Karypis, G., Schloegel, K., and Kumar, V.: ParMetis Parallel Graph Partitioning and Sparse Matrix Ordering Library, Version 3.1. University of Minnesota Department of Computer Science and Engineering, and Army HPC Research Center, Minneapolis, (2003). Open-source software distributed at http://www-users.cs.umn.edu/~karypis/metis.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....reduce edge cut and also exploits the unbalanced recursive bisection of Jones and Plasman [19] to reduce data transfer. The third mesh re partitioning module is based on existing software packages for parallel graph re partitioning: PARMETIS, developed by Karypis et al. University of Minneapolis [20,21] and PJOSTLE, developed by Walshaw, University of Greenwich [22] PARMETIS is included in the DRAMA library, and the co operation within the project with the University of Greenwich has led to a DRAMA interface to a modified version of PJOSTLE. Both packages contain recent developments enabling ....

....when the re partitioning attempts to balance the contact phase across many processes. For this reason, full code performance results are not presented. The various partitioning options used are given in Table 1, where all acronyms for the particular partitioning options are explained in [20 24]. Partitioner 6 is a single phase partitioner added for comparison. Tables 2 and 3, for the Audi and BMW models, respectively, give the minimum, maximum and mean total computational weights (as provided to the DRAMA Library from the application) for a 16 domain partition. The cost categories FE ....

G. Karypis, K. Schloegel, V. Kumar, PARMETIS parallel graph partitioning and sparse matrix ordering library, Version 2.0, Technical Report, Department of Computer Science, University of Minnesota, 1998.

....contact detection) to be covered. The DRAMA library contains geometric, e.g. recursive coordinate bisection, topological (graph) and local improvement (direct mesh migration) methods [2] It enables the use of leading graph partitioning algorithms through internal interfaces to ParMetis [8,10,11] and PJostle [15,16] In comparison with the direct use of graph partitioners, DRAMA has the following advantages: 1) DRAMA s interface is mesh based. Since an element node connectivity list is an essential component of mesh based application codes DRAMA can be easily integrated. Mesh to ....

....and nodes, i.e. node node and element element connections are omitted. For the BMW model we also consider an element graph representation, the classical extended dual graph [2,4] where elements are connected if they share one or more nodes. In the following, the methods listed in Table 2 [8 11,15,16] are tested for repartioning. Method 6 is a single phase partitioner and is added for comparison reasons, all other methods are multi phase multi constraint algorithms. Methods 1 and 2 are sequential multi partitioners, all other methods are parallel. MOC PARMETIS R (method 8) is a re partitioner ....

G. Karypis, V. Kumar, ParMetis: Parallel graph partitioning and sparse matrix ordering library, Technical Report # 97-060, 1997, University of Minnesota, Minneapolis.

....the element and node dependencies as an undirected graph since many common partitioning algorithms for FE meshes are based on graph theory. G(V; E) represents the element and or node graph of V vertices and E edges. Existing software tools can use the graph information as interface to the FE codes [4, 7, 8, 11, 12]. Vertices correspond to elements or nodes and carry a weight i (u) or w i (u) where the possible element types or node types u are specified by the user. Since elements consist of nodes the DRAMA cost model derives node types from element types. Therefore, in particular, the number of node ....

G. Karypis and V. Kumar, ParMetis: Parallel graph partitioning and sparse matrix ordering library, University of Minneapolis, technical report # 97-060.

....to the same processor. The structured block graph can be represented as an n 1 Theta n 2 matrix, where the matrix elements are integers representing the arithmetic work loads for the blocks. This is the input format used by the MISP algorithm. For ParMetis, we use its required graph format [2]. We have studied two test applications. One is the linearized Euler equations in a channel, where the refinements are scattered. The other is a scalar convection problem, where the refinements are strongly localized. These applications are communication dominated. Using the same applications as ....

G. Karypis, K. Schloegel, and V. Kumar. Parmetis---parallel graph partitioning and sparse matrix ordering library, version 2.0. Univ. of Minnesota, Minneapolis, MN, 1998.

