. One drawback of classical minimum cut methods is that they tend to produce small groups, which is why more balanced variants such as normalized and ratio cuts have seen more…
Many data types arising from data mining applications can be modeled as bipartite graphs, examples include terms and documents in a text corpus, customers and purchasing items in market basket analysis and reviewers and movies in a movie…
In this study, a graph-computing based grid splitting detection algorithm is proposed for contingency analysis in a graph-based EMS (Energy Management System). The graph model of a power system is established by storing its bus-branch…
Graph partitioning is the problem of dividing the nodes of a graph into balanced partitions while minimizing the edge cut across the partitions. Due to its combinatorial nature, many approximate solutions have been developed, including…
Matching and partitioning problems are fundamentals of computer vision applications with examples in multilabel segmentation, stereo estimation and optical-flow computation. These tasks can be posed as non-convex energy minimization…
A split graph is a graph whose vertex set can be partitioned into a clique and a stable set. Given a graph $G$ and weight function $w: V(G) \to \mathbb{Q}_{\geq 0}$, the Split Vertex Deletion (SVD) problem asks to find a minimum weight set…
We study the balanced $k$-way hypergraph partitioning problem, with a special focus on its practical applications to manycore scheduling. Given a hypergraph on $n$ nodes, our goal is to partition the node set into $k$ parts of size at most…
Vertex splitting replaces a vertex by two copies and partitions its incident edges amongst the copies. This problem has been studied as a graph editing operation to achieve desired properties with as few splits as possible, most often…
$ \def\vecc#1{\boldsymbol{#1}} $We design a polynomial time algorithm that for any weighted undirected graph $G = (V, E,\vecc w)$ and sufficiently large $\delta > 1$, partitions $V$ into subsets $V_1, \ldots, V_h$ for some $h\geq 1$, such…
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 define and study a spectral recombination algorithm, SpecReCom, for partitioning a graph into a given number of connected parts. It is straightforward to introduce additional constraints such as the requirement that the weight (or number…
A graph is well-covered if all its maximal independent sets have the same cardinality. This well studied concept was introduced by Plummer in 1970 and naturally generalizes to the weighted case. Given a graph $G$, a real-valued vertex…
Let $B=(X,Y,E)$ be a bipartite graph. A half-square of $B$ has one color class of $B$ as vertex set, say $X$; two vertices are adjacent whenever they have a common neighbor in $Y$. Every planar graph is a half-square of a planar bipartite…
This paper presents an optimal network topology control framework using cutting-plane methods for efficient network partitioning with controllable edges. The objective is to enable real-time reconfiguration of interconnected sub-networks…
We consider the problem of partitioning a graph into a non-fixed number of non-overlapping subgraphs of maximum density. The density of a partition is the sum of the densities of the subgraphs, where the density of a subgraph is its average…
Packing disjoint subgraphs in a given graph is a fundamental problem with many applications. Motivated by political districting, we focus on connected subgraphs that are compact (e.g., having constant radius from a single center vertex) and…
Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…