In particular, we describe for parallel coarsening, parallel greedy kway refinement and parallel multiphase refinement. The cluster ensemble problem is formulated as partitioning the hypergraph by cutting a. Approximate hypergraph partitioning and applications. Kahypar is a multilevel hypergraph partitioning framework providing direct kway and recursive bisection based partitioning algorithms. Parallel algorithms for hypergraph partitioning article in journal of parallel and distributed computing 685. In proceedings of the 27th acm on symposium on parallelism. The success of existing hypergraph partitioning based algorithms in other domains depends on sparsity of the hypergraph and explicit objective metrics. Jan 05, 2016 the fusion between graph theory and combinatorial optimization has led to theoretically profound and practically useful algorithms, yet there is no book that currently covers both areas together. The corresponding fiedler vector is related to the cheeger constant of the hypergraph. Handbook of graph theory, combinatorial optimization, and algorithms is the first to present a unified, comprehensive treatment of both graph theory and c. A balanced hypergraph partitioning algorithm for big. Although hypergraph partitioning is a np hard problem, there are still some excellent hypergraph partition algorithms. Hypergraph partitioning for parallel iterative solution of.
These algorithms, as illustrated in figure 1b, reduce the size of the graph or hypergraph by collapsing vertices and edges during the coarsening phase, partition the smaller graph initial partitioning phase, and then uncoarsen it to construct a partition for the original graph uncoarsening and re. Current techniques use a multilevel approach wherein an initial partitioning is performed after compressing the hypergraph to a predetermined level. Hypergraph models and algorithms for datapatternbased. Divided into 11 cohesive sections, the handbooks 44 chapters focus on graph theory, combinatorial optimization, and algorithmic issues. Hypergraph partitioning is important to many application domains including data mining, job scheduling, hardware software partitioning, vlsi circuit layout and numerical lin ear algebra.
Graph and hypergraph partitioning for parallel computing. Whilst algorithms for sequential hypergraph partition ing have been studied extensively and tool support exists e. The cluster ensemble problem is formulated as partitioning the hypergraph by cutting a minimal number of hyperedges. A multilevel hypergraph partitioning algorithm using rough.
Recent research efforts have focused on dyadic graph partitioning algorithms based on vertex partitioning a. This algorithm runs in time ok n, where n is the number of elements in the input set and k is the sum of elements in the input set the algorithm can be extended to the kway multipartitioning problem, but then takes onk. Karypis g, kumar v 1998 multilevel algorithms for multiconstraint hypergraph partitioning. With a hyperedge partitioning method, each hyperedge appears in only one partition, while vertices may be cut and replicated in more than one partition. Hypergraph is good at modeling multinode relationships in complex networks. An effective algorithm for multiway hypergraph partitioning.
Sandia national laboratories utrecht university dept. Consistency of spectral algorithms for hypergraphs under. Balanced hypergraph partitioning helps to optimize storage of large sets of hypergraphstructured data over multihosts in the cloud, and share the query loads. Kahypar karlsruhe hypergraph partitioning is a multilevel hypergraph partitioning framework providing direct kway and recursive bisection based partitioning algorithms that compute solutions of very high quality. A parallel algorithm for multilevel kway hypergraph partitioning. Black lines represent dependencies for ax, red lines represent additional dependencies for computing a2x. Hypergraph partitioning of social network could be adopted for user data allocation among fixed number of servers to improve interuser data access performance turk et al. This work addresses one method for this tradeoff by solving the hypergraph partitioning problem by finding vertex separators on graphs. In section 3, we provide the framework to develop algorithms using our hypergraph modularity function. Graph partitioning by charlesedmond bichot nook book. Hypergraph partitioning through vertex separators on graphs. It instantiates the multilevel approach in its most extreme version, removing only a single vertex in every level of the hierarchy.