....bandwidth than local memory and is therefore a bottleneck. Consequently this communication cost dominates the total data exchange time. The gridlib framework processes the grid geometrically and topologically in order to build an adjacency graph in parallel. From this graph, the parallel METIS [7] library computes an optimal partition which is evaluated by the gridlib for moving the geometry accordingly. For running CFD solvers, the partitioning criterion clearly has to minimize the number of partition boundary elements in order to minimize the communication cost. The rendering subsystem ....

G. Karypis, K. Schloegel, and V. Kumar. Parmetis: Parallel graph partitioning and sparse matrix ordering library. Technical report, Department of Computer Science and Engineering, University of Minnesota, 1997.

....partitioners, using a suite of five real world (2D and 3D) SAMR application kernels. The partitioners studied include existing (ISP[10] and G MISP[19] as well as new (G MISP SP, pBD ISP and SP) techniques and constitute a selection from popular software tools, viz. GrACE[10] ParMetis[6] and Vampire[18] Application kernels are taken from varied scientific and engineering domains, and demonstrate very different run time behavior. The experimental results are then used to characterize the behavior of the partitioners using a five component goodness metric, and to associate the ....

....(2) 5) are part of the parallel SAMR partitioning library Vampire [18] which combines structured and unstructured partitioning techniques in a fashion introduced by Rantakokko[11] The techniques (3) 5) are not described in the literature previously. The last algorithm is from ParMetis [6], a tool for unstructured graphs. For some of the partitioning techniques, granularity maybevaried. In this context, granularityis determined by the atomic unit, the smallest entity the partitioner can see and work with. By choosing a small atomic unit, the partitioner may split the grids (if ....

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G. Karypis, K. Schloegel, and V. Kumar. PARMETIS - parallel graph partitioning and sparse matrix ordering library,version 2.0. Univ. of Minnesota, Minneapolis, MN, 1998.

....dynamic domain based partitioners, using a suite of five real world (2D and 3D) SAMR application kernels. The partitioners studied include existing (ISP[4] and GMISP [3] as well as new (G MISP SP, pBD ISP and SP) techniques and constitute a selection from software tools, viz. GrACE[4] ParMetis[5] and Vampire[6] Application kernels are taken from varied scientific and engineering domains, and demonstrate very different run time behavior. The experimental results are then used to characterize the behavior of the partitioners using a five component goodness metric, and to associate the ....

....(2) 5) are part of the parallel SAMR partitioning library Vampire [6] which combines structured and unstructured partitioning techniques in a fashion introduced by Rantakokko [2] The techniques (3) 5) are not described in the literature previously. The last algorithm is from ParMetis [5], a tool for unstructured graphs. For some of the partitioning techniques, granularity may be varied. In this context, it is determined by an atomic unit, the smallest entity the partitioner can see and work with. If a small atomic unit is chosen, the partitioner may split the grids (if ....

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G. Karypis, K. Schloegel, and V. Kumar. PARMETIS - parallel graph partitioning and sparse matrix ordering library, version 2.0. Univ. of Minnesota, Minneapolis, MN, 1998.

....amount of data that must be shuffled. Publicly available Partitioners It should be noted that several partitioning packages are available online, which implement many of the algorithms described in this paper. The leading contenders seem to be the METIS and ParMETIS packages by Karypis and Kumar [29, 30] and the Jostle package by Walshaw et al. 47] METIS and ParMETIS implement Karypis and Kumar s multilevel, p way multilevel, and parallel p way multilevel algorithms. Jostle also supports parallel partitioning, with Walshaw s emphasis on minimizing vertex movement. Chaco [20] is Hendrickson and ....

George Karypis, Kirk Schloegel, and Vipin Kumar. ParMETIS: Parallel Graph Partitioning and Sparse Matrix Ordering Library. University of Minnesota, version 2.0 edition, July 1997. (the ParMETIS homepage is at http://www-users.cs.umn.edu/~karypis/metis/parmetis/main.shtml).

....to provide useful results. In other cases, the sequential algorithms could be modi ed in such a way to allow for general parallelization. Many of the techniques outlined in the following sections have been developed at the University of Minnesota by George Karypis, Vipin Kumar, and Kirk Schloegel [8] [7] Bruce Hendrickson et al. at Sandia National Laboratories have also provided very good research in the area of parallel partitioning [3] The following sections look at many of these techniques and explore their similarities, di erences, and advantages. 3.1 Motivation For Parallel ....

