Replicated partitioning for undirected hypergraphs

Cataloged from PDF version of article.Hypergraph partitioning (HP) and replication are diverse but powerful tools that are traditionally applied separately to minimize the costs of parallel and sequential systems that access related data or process related tasks. When combined together, these two techniques have the potential of achieving significant improvements in performance of many applications. In this study, we provide an approach involving a tool that simultaneously performs replication and partitioning of the vertices of an undirected hypergraph whose vertices represent data and nets represent task dependencies among these data. In this approach, we propose an iterative-improvement-based replicated bipartitioning heuristic, which is capable of move, replication, and unreplication of vertices. In order to utilize our replicated bipartitioning heuristic in a recursive bipartitioning framework, we also propose appropriate cut-net removal, cut-net splitting, and pin selection algorithms to correctly encapsulate the two most commonly used cutsize metrics. We embed our replicated bipartitioning scheme into the state-of-the-art multilevel HP tool PaToH to provide an effective and efficient replicated HP tool, rpPaToH. The performance of the techniques proposed and the tools developed is tested over the undirected hypergraphs that model the communication costs of parallel query processing in information retrieval systems. Our experimental analysis indicates that the proposed technique provides significant improvements in the quality of the partitions, especially under low replication ratios. (C) 2012 Elsevier Inc. All rights reserved

Replicated hypergraph partitioning

Ankara : The Department of Computer Engineering and the Institute of Engineering and Science of Bilkent University, 2010.Thesis (Master's) -- Bilkent University, 2010.Includes bibliographical references leaves 62-68.Hypergraph partitioning is recently used in distributed information retrieval (IR) and spatial databases to correctly capture the communication and disk access costs. In the hypergraph models for these areas, the quality of the partitions obtained using hypergraph partitioning can be crucial for the objective of the targeted problem. Replication is a widely used terminology to address different performance issues in distributed IR and database systems. The main motivation behind replication is to improve the performance of the targeted issue at the cost of using more space. In this work, we focus on replicated hypergraph partitioning schemes that improve the quality of hypergraph partitioning by vertex replication. To this end, we propose a replicated partitioning scheme where replication and partitioning are performed in conjunction. Our approach utilizes successful multilevel and recursive bipartitioning methodologies for hypergraph partitioning. The replication is achieved in the uncoarsening phase of the multilevel methodology by extending the efficient Fiduccia-Mattheyses (FM) iterative improvement heuristic. We call this extended heuristic replicated FM (rFM). The proposed rFM heuristic supports move, replication and unreplication operations on the vertices by introducing new algorithms and vertex states. We show rFM has the same complexity as FM and integrate the proposed replication scheme into the multilevel hypergraph partitioning tool PaToH. We test the proposed replication scheme on realistic datasets and obtain promising results.Selvitopi, Reha OğuzM.S

Balance preserving min-cut replication set for a K-way hypergraph partitioning

Ankara : The Department of Computer Engineering and the Institute of Engineering and Science of Bilkent University, 2010.Thesis (Master's) -- Bilkent University, 2010.Includes bibliographical references leaves 40-47.Replication is a widely used technique in information retrieval and database systems for providing fault-tolerance and reducing parallelization and processing costs. Combinatorial models based on hypergraph partitioning are proposed for various problems arising in information retrieval and database systems. We consider the possibility of using vertex replication to improve the quality of hypergraph partitioning. In this study, we focus on the Balance Preserving Min-Cut Replication Set (BPMCRS) problem, where we are initially given a maximum replication capacity and a K-way hypergraph partition with an initial imbalance ratio. The objective in the BPMCRS problem is finding optimal vertex replication sets for each part of the given partition such that the initial cutsize of the partition is improved as much as possible and the initial imbalance is either preserved or reduced under the given replication capacity constraint. In order to address the BPMCRS problem, we propose a model based on a unique blend of coarsening and integer linear programming (ILP) schemes. This coarsening algorithm is based on the Dulmage-Mendelsohn decomposition. Experiments show that the ILP formulation coupled with the Dulmage-Mendelsohn decomposition-based coarsening provides high quality results in feasible execution times for reducing the cost of a given K-way hypergraph partition.Yazıcı, VolkanM.S

