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k-way Hypergraph Partitioning via n-Level Recursive Bisection [article]

Sebastian Schlag, Vitali Henne, Tobias Heuer, Henning Meyerhenke, Peter Sanders, Christian Schulz
2015 arXiv   pre-print
(Karlsruhe Hypergraph Partitioning).  ...  Using several caching and lazy-evaluation techniques during coarsening and refinement, we reduce the running time by up to two-orders of magnitude compared to a naive n-level algorithm that would be adequate  ...  In Section 4.1, we start by explaining how to compute a k-way partition via recursive bisection.  ... 
arXiv:1511.03137v1 fatcat:3awdpgx5undm7pbdxtsvan3o3q

Multilevel k-way hypergraph partitioning

George Karypis, Vipin Kumar
1999 Proceedings of the 36th ACM/IEEE conference on Design automation conference - DAC '99  
In this paper, we present a new multilevel k-way hypergraph partitioning algorithm that substantially outperforms the existing stateof-the-art K-PM/LR algorithm for multi-way partitioning. both for optimizing  ...  Experiments on the ISPD98 benchmark suite show that the partitionings produced by our scheme are on the average 15% to 23% better than those produced by the K-PM/LR algorithm, both in terms of the hyperedge  ...  Conclusions The multilevel k-way partitioning scheme presented in this paper substantially outperforms the state-of-the-art K-PM/LR algorithm for multi-way partitioning [17] both for minimizing the hyperedge  ... 
doi:10.1145/309847.309954 dblp:conf/dac/KarypisK99 fatcat:xl3xqrybprdsze4vibkwimgjl4

Multilevel k-way Hypergraph Partitioning

George Karypis, Vipin Kumar
2000 VLSI design (Print)  
In this paper, we present a new multilevel k-way hypergraph partitioning algorithm that substantially outperforms the existing stateof-the-art K-PM/LR algorithm for multi-way partitioning. both for optimizing  ...  Experiments on the ISPD98 benchmark suite show that the partitionings produced by our scheme are on the average 15% to 23% better than those produced by the K-PM/LR algorithm, both in terms of the hyperedge  ...  Conclusions The multilevel k-way partitioning scheme presented in this paper substantially outperforms the state-of-the-art K-PM/LR algorithm for multi-way partitioning [17] both for minimizing the hyperedge  ... 
doi:10.1155/2000/19436 fatcat:yg5i6p6jlrfejljz6fk6ex6daq

Parkway 2.0: A Parallel Multilevel Hypergraph Partitioning Tool [chapter]

Aleksandar Trifunovic, William J. Knottenbelt
2004 Lecture Notes in Computer Science  
We recently proposed a coarse-grained parallel multilevel algorithm for the k-way hypergraph partitioning problem.  ...  Further, partition quality in terms of the k-1 metric is shown to be competitive with the best serial hypergraph partitioners and degrades only minimally as more processors are used.  ...  The k-way partition is typically computed either directly or by recursive bisection.  ... 
doi:10.1007/978-3-540-30182-0_79 fatcat:sm4m2ntrb5ej7gj2ceruuzkz4e

PaToH (Partitioning Tool for Hypergraphs) [chapter]

Bruce Leasure, David J. Kuck, Sergei Gorlatch, Murray Cole, Gregory R. Watson, Alain Darte, David Padua, Utpal Banerjee, Olaf Schenk, Klaus Gärtner, David Padua, Howard Jay Siegel (+43 others)
2011 Encyclopedia of Parallel Computing  
These considerations have motivated the two-level application of FM in hypergraph partitioning.  ...  Preliminaries Hypergraph Partitioning A hypergraph H = (V, N ) is defined as a set of vertices V and a set of nets (hyperedges) N among those vertices.  ...  The hypergraph partitioning problem is known to be NP-hard [19] . Recursive Bisection The K -way graph/hypergraph partitioning problem is usually solved by recursive bisection.  ... 
doi:10.1007/978-0-387-09766-4_93 fatcat:wfsvqf4yjndg3hdvuihdbgd2ti