....Multilevel Techniques One of the most promising parallel partitioning techniques explored in the recent past is the multilevel technique. The sequential multilevel technique is discussed in detail in section 2.4. Parallelizing this technique has been studied extensively by Karypis and Kumar [7] [8] as well as Stephen T. Barnard [1] Many diculties arise in the all three of the multilevel phases. In the coarsening phase, a parallel coloring technique is needed to adequately coarsen the graph. In the partitioning phase, an adequate initial partition must be made by some outside parallel ....

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G. Karypis, K. Schloegel, and V. Kumar. ParMetis: Parallel Graph Partitioning and Sparse Matrix Ordering Library. Version 2.0, 1998. 15

....is given. Section 3 then discusses the dynamic load balancing problem that arises when using parallel adaptivity. This is followed, in Section 4, by a brief description of four di erent families of parallel dynamic load balancing algorithm: two implemented in publicly available software tools ([9,24]) and two more which we have developed from existing published work ( 17,21] The paper concludes by reporting and discussing the results of a number of numerical tests which are used to contrast the load balancing algorithms for this particular solver. 2 A Parallel Adaptive Algorithm The ....

....no reason to expect that 1 to 4 above represent a consistent set of requirements. It is perhaps not surprising therefore that the vast majority of published dynamic load balancing algorithms are based heavily on heuristics. In the next section we introduce two such software tools, called Metis ([8,9]) and Jostle ( 23,24] respectively. We also brie y describe some further heuristics, based upon [17,21] which are also used in our comparisons. 4 Some Parallel Dynamic Load Balancing Algorithms This brief discussion of dynamic load balancing heuristics will rst provide an overview of the ....

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G. Karypis, K. Schloegel and V. Kumar, \ParMetis: Parallel Graph Partitioning and Sparse Matrix Ordering Library. Version 2.0", Department of Computer Science, University of Minnesota, 1998.

....generally support only a very limited class of applications. Users with non mainstream needs can find frameworks to be too restrictive and limited. Middle ground between these two extremes can be found in the many parallel utility libraries for linear algebra (e.g. 15, 1] partitioning (e.g. [6, 16]) and other common kernel operations. Although we personally prefer this library approach to parallel software development, it is not without its problems. A key challenge for the developers of parallel libraries is the design of easy to use and efficient interfaces. For instance, a linear algebra ....

G. Karypis and V. Kumar, Parmetis: Parallel graph partitioning and sparse matrix ordering library, Tech. Rep. 97-060, Department of Computer Science, University of Minnesota, 1997.

.... evolves, various regions of the mesh are dynamically refined, leading to load imbalance that hurts the overall performance [7, 9] Significant research has been done on parallel partitioning algorithms, and several state of the art MPI software packages are currently available on the web [3, 19]. We chose ParMETIS [4] as the basic partitioner for this work because of its good overall performance and wide availability. ParMETIS is a multilevel partitioner that consists of three main phases: coarsening the graph to be partitioned, partitioning the coarse graph, and projecting the ....

G. Karypis and V. Kumar, "ParMETIS: Parallel graph partitioning and sparse matrix ordering," University of Minnesota, http://www-users.cs.umn.edu/  karypis/metis

.... beyond the scope of this short paper to discuss these numerous heuristics in any detail, however we do note that in many cases there are efficient software implementations which are generally available (see [14, 16, 19, 23] for example) In some cases there are also parallel implementations (e.g. [17, 22]) however, for this application, the graph partitioning may be viewed as a pre processing step which can be undertaken sequentially if necessary. For the preliminary results presented in Section 5 a simple geometric partitioning rule (similar to recursive coordinate bisection [21] has been used. ....

G. Karypis, K. Schloegel and V. Kumar, "ParMetis: Parallel Graph Partitioning and Sparse Matrix Ordering Library. Version 2.0", Department of Computer Science, University of Minnesota, 1998.

