In the rst phase, a bottomup multilevel clustering is successively applied starting from the original graph by adopting various heuristics until number of. Knottenbelt department of computing, imperial college london south kensington campus, london sw7 2az, uk email. Many stateoftheart graph and hypergraph partitioners utilize the multilevel approach in multilevel methods, the original problem is iteratively coarsened by creating a hierarchy of smaller problems, until it becomes small enough to be solved. Aggregative coarsening for multilevel hypergraph partitioning. Implementation of the algorithm described in aggregative coarsening for multilevel hypergraph partitioning by shaydulin and safro sea 2018 rslnsaggregativecoarseningformultilevel. Key components of our contribution are new effective multilevel recombination and mutation operations that pro. The algorithms implemented in metis are based on the multilevel recursive bisection, multilevel kway, and multiconstraint partitioning schemes developed in.
Network flowbased refinement for multilevel hypergraph. The multilevel hypergraph bisection algorithm used in patoh consists of three phases. With focus on solution quality we develop the first multilevel memetic algorithm to. In its simpler form, hmetis only requires two inputs. In this paper, we use multilevel hypergraph partitioning to simulate. It can be viewed as a more sophisticated alternative to the traditional graph partitioning. Multilevel hypergraph partitioning is a significant and extensively researched problem in combinatorial optimization. Kahypar karlsruhe hypergraph partitioning is a multilevel hypergraph partitioning framework providing direct kway and recursive bisection based partitioning algorithms that. In mathematics, a graph partition is the reduction of a graph to a smaller graph by partitioning its set of nodes into mutually exclusive groups. It was the fastest hypergraph partitioner when i wrote it, and. Hypergraph partitioning is an important problem with extensive application to many areas, including vlsi design alpert and kahng, 1995, efficient storage of large databases on. Hypergraph partitioning is particularly suited to parallelsparsematrixvectormultiplication,acommonkernel in scienti. This paper presents a formal analysis of the algorithms scalability in terms of its isoefficiency function, describes its implementation in the parkway 2.
Kahypar karlsruhe hypergraph partitioning a multilevel. Kahypar is a multilevel hypergraph partitioning framework for optimizing the cut and the. Parallel hypergraph partitioning for scientific computing. Patoh partitioning tool for hypergraphs springerlink. Application in vlsi domain george karypis, rajat aggarwal, vipin kumar, and shashi shekhar f karypis, rajat, kumar, shekhar g cs. In mathematics, a hypergraph is a generalization of a graph in which an edge can join any number of vertices. The authors present a cooperative multilevel search algorithm comhp and describe a parallel implementation on the sgi o2000 system. Family of graph and hypergraph partitioning software karypis lab. In this paper, we present a multilevel hypergraph partitioning. In this approach, a given hypergraph is coarsened to a much smaller one, a partition is obtained on the the smallest hypergraph, and that partition is projected to the original hypergraph while refining it on the intermediate hypergraphs. We present a parallel software package for hypergraph and sparse matrix partitioning developed at sandia national labs. Relaxationbased coarsening for multilevel hypergraph.
B multithreaded clustering for multilevel hypergraph. A single coarsening step is performed by merging the vertices of the original hypergraph together to form. In mathematics, a graph partition is the reduction of a graph to a smaller graph by partitioning its nodes into mutually exclusive groups. Abstractrequirements for efficient parallelization of many complex and irregular applications can be cast as a hypergraph partitioning problem.