Balanced Coarsening for Multilevel Hypergraph Partitioning via Wasserstein Discrepancy [article]

Zhicheng Guo, Jiaxuan Zhao, Licheng Jiao, Xu Liu
2021 arXiv   pre-print
We propose a balanced coarsening scheme for multilevel hypergraph partitioning. In addition, an initial partitioning algorithm is designed to improve the quality of k-way hypergraph partitioning.  ...  By assigning vertex weights through the LPT algorithm, we generate a prior hypergraph under a relaxed balance constraint.  ...  In this paper, we only consider the recursive bisection of multilevel approach, and the hypergraph is divided two blocks at each level. When k partitions are found, the multilevel partitioning ends.  ... 
arXiv:2106.07501v1 fatcat:vwxsskx2kzdaxmchkk7c3kmkxm

A nested dissection partitioning method for parallel sparse matrix-vector multiplication

Erik G. Boman, Michael M. Wolf
2013 2013 IEEE High Performance Extreme Computing Conference (HPEC)  
We have implemented our algorithm using hypergraph partitioning software to enable a fair comparison with existing methods.  ...  Our main contributions are: (i) an exact graph model for communication with general (two-dimensional) matrix distribution, and (ii) a recursive partitioning algorithm based on nested dissection that approximately  ...  This recursive bisection technique has been effectively used in many graph and hypergraph partitioning methods [2] , [15] .  ... 
doi:10.1109/hpec.2013.6670333 dblp:conf/hpec/BomanW13 fatcat:5gfxh4alerhvvpe6vgf5tofuem

Multi-level direct K-way hypergraph partitioning with multiple constraints and fixed vertices

Cevdet Aykanat, B. Barla Cambazoglu, Bora Uçar
2008 Journal of Parallel and Distributed Computing  
We describe a careful implementation of a multi-level direct K-way hypergraph partitioning algorithm, which performs better than a well-known recursive-bisection-based partitioning algorithm in hypergraph  ...  We claim that hypergraph partitioning with multiple constraints and fixed vertices should be implemented using direct K-way refinement, instead of the widely adopted recursive bisection paradigm.  ...  In the RB paradigm, a hypergraph is recursively bisected (i.e., two-way partitioned) until the desired number of parts is obtained.  ... 
doi:10.1016/j.jpdc.2007.09.006 fatcat:llskgjf475fwznflepehkkqw64

Multi-objective hypergraph partitioning algorithms for cut and maximum subdomain degree minimization

N. Selvakkumaran, G. Karypis
2003 ICCAD-2003. International Conference on Computer Aided Design (IEEE Cat. No.03CH37486)  
In this paper we present a family of multi-objective hypergraph partitioning algorithms based on the multilevel paradigm, which are capable of producing solutions in which both the cut and the maximum  ...  This type of partitionings are critical for existing and emerging applications in VLSI CAD as they allow to both minimize and evenly distribute the interconnects across the physical devices.  ...  Moreover, direct £ -way partitioning can potentially produce much better solutions than a method that computes a £ -way partitioning via recursive bisection.  ... 
doi:10.1109/iccad.2003.159757 fatcat:cdjt6fh5mbfxniaipqsvtwomtu

Social Hash Partitioner: A Scalable Distributed Hypergraph Partitioner [article]

Igor Kabiljo and Brian Karrer and Mayank Pundir and Sergey Pupyrev and Alon Shalita and Alessandro Presta and Yaroslav Akhremtsev
2017 arXiv   pre-print
We design and implement a distributed algorithm for balanced k-way hypergraph partitioning that minimizes fanout, a fundamental hypergraph quantity also known as the communication volume and (k-1)-cut  ...  We call the resulting tool Social Hash Partitioner (SHP), and accompanying this paper, we open-source the most scalable version based on recursive bisection.  ...  Evaluation We evaluate two versions of our algorithm, direct partitioning into k buckets (SHP-k) and recursive bisection with log 2 k levels (SHP-2).  ... 
arXiv:1707.06665v1 fatcat:tjjrqcxvojfdznj6b4czm73n2a

