Related papers: Optimizing Connected Components Graph Partitioning…
We study a graph partitioning problem motivated by the simulation of the physical movement of multi-body systems on an atomistic level, where the forces are calculated from a quantum mechanical description of the electrons. Several advanced…
Matrix partition problems generalize a number of natural graph partition problems, and have been studied for several standard graph classes. We prove that each matrix partition problem has only finitely many minimal obstructions for split…
Index coding, or broadcasting with side information, is a network coding problem of most fundamental importance. In this problem, given a directed graph, each vertex represents a user with a need of information, and the neighborhood of each…
Graph clustering aims to divide the graph into different clusters. The recently emerging deep graph clustering approaches are largely built on graph neural networks (GNN). However, GNN is designed for general graph encoding and there is a…
This paper investigates graph clustering in the planted cluster model in the presence of {\em small clusters}. Traditional results dictate that for an algorithm to provably correctly recover the clusters, {\em all} clusters must be…
Clustering is the problem of separating a set of objects into groups (called clusters) so that objects within the same cluster are more similar to each other than to those in different clusters. Spectral clustering is a now well-known…
We study sublinear algorithms for two fundamental graph problems, MAXCUT and correlation clustering. Our focus is on constructing core-sets as well as developing streaming algorithms for these problems. Constant space algorithms are known…
We address the problem of partitioning a vertex-weighted connected graph into $k$ connected subgraphs that have similar weights, for a fixed integer $k\geq 2$. This problem, known as the \emph{balanced connected $k$-partition problem}…
The (constrained) minimization of a ratio of set functions is a problem frequently occurring in clustering and community detection. As these optimization problems are typically NP-hard, one uses convex or spectral relaxations in practice.…
Efficient resource allocation and optical switching promise high key rates, network adaptability, and cost reduction in repeaterless quantum communication networks. However, identifying optimal switching configurations remains a significant…
We are interested in multilayer graph clustering, which aims at dividing the graph nodes into categories or communities. To do so, we propose to learn a clustering-friendly embedding of the graph nodes by solving an optimization problem…
The paper develops a general framework for constrained clustering which is based on the close connection of geometric clustering and diagrams. Various new structural and algorithmic results are proved (and known results generalized and…
Multi-band transmission is a promising technical direction for spectrum and capacity expansion of existing optical networks. Due to the increase in the number of usable wavelengths in multi-band optical networks, the complexity of resource…
Coresets have become an invaluable tool for solving $k$-means and kernel $k$-means clustering problems on large datasets with small numbers of clusters. On the other hand, spectral clustering works well on sparse graphs and has recently…
This paper investigates the column generation (CG) for solving cutting stock problems (CSP). Traditional CG method, which repeatedly solves a restricted master problem (RMP), often suffers from two critical issues in practice -- the loss of…
As a fundamental tool in hierarchical graph clustering, computing connected components has been a central problem in large-scale data mining. While many known algorithms have been developed for this problem, they are either not scalable in…
We consider a class of nonsmooth fractional programming problems with fixed-point constraints, where the numerator is convex and the denominator is concave. To solve this problem, we propose splitting algorithms that compute subgradient…
The {\sc $c$-Balanced Separator} problem is a graph-partitioning problem in which given a graph $G$, one aims to find a cut of minimum size such that both the sides of the cut have at least $cn$ vertices. In this paper, we present new…
Combinatorial optimization is a fundamental problem found in many fields. In many real life situations, the constraints and the objective function forming the optimization problem are naturally distributed amongst different sites in some…
We study the problem of partitioning a given simple polygon $P$ into a minimum number of connected polygonal pieces, each of bounded size. We describe a general technique for constructing such partitions that works for several notions of…