In this paper, we use multilevel hypergraph partitioning to simulate scramjet engine, and define the vertex weight and hyperedge cost by using the averagely measured time. In this paper, we present a new hypergraph partitioning algorithm that is based on the multilevel paradigm. Our multilevel hypergraph partitioning algorithm scales very well for large hypergraphs. Patoh is a sequential, multilevel, hypergraph partitioning tool that can be used to solve various combinatorial scientific computing problems that could be modeled as hypergraph partitioning problem, including sparse matrix partitioning, ordering, and load balancing for parallel processing. The standalone program can be built via make kahypar. Hypergraph partitioning is an important problem with extensive application to many areas, including vlsi design alpert and kahng, 1995, efficient storage of large databases on disks shekhar and liu, 1996, and data mining mobasher et al. Hypergraph partitioning and clustering electrical engineering. Multilevel kwaypartitioning initial partitioning phase figure the various phases of the multilevel kway partitioning algorithm. Multithreaded clustering for multilevel hypergraph. In this paper, we study on a general algorithm for scramjet design, and subdivide the computing domain by using a multilevel hypergraph partitioning algorithm. Wellknown multilevel hgp software packages with certain distinguish. The algorithm is a variation on multilevel partitioning. Edges of the original graph that cross between the. A parallel algorithm for multilevel kway hypergraph partitioning.
It supports both recursive bisection and direct kway partitioning. Applications in vlsi domain george karypis, rajat aggarwal, vipin kumar, senior member, ieee, and shashi shekhar, senior member, ieee abstract in this. Engineering fast multilevel support vector machines, machine learning, springer, download, 2019 relaxationbased coarsening for multilevel hypergraph partitioning, siam multiscale modeling and simulations, download, 2019. Applications in vlsi domain george karypis, rajat aggarwal, vipin kumar, senior member, ieee, and shashi shekhar, senior member, ieee abstract in this paper, we present a new hypergraphpartitioning algorithm that is based on the multilevel paradigm. In contrast, in an ordinary graph, an edge connects exactly two vertices. Parallel hypergraph partitioning for scientific computing sandia. We recently proposed a coarsegrained parallel multilevel algorithm for the kway hypergraph partitioning problem. Edges of the original graph that cross between the groups will produce edges in the partitioned graph. Multilevel cooperative search for the circuithypergraph. Hypergraph partitioning is particularly suited to parallel sparse matrixvector multiplication, a common kernel in scientific computing. Sample empirical results are given in the appendix. In the multilevel paradigm, a sequence of successively. A parallel algorithm for multilevel kway hypergraph partitioning aleksandar trifunovic william j. Engineering fast multilevel support vector machines, machine learning, springer, download, 2019 relaxationbased coarsening for multilevel hypergraph partitioning, siam multiscale.
A bisection of the smallest hypergraph is computed and it is used to obtain a bisection of the. Patoh partitioning tools for hypergraph is a multilevel hypergraph partitioning tool that i developed during my doctoral studies at bilkent university 19941999. We present a refinement framework for multilevel hypergraph partitioning that uses maxflow computations on pairs of blocks to improve the solution quality of a kway partition. Patoh is a sequential, multilevel, hypergraph partitioning tool that can be used to solve various combinatorial scientific computing problems that could be modeled as hypergraph partitioning. Concurrent work on parallel hypergraph partitioning algorithms concurrent to our work, 19 presented a parallel multilevel hypergraph partitioning algorithm that uses a twodimensional. A parallel multilevel hypergraph partitioning tool 791 2. Key components of our contribution are new effective multilevel recombination and mutation operations that provide a large amount of diversity. Efficient and scalable hypergraph partitioning algorithms are also important for processing large scale hypergraphs in machine learning tasks. Parallel simulation of scramjet with multilevel hypergraph. Parallel computing using multilevel hypergraph partitioning. Hypergraph partitioning has a wide range of applications such as vlsi design or scientific computing. The most successful partitioning tools are based on the multilevel approach. During the coarsening phase, the size of the hypergraph is successively decreased. Several software packages for hypergraph partitioning exist.
