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Correspondence between Multilevel Graph Partitions and Tree Decompositions

Michael Hamann, Ben Strasser
2019 Algorithms  
We present a mapping between rooted tree decompositions and node separator based multilevel graph partitions. Significant research into both tree decompositions and graph partitions exists.  ...  We hope that our result allows for an easier knowledge transfer between the two research avenues.  ...  Correspondence between Multilevel Graph Partitioning and Tree Decompositions In this section, we present the central result of our paper: a theorem to translate tree decomposition and multilevel graph  ... 
doi:10.3390/a12090198 fatcat:xf6w5uutm5g7bdstuqxwmxiu7u

Computing Tree Decompositions with FlowCutter: PACE 2017 Submission [article]

Ben Strasser
2017 arXiv   pre-print
The algorithm was originally developed in the context of accelerating shortest path computation on road graphs using multilevel partitions.  ...  We illustrate how this seemingly unrelated field fits into tree decomposition and parameterized complexity theory.  ...  It made the experimental evaluation easier and less error-prone. I thank Michael Hamann for fruitful discussions.  ... 
arXiv:1709.08949v1 fatcat:gl7wrbv3gfbbjfiotiqkr3f7fy

Automated structure detection for distributed process optimization

Ehecatl Antonio del Rio-Chanona, Fabio Fiorelli, Vassilios S. Vassiliadis
2016 Computers and Chemical Engineering  
The second approach uses a multilevel graph bisection algorithm to find the optimal partition, given a desired number of sub-problems.  ...  The partitioned graphs are translated back into decomposed sets of sub-problems with a minimal number of coupling constraints.  ...  These are called multilevel graph partitioning schemes (Cheng and Wei, 1991; Hagen and Kahng, 1992b,a; Garbers et al., 1990) .  ... 
doi:10.1016/j.compchemeng.2016.03.014 fatcat:pupohwsesfbbvo3fsii6ccc3a4

Multilevel Compound Tree – Construction Visualization and Interaction [chapter]

François Boutin, Jérôme Thièvre, Mountaz Hascoët
2005 Lecture Notes in Computer Science  
graphs and social graphs.  ...  Resulting Multilevel Silhouette Tree (MuSi-Tree) has a specific structure called multilevel compound tree. This work builds upon previous work on a compound tree structure called MO-Tree.  ...  The silhouette tree decomposition can be applied to graph G but also to any connected sub graph G' of G. Considering a silhouette of G', it naturally belongs to one silhouette of G.  ... 
doi:10.1007/11555261_67 fatcat:faimd2cmezhhfeqofrb2j3g4aa

Dual multilevel optimization

Timothy A. Davis, William W. Hager
2006 Mathematical programming  
As a result, techniques for ordering sparse matrices based on nested dissection or graph partitioning can be used to decompose a dual optimization problem into independent subproblems that could be solved  ...  The performance of a multilevel implementation of the Dual Active Set Algorithm is compared with CPLEX Simplex and Barrier codes using Netlib linear programming test problems.  ...  The algorithm exploits a multilevel decomposition and moves up and down the multilevel tree in a way loosely related to that of multilevel methods for graph partitioning or multigrid methods for partial  ... 
doi:10.1007/s10107-006-0022-3 fatcat:2qltahxyqndsbe6fcdlfvjiway

MARS-a multilevel full-chip gridless routing system

J. Cong, Jie Fang, Min Xie, Yan Zhang
2005 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems  
We introduced a number of efficient techniques in the multilevel routing scheme, including resource reservation, graph-based Steiner tree heuristic and history-based iterative refinement.  ...  The multilevel framework with recursive coarsening and refinement allows for scaling of our gridless routing system to very large designs.  ...  Graph-Based Steiner Tree Generation and Refinement Usually, rectilinear Steiner trees (RSTs) are used in the decomposition of multipin nets in the global routing phase.  ... 
doi:10.1109/tcad.2004.842803 fatcat:odozid7xcna6bc4vaecv35bgka

Multi-Constraint Mesh Partitioning for Contact/Impact Computations

George Karypis
2003 Proceedings of the 2003 ACM/IEEE conference on Supercomputing - SC '03  
The second goal is achieved by using a decision tree to decompose the space into rectangular or box-shaped regions that contain contact points from a single partition.  ...  Effective decomposition of these computations poses a number of challenges as it needs to both balance the computations and minimize the amount of communication that is performed during the finite element  ...  We achieve that by inducing a decision tree on the entire set of vertices of the graph (i.e., both those corresponding to contact points and those that do not), and then using this tree to guide the modification  ... 
doi:10.1145/1048935.1050206 dblp:conf/sc/Karypis03 fatcat:vilwvxwoavf2vltj2r6sdgxyq4

