Results 1  10
of
180
Partitioning Graphs into Balanced Components
, 2009
"... We consider the kbalanced partitioning problem, where the goal is to partition the vertices of an input graph G into k equally sized components, while minimizing the total weight of the edges connecting different components. We allow k to be part of the input and denote the cardinality of the verte ..."
Abstract

Cited by 22 (2 self)
 Add to MetaCart
We consider the kbalanced partitioning problem, where the goal is to partition the vertices of an input graph G into k equally sized components, while minimizing the total weight of the edges connecting different components. We allow k to be part of the input and denote the cardinality
Fast Balanced Partitioning Is Hard Even on Grids and Trees
 MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE
, 2012
"... Two kinds of approximation algorithms exist for the kBALANCED PARTITIONING problem: those that are fast but compute unsatisfying approximation ratios, and those that guarantee high quality ratios but are slow. In this paper we prove that this tradeoff between runtime and solution quality is neces ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
on two combinatorially simple but very different classes, namely trees and solid grid graphs. The latter are finite connected subgraphs of the infinite 2D grid without holes. First we use the framework to show that for solid grid graphs it is NPhard to approximate the optimum number of cut edges within
Approximation and Inapproximability Results on Balanced Connected Partitions of Graphs
, 2007
"... Let G = (V, E) be a connected graph with a weight function w: V → Z+ and let q ≥ 2 be a positive integer. For X ⊆ V, let w(X) denote the sum of the weights of the vertices in X. We consider the following problem on G: find a qpartition P = (V1, V2,..., Vq) of V such that G[Vi] is connected (1 ≤ i ≤ ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
≤ q) and P maximizes min{w(Vi) : 1 ≤ i ≤ q}. This problem is called Max Balanced Connected qPartition and is denoted by BCPq. We show that for q ≥ 2 the problem BCPq is NPhard in the strong sense, even on qconnected graphs, and therefore does not admit a FPTAS, unless P = NP. We also show another
Mesh Partitioning: a Multilevel Balancing and Refinement Algorithm
, 1998
"... Multilevel algorithms are a successful class of optimisation techniques which address the mesh partitioning problem. They usually combine a graph contraction algorithm together with a local optimisation method which refines the partition at each graph level. In this paper we present an enhancement o ..."
Abstract

Cited by 81 (22 self)
 Add to MetaCart
improved results. Keywords: graphpartitioning, mesh partitioning, loadbalancing, multilevel algorithms. 1 Introduction The need for mesh partitioning arises naturally in many finite element (FE) and finite volume (FV) applications. Meshes composed of elements such as triangles or tetrahedra are often
Grids
, 2011
"... We shall prove theorems of the following flavor (see textbook/papers for precise statements and proofs). Thm. For any planar graph G = (V, E) on n = V  vertices and for any 1 weight function w: V → R +, we can partition V into A, B, S ⊆ V such that • [α–balanced] w(A), w(B) ≤ α · w(V) for some α ..."
Abstract
 Add to MetaCart
We shall prove theorems of the following flavor (see textbook/papers for precise statements and proofs). Thm. For any planar graph G = (V, E) on n = V  vertices and for any 1 weight function w: V → R +, we can partition V into A, B, S ⊆ V such that • [α–balanced] w(A), w(B) ≤ α · w(V) for some α
Balanced Partitions of Trees and Applications
, 2012
"... We study the kBALANCED PARTITIONING problem in which the vertices of a graph are to be partitioned into k sets of size at most ⌈n/k ⌉ while minimising the cut size, which is the number of edges connecting vertices in different sets. The problem is well studied for general graphs, for which it canno ..."
Abstract

Cited by 9 (3 self)
 Add to MetaCart
We study the kBALANCED PARTITIONING problem in which the vertices of a graph are to be partitioned into k sets of size at most ⌈n/k ⌉ while minimising the cut size, which is the number of edges connecting vertices in different sets. The problem is well studied for general graphs, for which
PARTITIONING GENERIC GRAPHS INTO K BALANCED SUBGRAPHS
, 2011
"... Graph partitioning is a classical graph theory problem that has proven to be NPhard. Most of the research in literature has focused its attention on a particular case of the problem called the graph bisection problem, where k = 2, such that the parts have approximately equal weight and minimizing ..."
Abstract
 Add to MetaCart
the size of the edge cut. In this article, we describe how to obtain balanced partitioning on a given undirected, connected and weighted graph into an arbitrary number k of regions (subgraphs), by hierarchically employing a multilevel bisection algorithm not only in the general graph, but also
On the Parameterized Complexity of Computing Balanced Partitions in Graphs
 THEORY OF COMPUTING SYSTEMS
, 2014
"... A balanced partition is a clustering of a graph into a given number of equalsized parts. For instance, the Bisection problem asks to remove at most k edges in order to partition the vertices into two equalsized parts. We prove that Bisection is FPT for the distance to constant cliquewidth if we a ..."
Abstract
 Add to MetaCart
A balanced partition is a clustering of a graph into a given number of equalsized parts. For instance, the Bisection problem asks to remove at most k edges in order to partition the vertices into two equalsized parts. We prove that Bisection is FPT for the distance to constant cliquewidth if we
Optimizing Partitions of Percolating Graphs
 Physica A
, 1999
"... The partitioning of random graphs is investigated numerically using "simulated annealing" and "extremal optimization." While generally an NPhard problem, it is shown that the optimization of the graph partitions is particularly difficult for sparse graphs with average connectivi ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
optimal partitions with bounded error at any low connectivity at a comparable computational cost. Key words: Optimization; Graph Partitioning; Percolation; Simulated Annealing; Extremal Optimization; SelfOrganized Criticality; The partitioning of graphs is generally an NPhard optimization problem with many
A local clustering algorithm for massive graphs and its application to nearlylinear time graph partitioning
, 2013
"... We study the design of local algorithms for massive graphs. A local graph algorithm is one that finds a solution containing or near a given vertex without looking at the whole graph. We present a local clustering algorithm. Our algorithm finds a good cluster—a subset of vertices whose internal conn ..."
Abstract

Cited by 60 (9 self)
 Add to MetaCart
with nearly optimal balance. Our algorithm takes time nearly linear in the number edges of the graph. Using the partitioning algorithm of this paper, we have designed a nearly linear time algorithm for constructing spectral sparsifiers of graphs, which we in turn use in a nearly linear time algorithm
Results 1  10
of
180