....and boundary conditions for the anastomosis example. In gure 6 we show the mesh partition (nodes assigned to each processor) for a typical run in eight identical processors. This partition is obtained automatically by the solver through a call to the parallel graph partitioning package PARMETIS [15]. 7 6 5 4 3 0 1 2 Figure 6: Mesh partition for the anastomosis example in 8 processors. In Figure 7 (a) we show a photograph from [14] showing particles in the ow at the symmetry plane. Particle s traces are indicators of the uid velocity, and when they are overlapped they provide an ....

G. Karypis, K. Schloegel, and V. Kumar. \ParMetis: Parallel graph partitioning and sparse matrix ordering library" Technical report, University of Minnesota, Department of Computer Science and Engineering, 1997.

....of this algorithm have been developed [23, 30] parallel implementations have proved to be quite difficult. Both the construction of the smaller approximations and the refinement operation are challenging to parallelize. These challenges have been addressed in two recent efforts: ParMETIS [31, 32, 46] and JOSTLE [54, 55] These tools essentially perform a local improvement like those described in x3.4, but they use a multilevel approach to select which objects to move. This makes them more powerful than other local improvement algorithms, but they are also more expensive in both runtime and ....

G. Karypis and V. Kumar, Parmetis: Parallel graph partitioning and sparse matrix ordering library, Tech. Rep. 97-060, Department of Computer Science, University of Minnesota, 1997. Available on the WWW at URL http://www.cs.umn.edu/~metis.

....processor can only have a set of consecutive rows of the global matrix. This is a small restriction since the user can use one of many reordering packages to reorder the sparse matrix so that the required simple partitioning scheme does not harm the parallel performance of the iterative methods [29]. When the conversion function is used, the user s data structure is implicitly used. Even though no further operations of BlockSolve explicitly involves the user data structure, the user s distributed CSR data structure can not be modified or deallocated. Once the user data is converted to the ....

G. Karypis, K. Schloegel, and V. Kumar. ParMETIS: parallel graph partitioning and sparse matrix ordering library, 1998. Further information available at http://www.cs.umn.edu/karypis.

....guaranteed to be contiguous. This method is very similar to the Octree Partition method [1] and can be related to space filling curve methods [7] The final partitioning algorithm is the multilevel diffusion algorithm [8] with local balancing criteria implemented in the popular ParMETIS library [2]. Other methods in ParMETIS were also considered, but preliminary results and papers on ParMETIS indicated that this algorithm performs best in the given context. This algorithm consists of three phases: coarsening, multilevel diffusion and multilevel refinement. The coarsening phase merges nodes ....

G. Karypis, K. Schloegel, and V. Kumar, ParMETIS: Parallel Graph Partitioning and Sparse Matrix Ordering Library, Version 2.0, http://www.cs.umn.edu/ karypis/metis/metis.html.

....University, which seeks to efficient parallelize CFD applications by incorporating load balancing via Fractiling. To determine which graph partitioning algorithm to implement with Fractiling, several graph partitioning packages have been analyzed: Chaco [13] Jostle [24] METIS [16] ParMETIS [17], and Party [22] The rest of this paper is arranged as follows: Section 2 discusses load imbalance and describes Fractiling; Section 3 provides a formal definition of the graph partitioning problem; Section 4 details the various constraints imposed on the experiments conducted and reported in ....

....for this paper, this was not possible for METIS. The algorithms reported for METIS are multilevel in nature. So to completely avoid multilevel algorithms would have meant that the METIS package could not have been included in this paper. 4 M. L. BILDERBACK AND P. SONI 4.1.3. ParMETIS. ParMETIS [17], developed by George Karypis, Kirk Schloegel and Vipin Kumar at the University of Minnesota, operates as a library of graph partitioning functions which may be linked into other applications and accessed through function calls. The algorithms are MPIbased parallel graph partitioning algorithms ....

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G. Karypis, K. Schloegel, and V. Kumar, ParMETIS: Parallel Graph partitioning and sparse Matrix ordering library version 1.0, Technical Report, Department of Computer Science, University of Minnesota, 1997.

....element and node dependencies as an undirected graph since many common partitioning algorithms for FE meshes are based on graph theory. G(V; E) represents the element and or node graph of V vertices and E edges. Existing software tools can use the graph information as interface to the FE codes [4, 7, 8, 11, 12]. Vertices correspond to elements or nodes and carry a weight w e i (u) or w n i (u) where the possible element types or node types u are specified by the user. Since elements consist of nodes the DRAMA cost model derives node types from element types. Therefore, in particular, the number of ....

