Partitioning sparse matrices with eigenvectors of graphs
SIAM Journal on Matrix Analysis and Applications
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Algorithms for random generation and counting: a Markov chain approach
Algorithms for random generation and counting: a Markov chain approach
Graph contraction for mapping data on parallel computers: a quality-cost tradeoff
Scientific Programming
A multilevel algorithm for partitioning graphs
Supercomputing '95 Proceedings of the 1995 ACM/IEEE conference on Supercomputing
Fast and effective algorithms for graph partitioning and sparse-matrix ordering
IBM Journal of Research and Development - Special issue: optical lithography I
How Good is Recursive Bisection?
SIAM Journal on Scientific Computing
Multilevel k-way partitioning scheme for irregular graphs
Journal of Parallel and Distributed Computing
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
Efficient schemes for nearest neighbor load balancing
Parallel Computing - Special issue on parallelization techniques for numerical modelling
Diffusive load balancing schemes on heterogeneous networks
Proceedings of the twelfth annual ACM symposium on Parallel algorithms and architectures
Quality matching and local improvement for multilevel graph-partitioning
Parallel Computing - Special issue on graph partioning and parallel computing
New spectral bounds on k-partitioning of graphs
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On the Approximation of Complicated Dynamical Behavior
SIAM Journal on Numerical Analysis
Optimal and Alternating-Direction Load Balancing Schemes
Euro-Par '99 Proceedings of the 5th International Euro-Par Conference on Parallel Processing
A linear-time heuristic for improving network partitions
DAC '82 Proceedings of the 19th Design Automation Conference
On the Edge-Expansion of Graphs
Combinatorics, Probability and Computing
Introduction to Algorithms, Third Edition
Introduction to Algorithms, Third Edition
| Hi-index | 0.00 |
An almost invariant set of a dynamical system is a subset of state space where typical trajectories stay for a long period of time before they enter other parts of state space. These sets are an important characteristic for analyzing the macroscopic behavior of a given dynamical system. For instance, recently the identification of almost invariant sets has successfully been used in the context of the approximation of so-called chemical conformations for molecules. In this paper we propose new numerical and algorithmic tools for the identification of the number and the location of almost invariant sets in state space. These techniques are based on the use of set oriented numerical methods by which a graph is created which models the underlying dynamical behavior. In a second step graph theoretic methods are utilized in order to both identify the number of almost invariant sets and for an approximation of these sets. These algorithmic methods make use of the notion of congestion which is a quantity specifying bottlenecks in the graph. We apply these new techniques to the analysis of the dynamics of the molecules Pentane and Hexane. Our computational results are compared to analytical bounds which again are based on the congestion but also on spectral information on the transition matrix for the underlying graph.