During the last 40 years, the literature has strongly increased and big improvements have been made. Hypergraph partitioning algorithm hgpa the second algorithm is a direct approach to cluster ensembles that repartitions the data using the given clusters as indications of strong bonds. Multiobjective hypergraphpartitioning algorithms for cut and. We show that our proposed algorithm gives on average between 18. Examples arise in transportation problems, supply chain man. This includes partitioning algorithms for graphs corresponding to finite element meshes, multilevel nested dissection, parallel graphmesh partitioning, dynamicadaptive graph repartitioning, multiconstraint and multiobjective partitioning, and circuit and hypergraph partitioning. We propose an hypergraph partitioning algorithm and a few illustrative examples in section 4.
The fusion between graph theory and combinatorial optimization has led to theoretically profound and practically useful algorithms, yet there is no book that currently covers both areas together. In this paper, we present a family of multiobjective hypergraph partitioning algorithms based on the multilevel paradigm, which are capable of producing solutions in which both the cut and the maximum subdomain degree are simultaneously. A serial multilevel hypergraph partitioning algorithm 7 an advan tage of the multilevel approach is that it provides a tradeo. From graph partitioning to timing closure introduces and compares algorithms that are used during the physical design phase of integratedcircuit design, wherein a geometric chip layout is produced starting from an abstract circuit design. Experimental results on an extensive set of matrices show that the mohp algorithm obtains a smaller profile than the stateoftheart profile reduction algorithms, which then results in considerable improvements. Balanced hypergraph partitioning helps to optimize storage of large sets of hypergraph structured data over multihosts in the cloud, and share the query loads. A serial multilevel hypergraph partitioning algorithm. The emphasis is on essential and fundamental techniques, ranging from hypergraph partitioning and circuit placement to timing closure. Handbook of graph theory, combinatorial optimization, and. The existing hypergraph partition methods can be classified into three categories. Eldar fischery arie matsliahz asaf shapirax abstract szemeredis regularity lemma is a cornerstone result in extremal combinatorics.
It roughly asserts that any dense graph is composed of a. Once i discovered the limitations of the locking mechanism, i changed my research direction towards what. Handbook of graph theory, combinatorial optimization, and algorithms is the first to present a unified, comprehensive treatment of both graph theory and combinatorial optimization. We consider spectral algorithms for partitioning clique and star expansions of hypergraphs, and study their consistency under a sparse planted partition model. However, since partitioning is critical in several practical applications, heuristic algorithms were developed with nearlinear runtime. For this, we propose a twophase clustering approach for the above hypergraph, which is expected to be dense. Metis 25 is a wellknown vertex partitioning tool that applies multilevel framework, and parmetis 26 is a parallel version of metis.
Parallel algorithms for hypergraph partitioning aleksandar trifunovi. Such movebased heuristics for kway hypergraph partitioning appear in 46, 27, 14, with renements given by 47, 58, 32, 49, 24, 10, 20, 35, 41. In proceedings of the 27th acm on symposium on parallelism in algorithms and architectures, spaa 15, pages 8688. A distributed algorithm for balanced hypergraph partitioning.
For this purpose, we extend the normalized laplacian matrix of a simple graph to the normalized laplacian tensor of an evenuniform hypergraph. Once i discovered the limitations of the locking mechanism, i changed my research direction towards what would become plm and pfm. Sa is extensively used as a benchmark in performance comparison for different multiway hypergraph partitioning algorithms. Balanced partitioning typically represents the divide step of divideandconquer algorithms and seeks. In this paper, we propose a sequential multilevel hypergraph partitioning algorithm. The hypergraph partitioning problem has many applications in scienti c computing and provides a more accurate interprocessor communication model for distributed systems than the equivalent graph problem. Multilevel partitioning algorithms, on the other hand, take a completely different approach6, 9, 8, 10. Sanchiss algorithm is the first hypergraph multiway partitioning algorithm since all previous algorithms arefor twoway partitioning. A hypergraph is a generalization of a graph wherein edges can connect more than two ver tices and are called hyperedges. Hypergraph partitioning for parallel sparse matrixmatrix multiplication. Several centralized vertex partitioning algorithms have been developed to address this problem. In this paper, we present parallel multilevel algorithms for the hypergraph partitioning problem. The results of hypergraph partitioning can be further extended to address the wellknown hypergraph vertex coloring problem, where the objective is to color the vertices such that. Siam journal on scientific computing society for industrial.
