Related papers: Optimizing Connected Components Graph Partitioning…
We describe a new optimization scheme for finding high-quality correlation clusterings in planar graphs that uses weighted perfect matching as a subroutine. Our method provides lower-bounds on the energy of the optimal correlation…
Partitioning a graph into balanced components is important for several applications. For multi-objective problems, it is useful not only to find one solution but also to enumerate all the solutions with good values of objectives. However,…
Graph clustering aims at discovering a natural grouping of the nodes such that similar nodes are assigned to a common cluster. Many different algorithms have been proposed in the literature: for simple graphs, for graphs with attributes…
Computing high-quality graph partitions is a challenging problem with numerous applications. In this paper, we present a novel meta-heuristic for the balanced graph partitioning problem. Our approach is based on integer linear programs that…
Cell formation is a critical step in the design of cellular manufacturing systems. Recently, it was tackled using a cut-based-graph-partitioning model. This model meets real-life production systems requirements as it uses the actual amount…
Many problems of interest for cyber-physical network systems can be formulated as Mixed-Integer Linear Programs in which the constraints are distributed among the agents. In this paper we propose a distributed algorithmic framework to solve…
Many problems in computational geometry are not stated in graph-theoretic terms, but can be solved efficiently by constructing an auxiliary graph and performing a graph-theoretic algorithm on it. Often, the efficiency of the algorithm…
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…
This article empirically examines the computational cost of solving a known hard problem, graph clustering, using novel purpose-built computer hardware. We express the graph clustering problem as an intra-cluster distance or dissimilarity…
Spectral clustering is one of the most popular clustering methods. However, the high computational cost due to the involved eigen-decomposition procedure can immediately hinder its applications in large-scale tasks. In this paper we use…
The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several…
Spectral clustering is a popular method for community detection in network graphs: starting from a matrix representation of the graph, the nodes are clustered on a low dimensional projection obtained from a truncated spectral decomposition…
Spectral sparsification is a technique that is used to reduce the number of non-zero entries in a positive semidefinite matrix with little changes to its spectrum. In particular, the main application of spectral sparsification is to…
This paper studies the Graph-Connected Clique-Partitioning Problem (GCCP), a clustering optimization model in which units are characterized by both individual and relational data. This problem, introduced by Benati et al. (2017) under the…
The objective functions used in spectral clustering are usually composed of two terms: i) a term that minimizes the local quadratic variation of the cluster assignments on the graph and; ii) a term that balances the clustering partition and…
Given a hypergraph $H$, the Minimum Connectivity Inference problem asks for a graph on the same vertex set as $H$ with the minimum number of edges such that the subgraph induced by every hyperedge of $H$ is connected. This problem has…
Modern graph or network datasets often contain rich structure that goes beyond simple pairwise connections between nodes. This calls for complex representations that can capture, for instance, edges of different types as well as so-called…
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…
We study the percolation properties of graph partitioning on random regular graphs with N vertices of degree $k$. Optimal graph partitioning is directly related to optimal attack and immunization of complex networks. We find that for any…
Graph clustering has many important applications in computing, but due to the increasing sizes of graphs, even traditionally fast clustering methods can be computationally expensive for real-world graphs of interest. Scalability problems…