The fiducciamattheyses heuristic is described in detail in section 5 and the multilevel fiducciamattheyses extension is discussed in section 6. Furthermore, our partitioning algorithm is significantly faster, often requiring 4 to 10 times less time than that required by the other schemes. Kahypar is a multilevel hypergraph partitioning framework providing direct kway and recursive. In the following, we focus on issues closely related to the contributions of our paper. Python inferface for the karlsruhe hypergraph partitioning framework kahypar. Kahypar karlsruhe hypergraph partitioning kahypar is a. In particular, we use the multilevel algorithm of the publicly available tool hmetis karypis and kumar, 1998. Patoh partitioning tools for hypergraph is a multilevel hypergraph. Algorithms for many hypergraph problems, including. A parallel multilevel hypergraph partitioning tool. Hypergraph partitioning is nphard and relies on heuristics in practice.
Available software and benchmarks are briey described in section 7. For more recent software, please visit tda labs software page. Patoh partitioning tools for hypergraph is a multilevel hypergraph partitioning tool that i developed during my doctoral studies at bilkent university. During the coarsening phase, the size of the hypergraph is. Parallel multilevel algorithms for hypergraph partitioning. Family of graph and hypergraph partitioning software. Hypergraph partitioning hypergraph partitioning is a useful partitioning and load balancing method when connectivity data is available. Thealgorithmisavariation on multilevel partitioning. The algorithms implemented by hmetis are based on the multilevel hypergraph. Hypergraph partitioning is particularly suited to parallel sparse matrixvector multiplication, a common kernel in scienti. The problem of placing circuits on a chip or distributing sparse matrix operations can be modeled as the hypergraph partitioning problem. In this paper, we present a multilevel hypergraph partitioning algorithm based on simulated annealing approach for global optimization. Implementation of the algorithm described in aggregative coarsening for multilevel hypergraph partitioning by shaydulin and safro sea 2018 rslnsaggregativecoarseningfor multilevel hypergraph partitioning. The algorithms implemented by hmetis are based on the multilevel hypergraph partitioning schemes developed in our lab.
Meanwhile, the efficiency of parallel simulation using the domain decomposition method is not very satisfactory. Apr 29, 2006 hypergraph partitioning is particularly suited to parallel sparse matrixvector multiplication, a common kernel in scientific computing. Patoh partitioning tools for hypergraph is an extremely fast multilevel hypergraph partitioning tool. Knottenbelt department of computing, imperial college london south kensington campus. As a multilevel algorithm, it consist of three phases. Wellknown multilevel hgp software packages with certain distinguishing char. Graph partitioning and in particular, hypergraph partitioning has many applications to ic design and parallel computing. Citeseerx document details isaac councill, lee giles, pradeep teregowda. In this paper, we study on a general algorithm for scramjet design, and. We present a parallel software package for hypergraph and sparse matrix partitioning developedatsandianationallabs. Multithreaded clustering for multilevel hypergraph partitioning. A parallel algorithm for multilevel kway hypergraph. We refer to existing literature 7, 17, 52, 65, 68 for an extensive overview.
In the multilevel paradigm, a sequence of successively coarser hypergraphs is. If the number of resulting edges is small compared to the original graph, then the partitioned graph may. With focus on solution quality we develop the first multilevel memetic algorithm to tackle the problem. Hypergraph partitioning has a wide range of important applications such as vlsi design or scienti. In the multilevel paradigm, a sequence of successively coarser hypergraphs is constructed. A multilevel hypergraph partitioning algorithm based on. Hypergraphs with over 100,000 vertices can be bisected in a few minutes on todays workstations. In this paper, we present a new hypergraphpartitioning algorithm that is based on the multilevel paradigm. Meanwhile, the efficiency of parallel simulation using the domain decomposition method or graph partitioning software is low. The algorithms implemented in metis are based on the multilevel recursivebisection, multilevel kway, and multiconstraint partitioning schemes developed in. Experiments on ispd98 benchmark suite of circuits show, for fourway and eightway partitioning, a reduction of 3% to 15% in the size of hyperedge cuts compared to those obtained by hmetis.
1018 6 396 692 831 519 1471 1370 1103 829 734 177 770 1252 606 1225 106 1096 526 1156 890 598 1030 628 53 477 200 822 1047 311 503 2 932 325