Balanced Partitioning of Grids and Related Graphs. A Theoretical Study of Data Distribution in Parallel Finite Element Model Simulations

Language: English

Published by Cuvillier, Cuvillier Jun 2012, 2012

3954041251 / 9783954041251

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This item is printed on demand - Print on Demand Titel. Neuware -This thesis considers the k-BALANCED PARTITIONING problem, which is defined as follows. Find the minimum number of edges in a graph that, when cut, partition the vertices into k (almost) equally sized sets. Amongst others, the problem derives its importance from the need to distribute data within a parallel-computing architecture. In this setting we are particularly interested in 2D finite element model (FEM) simulations. We therefore model the input as a regular quadrilateral tiling of the plane. More precisely, we focus on solid grid graphs. These are finite connected subgraphs of the infinite 2D grid without holes. However we also consider other graph classes. In particular, trees often give surprising conclusions to the problem on grid graphs.We provide several efficient algorithms computing provably good solutions. For the case when k=2 (the BISECTION problem) these include methods to compute optimal as well as approximate solutions. When k can take arbitrary values we provide two kinds of approximation algorithms. First we give a method that is fast but, for practical applications, has unsatisfactory approximation ratios. Additionally we provide an algorithm computing near-optimal solutions, which however is too slow to be used in practice. We also prove that the gained tradeoff between fast runtime and good approximation factors is unavoidable. For this we provide corresponding hardness results.Cuvillier Verlag, Nonnenstieg 8, 37075 Göttingen 218 pp. Englisch.…

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Title
Balanced Partitioning of Grids and Related Graphs. A Theoretical Study of Data Distribution in Parallel Finite Element Model Simulations
Author
Andreas Emil Feldmann
Publisher
Cuvillier, Cuvillier Jun 2012
Publication year
2012
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
3954041251
ISBN 13
9783954041251
Item weight
289 grams
Dimensions
210x148x13 mm

buchversandmimpf2000

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