Hypergraph Partitioning-Based Fill-Reducing Ordering for Symmetric Matrices

Ümit V. Çatalyürek, Cevdet Aykanat, Enver Kayaaslan
2011 SIAM Journal on Scientific Computing  
After multiple coarsening levels, an initial partition is found on the coarsest graph/hypergraph, and this partition is projected back to a partition of the original graph/hypergraph in the uncoarsening  ...  Thus, V S = {v i..n } is a valid and narrow vertex separator for level m. The GPVS tool computes the cost of this separator as n+1 at this level.  ...  Note that the 2-way separators at the same level of the recursive bisection tree can be ordered independently.  ... 
doi:10.1137/090757575 fatcat:s6igkfajpbckfb2b3swx7obebq

Can recursive bisection alone produce routable placements?

Andrew E. Caldwell, Andrew B. Kahng, Igor L. Markov
2000 Proceedings of the 37th conference on Design automation - DAC '00  
From among recently proposed improvements to recursive bisection, Capo incorporates a leading-edge multilevel min-cut partitioner [7], techniques for partitioning with small tolerance [8], optimal min-cut  ...  We summarize the stateof-the-art after two decades of research in recursive bisection placement and implement a new placer, called Capo, to empirically study the achievable limits of the approach.  ...  placers [1] and also (ii) via analytical placement and network flow methods without hypergraph partitioning [34] .  ... 
doi:10.1145/337292.337549 dblp:conf/dac/CaldwellKM00 fatcat:el2rq7mp5vb3be6aicpuv2e3cy

Social hash partitioner

Igor Kabiljo, Brian Karrer, Mayank Pundir, Sergey Pupyrev, Alon Shalita
2017 Proceedings of the VLDB Endowment  
We design and implement a distributed algorithm for balanced k-way hypergraph partitioning that minimizes fanout, a fundamental hypergraph quantity also known as the communication volume and (k − 1)-cut  ...  We call the resulting tool Social Hash Partitioner, and accompanying this paper, we open-source the most scalable version based on recursive bisection.  ...  Evaluation We evaluate two versions of our algorithm, direct partitioning into k buckets, SHP-k, and recursive bisection with log 2 k levels, SHP-2.  ... 
doi:10.14778/3137628.3137650 fatcat:eit4ifq2gbfprlosimkonejcw4

A Matrix Partitioning Interface to PaToH in MATLAB

Bora Uçar, Ümit V. Çatalyürek, Cevdet Aykanat
2010 Parallel Computing  
We have performed extensive comparison of the proposed method against our implementation of orthogonal recursive bisection and fine-grain methods on a large set of publicly available test matrices.  ...  The interface provides support for hypergraph-based sparse matrix partitioning methods which are used for efficient parallelization of sparse matrix-vector multiplication operations.  ...  Orthogonal recursive bisection based partitioning function [pvr, pvc, pids]=orbPartAux(Klow, Kup, rlist, clist) m = length(rlist); n = length(clist); submat = A(rlist, clist); if(m<n), [npv1, opv1,  ... 
doi:10.1016/j.parco.2009.12.008 fatcat:6lnoajpg6bhk5fvspu5xnevdnq

A repartitioning hypergraph model for dynamic load balancing

Umit V. Catalyurek, Erik G. Boman, Karen D. Devine, Doruk Bozdağ, Robert T. Heaphy, Lee Ann Riesen
2009 Journal of Parallel and Distributed Computing  
To the best of our knowledge, this is the first implementation for dynamic load balancing based on hypergraph partitioning.  ...  We show that the new model can be realized using hypergraph partitioning with fixed vertices and describe our parallel multilevel implementation within the Zoltan load-balancing toolkit.  ...  Handling Fixed Vertices in Recursive Bisection The Zoltan hypergraph partitioner uses recursive bisection (repeated subdivision of parts into two parts) to obtain a k-way partition.  ... 
doi:10.1016/j.jpdc.2009.04.011 fatcat:ogrycndn3rhsrgoxrkzfkpkuf4
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