Fms fiducciamattheysessanchis, plm partitioning by locked moves, pfm partitioning by free moves, sa simulated annealing 2 versions, and rsa simulated annealing with ratio cut model 2way partitioning only, as detailed in daay97. Hypergraph partitioning for computing matrix powers. Neither the modeling flexibility of hypergraphs, nor the runtime efficiency of graph algorithms can be overlooked. Multiobjective hypergraph partitioning algorithms for cut and maximum subdomaindegree minimization abstract. Divided into 11 cohesive sections, the handbooks 44 chapters focus on graph theory. These algorithms, as illustrated in figure 1b, reduce the size of the graph or hypergraph by collapsing vertices and edges during the coarsening phase, partition the smaller graph initial. Catalyurek abstract graph partitioning is often used for load balancing in parallel computing, but it is known that hypergraph partitioning has several advantages. Constructing the full klevel column nets is a significant preprocessing cost can we reduce the cost of constructing and partitioning the hypergraph by using heuristics. Parallel multilevel algorithms for hypergraph partitioning. Coarsen graph by collapsing appropriate vertices initial partitioning of simplified graph uncoarsen graph and refine partitioning a hypergraph is a graph whose edges can connect more than two vertices hyperedges. Hypergraph partitioning for parallel iterative solution of general sparse linear systems. In addition, open source tools, such as hmetis 9, patoh 10, and parkway 11, are available to implement highquality hypergraph partitioning.
Then, we develop a novel tensorbased spectral method for partitioning vertices of the hypergraph. During my msc years, my eventual goal was to implement graph and hypergraph partitioning using genetic algorithms on a hypercube connected parallel computer from intel. Hypergraph partitioning for social networks based on. Hypergraphs are generalization of graphs where each edge hyperedge can connect more than two vertices. During the last 40 years, the literature has strongly increased and big. Currently, the best available algorithms use the klalgorithm or spectral bisection in a multilevel framework which has three stages. A hypergraph partitioning model for profile minimization. In particular, we describe for parallel coarsening, parallel greedy k. This section covers works done for hypergraph partitioning and summarizing their analysis.
Pdf a serial multilevel hypergraph partitioning algorithm. Graph partitioning is a theoretical subject with applications in many areas, principally. With certain constraints such as balance, the problem of optimally partitioning a hypergraph is known to be nphard borndorfer and heismann. In simple terms, the hypergraph partitioning problem can be defined as the task of dividing a hypergraph into two or more roughly equalsized parts such that a cost function on the hyperedges connecting vertices in different parts is minimized.
We show the correctness of the mohp algorithm and describe how the existing partitioning tools can be utilized for its implementation. Planning and partitioning are fundamental combinatorial problems and capture a widevariety of natural optimization problems. Nov 10, 2016 hypergraph is good at modeling multinode relationships in complex networks. In this paper, we present a family of multiobjective hypergraphpartitioning algorithms based on the multilevel paradigm, which are capable of producing solutions in which both the cut and the maximum subdomain degree are simultaneously. We then propose a generalization of the chunglu model for hypergraphs, as well as a hypergraph modularity function. Multiobjective hypergraphpartitioning algorithms for cut and maximum subdomaindegree minimization abstract. Markov university of michigan, eecs department, ann arbor, mi 481092121. This level is typically chosen to produce very coarse hypergraphs in which heuristic algorithms are fast and effective. This algorithm does not suffer from the disruption of building blocks known from the standard genetic algorithms.
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