Related papers: Graph splitting methods: Fixed points and strong c…
Graph similarity computation is one of the core operations in many graph-based applications, such as graph similarity search, graph database analysis, graph clustering, etc. Since computing the exact distance/similarity between two graphs…
Semi-supervised clustering is a basic problem in various applications. Most existing methods require knowledge of the ideal cluster number, which is often difficult to obtain in practice. Besides, satisfying the must-link constraints is…
We establish tightness of graph-based stochastic processes in the space $D[0+\epsilon,1-\epsilon]$ with $\epsilon >0$ that allows for discontinuities of the first kind. The graph-based stochastic processes are based on statistics…
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…
Normalized-cut graph partitioning aims to divide the set of nodes in a graph into $k$ disjoint clusters to minimize the fraction of the total edges between any cluster and all other clusters. In this paper, we consider a fair variant of the…
The emerging theory of graph limits exhibits an analytic perspective on graphs, showing that many important concepts and tools in graph theory and its applications can be described more naturally (and sometimes proved more easily) in…
In this article we discuss a possibility to implement a well-known scheme of proof for contraction mapping theorems in a situation, when convergence, families of Cauchy sequences, and contractiveness of mappings are defined axiomatically.…
The minimum $s$-$t$ cut problem in graphs is one of the most fundamental problems in combinatorial optimization, and graph cuts underlie algorithms throughout discrete mathematics, theoretical computer science, operations research, and data…
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…
In this paper, we deal with a notion of Banach space-valued mappings defined on a set consisting of finite graphs with uniformly bounded vertex degree. These functions will be endowed with certain boundedness and additivity criteria. We…
Fixed point results with respect to generalized rational contractive mappings in semi-metric spaces endowed with a directed graph are proved. Some examples are provided to illustrate the results. The obtained results extend, improve and…
As two fundamental problems, graph cuts and graph matching have been investigated over decades, resulting in vast literature in these two topics respectively. However the way of jointly applying and solving graph cuts and matching receives…
We consider the problem of estimating graph limits, known as graphons, from observations of sequences of sparse finite graphs. In this paper we show a simple method that can shed light on a subset of sparse graphs. The method involves…
Operator learning has been highly successful for continuous mappings between infinite-dimensional spaces, such as PDE solution operators. However, many operators of interest-including differential operators-are discontinuous or set-valued,…
A graph is a split graph if its vertex set can be partitioned into a clique and a stable set. A split graph is unbalanced if there exist two such partitions that are distinct. Cheng, Collins and Trenk (2016), discovered the following…
In this article we introduce a new type of cyclic contraction mapping on a pair of subsets of a metric space with a graph and prove best proximity points results for the same. Also, we demonstrate that the number of such points is same with…
The sparsest cut problem consists of identifying a small set of edges that breaks the graph into balanced sets of vertices. The normalized cut problem balances the total degree, instead of the size, of the resulting sets. Applications of…
Compression and sparsification algorithms are frequently applied in a preprocessing step before analyzing or optimizing large networks/graphs. In this paper we propose and study a new framework contracting edges of a graph (merging vertices…
We consider the problem of finding a fixed point of a nonexpansive mapping, which is also a solution of a pseudo-monotone equilibrium problem, where the bifunction in the equilibrium problem is the sum of two ones. We propose a splitting…
Random geometric graphs result from taking $n$ uniformly distributed points in the unit cube, $[0,1]^d$, and connecting two points if their Euclidean distance is at most $r$, for some prescribed $r$. We show that monotone properties for…