Assessing the quality of multilevel graph clustering

François Queyroi, Maylis Delest, Jean-Marc Fédou, Guy Melançon
2013 Data mining and knowledge discovery  
The popularity of graph hierarchies certainly relates to the relevance of multilevel models appearing in the natural and social sciences.  ...  The main results of this paper contribute to such a multilevel clustering theory, by designing and studying a multilevel modularity measure for hierarchically clustered graphs, explicitly taking the nesting  ...  Several conclusions can be made: -As said before the MLR-MCL clustering result is very close to the multilevel partition into conference and division.  ... 
doi:10.1007/s10618-013-0335-9 fatcat:trvgtnnfcje5hbx57qifro665m

Fast Graph Drawing Algorithm Revealing Networks Cores

Romain Giot, Romain Bourqui
2015 2015 19th International Conference on Information Visualisation  
We are interested with the node-links diagram which represents each node as a glyph and edge as a line between the corresponding nodes.  ...  Graph is a powerful tool to model relationships between elements and has been widely used in different research areas.  ...  between the corresponding nodes.  ... 
doi:10.1109/iv.2015.54 dblp:conf/iv/GiotB15 fatcat:jmnqsupx4bdoxl3unyqn65caaq

An algebraic approach for $${\mathcal{H}}$$ -matrix preconditioners

S. Oliveira, F. Yang
2007 Computing  
In this paper we present an algebraic approach for constructing H-matrices which combines multilevel clustering methods with H-matrix arithmetic to compute the H-inverse, H-LU, and the H-Cholesky factors  ...  The numerical results show that this method is efficient and greatly speeds up convergence compared to other approaches, such as JOR or AMG, for solving some large, sparse linear systems, and is comparable  ...  Acknowledgements I would like to thank the referees for various suggestions regarding the presentation of the paper, and also Prof. Kendall Atkinson for proofreading the final version.  ... 
doi:10.1007/s00607-007-0224-4 fatcat:c3jbdgmdajfhho2ngj6lgxzlp4

Review of domain-decomposition methods for the implementation of FEM on massively parallel computers

L. Hamandi, R. Lee, F. Ozguner
1995 IEEE Antennas & Propagation Magazine  
There is a tradeoff between the quality of the final partitions and the execution time of the DD method The DD problem can be viewed as a graph-partitioning problem We can define a task graph T(VT,ET),  ...  Although the complexity is the same between the RSB and the multilevel RSB, our numerical experiments indicate that the multilevel RSB is more efficient by a factor of 10. Comments.  ... 
doi:10.1109/74.370594 fatcat:5revky7ggzgodbxxke27ovby5q

An enhanced multilevel routing system

Jason Cong, Min Xie, Yan Zhang
2002 Computer-Aided Design (ICCAD), IEEE International Conference on  
Our contributions include: (1) resource reservation for local nets during the coarsening process, (2) congestion-driven, graph-based Steiner tree construction during the initial routing and the refinement  ...  In this paper, we present several novel techniques that make the recently published multilevel routing scheme [19] more effective and complete.  ...  The Steiner tree-based net decomposition results in better wirelength and routability than the MST based decomposition.  ... 
doi:10.1145/774572.774580 dblp:conf/iccad/CongXZ02 fatcat:t5lt3i7gtzbippddbfcgnp6ydu

Factorization-Based Graph Repartitionings [chapter]

Kateřina Jurková, Miroslav Tůma
2010 Lecture Notes in Computer Science  
It is well-known that the partitioned graph may have both a small separator and well-balanced domains but sparse matrix decompositions on domains can be completely unbalanced.  ...  The paper deals with the parallel computation of matrix factorization using graph partitioning-based domain decomposition.  ...  The elimination tree T is the rooted tree with the same vertex set as the adjacency graph G of A and with the vertex n as its root.  ... 
doi:10.1007/978-3-642-12535-5_92 fatcat:xyoiayjaongshil2rsgay6ttqa

Pathway Preserving Representation of Metabolic Networks

A. Lambert, J. Dubois, R. Bourqui
2011 Computer graphics forum (Print)  
Our technique combines partitioning, node placement and edge bundling to provide a pseudo-orthogonal visualization of the metabolic network.  ...  These constraints complicate the automatic generation of such visualization as it raises graph drawing issues.  ...  A clustered (partitioned) graph is usually modeled by a pair (G, T G ) (see [EF96] ) where G is a graph and T G is the hierarchy tree representing the multilevel partition of the nodes.  ... 
doi:10.1111/j.1467-8659.2011.01951.x fatcat:z2mfsmsgxfbu3p46ws7fgaw2ie

Optimizing a Hierarchical Community Structure of a Complex Network [chapter]

François Queyroi
2014 Studies in Computational Intelligence  
We test our method on random graphs and real world examples.  ...  We propose a method to validate and, if necessary, to optimize the multi-scale decomposition produced by such methods.  ...  This measure is used to access the similarity between two partitions of the same set. The result is a score between 0 (the partitions are completely different) and 1 (the partitions are the same).  ... 
doi:10.1007/978-3-319-02999-3_1 fatcat:qxan44rp5rawhky4moypf25srm
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