2,913 research outputs found
Memetic Multilevel Hypergraph Partitioning
Hypergraph partitioning has a wide range of important applications such as
VLSI design or scientific computing. With focus on solution quality, we develop
the first multilevel memetic algorithm to tackle the problem. Key components of
our contribution are new effective multilevel recombination and mutation
operations that provide a large amount of diversity. We perform a wide range of
experiments on a benchmark set containing instances from application areas such
VLSI, SAT solving, social networks, and scientific computing. Compared to the
state-of-the-art hypergraph partitioning tools hMetis, PaToH, and KaHyPar, our
new algorithm computes the best result on almost all instances
Parallel Graph Partitioning for Complex Networks
Processing large complex networks like social networks or web graphs has
recently attracted considerable interest. In order to do this in parallel, we
need to partition them into pieces of about equal size. Unfortunately, previous
parallel graph partitioners originally developed for more regular mesh-like
networks do not work well for these networks. This paper addresses this problem
by parallelizing and adapting the label propagation technique originally
developed for graph clustering. By introducing size constraints, label
propagation becomes applicable for both the coarsening and the refinement phase
of multilevel graph partitioning. We obtain very high quality by applying a
highly parallel evolutionary algorithm to the coarsened graph. The resulting
system is both more scalable and achieves higher quality than state-of-the-art
systems like ParMetis or PT-Scotch. For large complex networks the performance
differences are very big. For example, our algorithm can partition a web graph
with 3.3 billion edges in less than sixteen seconds using 512 cores of a high
performance cluster while producing a high quality partition -- none of the
competing systems can handle this graph on our system.Comment: Review article. Parallelization of our previous approach
arXiv:1402.328
Recent Advances in Graph Partitioning
We survey recent trends in practical algorithms for balanced graph
partitioning together with applications and future research directions
Incorporating Road Networks into Territory Design
Given a set of basic areas, the territory design problem asks to create a
predefined number of territories, each containing at least one basic area, such
that an objective function is optimized. Desired properties of territories
often include a reasonable balance, compact form, contiguity and small average
journey times which are usually encoded in the objective function or formulated
as constraints. We address the territory design problem by developing graph
theoretic models that also consider the underlying road network. The derived
graph models enable us to tackle the territory design problem by modifying
graph partitioning algorithms and mixed integer programming formulations so
that the objective of the planning problem is taken into account. We test and
compare the algorithms on several real world instances
Advanced Multilevel Node Separator Algorithms
A node separator of a graph is a subset S of the nodes such that removing S
and its incident edges divides the graph into two disconnected components of
about equal size. In this work, we introduce novel algorithms to find small
node separators in large graphs. With focus on solution quality, we introduce
novel flow-based local search algorithms which are integrated in a multilevel
framework. In addition, we transfer techniques successfully used in the graph
partitioning field. This includes the usage of edge ratings tailored to our
problem to guide the graph coarsening algorithm as well as highly localized
local search and iterated multilevel cycles to improve solution quality even
further. Experiments indicate that flow-based local search algorithms on its
own in a multilevel framework are already highly competitive in terms of
separator quality. Adding additional local search algorithms further improves
solution quality. Our strongest configuration almost always outperforms
competing systems while on average computing 10% and 62% smaller separators
than Metis and Scotch, respectively
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JOSTLE: multilevel graph partitioning software: an overview
In this chapter we look at JOSTLE, the multilevel graph-partitioning software package, and highlight some of the key research issues that it addresses. We first outline the core algorithms and place it in the context of the multilevel refinement paradigm. We then look at issues relating to its use as a tool for parallel processing and, in particular, partitioning in parallel. Since its first release in 1995, JOSTLE has been used for many mesh-based parallel scientific computing applications and so we also outline some enhancements such as multiphase mesh-partitioning, heterogeneous mapping and partitioning to optimise subdomain shap
Tree-based Coarsening and Partitioning of Complex Networks
Many applications produce massive complex networks whose analysis would
benefit from parallel processing. Parallel algorithms, in turn, often require a
suitable network partition. For solving optimization tasks such as graph
partitioning on large networks, multilevel methods are preferred in practice.
Yet, complex networks pose challenges to established multilevel algorithms, in
particular to their coarsening phase.
One way to specify a (recursive) coarsening of a graph is to rate its edges
and then contract the edges as prioritized by the rating. In this paper we (i)
define weights for the edges of a network that express the edges' importance
for connectivity, (ii) compute a minimum weight spanning tree with
respect to these weights, and (iii) rate the network edges based on the
conductance values of 's fundamental cuts. To this end, we also (iv)
develop the first optimal linear-time algorithm to compute the conductance
values of \emph{all} fundamental cuts of a given spanning tree. We integrate
the new edge rating into a leading multilevel graph partitioner and equip the
latter with a new greedy postprocessing for optimizing the maximum
communication volume (MCV). Experiments on bipartitioning frequently used
benchmark networks show that the postprocessing already reduces MCV by 11.3%.
Our new edge rating further reduces MCV by 10.3% compared to the previously
best rating with the postprocessing in place for both ratings. In total, with a
modest increase in running time, our new approach reduces the MCV of complex
network partitions by 20.4%
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