Minimizing communication through computational redundancy in parallel iterative solvers

Ankara : The Department of Computer Engineering and the Graduate School of Engineering and Science of Bilkent University, 2011.Thesis (Master's) -- Bilkent University, 2011.Includes bibliographical references leaves 55-60.Sparse matrix vector multiplication (SpMxV) of the form y = Ax is a kernel operation in iterative linear solvers used in scientific applications. In these solvers, the SpMxV operation is performed repeatedly with the same sparse matrix through iterations until convergence. Depending on the matrix and its decomposition, parallel SpMxV operation necessitates communication among processors in the parallel environment. The communication can be reduced by intelligent decomposition. However, we can further decrease the communication through data replication and redundant computation. The communication occurs due to the transfer of x-vector entries in row-parallel SpMxV computation. The input vector x of the next iteration is computed from the output vector of the current iteration through linear vector operations. Hence, a processor may compute a y-vector entry redundantly, which leads to a x-vector entry in the following iteration, instead of receiving that x-vector entry from another processor. Thus, redundant computation of that y-vector entry may lead to reduction in communication. In this thesis, we devise a directed-graph-based model that correctly captures the computation and communication pattern for above-mentioned iterative solvers. Moreover, we formulate the communication minimization by utilizing redundant computation of y-vector entries as a combinatorial problem on this directed graph model. We propose two heuristics to solve this combinatorial problem. Experimental results indicate that the communication reducing strategy by redundantly computing is promising.Torun, Fahreddin ŞükrüM.S

High-Quality Hypergraph Partitioning

This dissertation focuses on computing high-quality solutions for the NP-hard balanced hypergraph partitioning problem: Given a hypergraph and an integer $k$, partition its vertex set into $k$ disjoint blocks of bounded size, while minimizing an objective function over the hyperedges. Here, we consider the two most commonly used objectives: the cut-net metric and the connectivity metric. Since the problem is computationally intractable, heuristics are used in practice - the most prominent being the three-phase multi-level paradigm: During coarsening, the hypergraph is successively contracted to obtain a hierarchy of smaller instances. After applying an initial partitioning algorithm to the smallest hypergraph, contraction is undone and, at each level, refinement algorithms try to improve the current solution. With this work, we give a brief overview of the field and present several algorithmic improvements to the multi-level paradigm. Instead of using a logarithmic number of levels like traditional algorithms, we present two coarsening algorithms that create a hierarchy of (nearly) $n$ levels, where $n$ is the number of vertices. This makes consecutive levels as similar as possible and provides many opportunities for refinement algorithms to improve the partition. This approach is made feasible in practice by tailoring all algorithms and data structures to the $n$-level paradigm, and developing lazy-evaluation techniques, caching mechanisms and early stopping criteria to speed up the partitioning process. Furthermore, we propose a sparsification algorithm based on locality-sensitive hashing that improves the running time for hypergraphs with large hyperedges, and show that incorporating global information about the community structure into the coarsening process improves quality. Moreover, we present a portfolio-based initial partitioning approach, and propose three refinement algorithms. Two are based on the Fiduccia-Mattheyses (FM) heuristic, but perform a highly localized search at each level. While one is designed for two-way partitioning, the other is the first FM-style algorithm that can be efficiently employed in the multi-level setting to directly improve $k$-way partitions. The third algorithm uses max-flow computations on pairs of blocks to refine $k$-way partitions. Finally, we present the first memetic multi-level hypergraph partitioning algorithm for an extensive exploration of the global solution space. All contributions are made available through our open-source framework KaHyPar. In a comprehensive experimental study, we compare KaHyPar with hMETIS, PaToH, Mondriaan, Zoltan-AlgD, and HYPE on a wide range of hypergraphs from several application areas. Our results indicate that KaHyPar, already without the memetic component, computes better solutions than all competing algorithms for both the cut-net and the connectivity metric, while being faster than Zoltan-AlgD and equally fast as hMETIS. Moreover, KaHyPar compares favorably with the current best graph partitioning system KaFFPa - both in terms of solution quality and running time