G. Karypis and V. Kumar, ParMetis: Parallel graph partitioning and sparse matrix ordering library, University of Minneapolis, technical report # 97-060.

....INTEGER choice choice equal to 0 indicates that the graph partitioner ParMETIS PartKway shall be used. The value 1 selects ParMETIS RepartLDiffusion, 2 ParMETIS RepartGDiffusion, 3 ParMETIS RepartRemap, 4 ParMETIS RepartMLRemap, 5 Multi constraint METIS, 6 pjostle, and 7 Multi phase JOSTLE [6, 7, 8, 9]. The default single phase graph partitioner is ParMETIS RepartGDiffusion, the default multi phase graph partitioner is Multi constraint METIS. Routine DRAMA SET PART OPTIONS Figure 20 shows DRAMA s subroutine for setting partitioner options. C prototype: void DRAMA SET PART OPTIONS ( int ....

....OPTIONS( options ) Figure 20: DRAMA subroutine: setting partitioner options. Parameters of DRAMA SET PART OPTIONS INTEGER options( 3 ) The value 0 for the first element of options selects that a serial partitioning algorithm is used to partition the coarsest graph for the ParMETIS PartKway method [7], 1 selects a parallel partitioning algorithm. The default is using a parallel partitioning algorithm. The second element of options specifies a parameter of ParMETIS PartKway to control successive folding [7] It is used to optimise the run time of the partitioning algorithm. The default is 1. ....

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G. Karypis, K. Schloegel and V. Kumar, PARMETIS: Parallel Graph Partitioning and Sparse Matrix Ordering Library, Version 2.0, userguide, Minneapolis, September 1998.

....Finite Volume, adaptive mesh refinement, contact detection) to be covered. The DRAMA library contains geometric (RCB) topological (graph) and local improvement (direct mesh migration) methods [3] It enables the use of leading graph partitioning algorithms through internal interfaces to ParMetis [6] and PJostle [10] Over using the graph partitioners directly, DRAMA has the following advantages. 1. DRAMA s interface is mesh based. Since an element node connectivity list is an essential component of mesh based application codes DRAMA can be easily integrated. Mesh to abstract graph conversion ....

....and nodes where the connections are only between elements and nodes, i.e. node node and element element connections are omitted. For the BMW model we also consider an extended dual graph [2, 3] where elements are connected if they share one or more nodes. We consider the following methods [6, 7, 10]. method graph representation partitioner 1 combined graph METIS mCPartGraphkway, sequential 2 combined graph MJostle, sequential 3 combined graph MOC PARMETIS Partkway 4 combined graph MOC PARMETIS SR 5 combined graph MJostle, parallel, exclusive 6 combined graph MJostle, parallel, inclusive 7 ....

G. Karypis and V. Kumar, ParMetis: Parallel graph partitioning and sparse matrix ordering library, University of Minneapolis, technical report # 97-060.

....is used for the whole simulation run. Most static partitioning libraries run on a sequential computer (Chaco [9] Jostle [23] Metis [12] Scotch [15] We are aware of only one library in the public domain that allows to do static (graph) partitioning in parallel, i.e. ParMetis [13]. Jostle [24] can also be used in parallel for static partitioning but parallel Jostle is not into the public domain. From the Greenwich papers, it is an alternative to ParMetis. Although the parallel partitioner may lead to a partitioning of lower quality than the sequential partitioners, it may ....

....in which at the coarsest level a diffusion scheme is used. This approach is implemented in the software packages ParMetis and Jostle, see below. 3. 2 Existing graph based re partitioning tools: ParMetis and Jostle Two libraries for parallel graph re partitioning exist so far, i.e. ParMetis [13] and Jostle [24] Both libraries use multilevel techniques to obtain a new partitioning. The re partitioning of the coarsest graph is based on a diffusion scheme. The diffusion algorithm of Hu Blake [11] has a global view. It minimizes the Euclidian norm of the data movement based on the ....

G. Karypis, K. Schloegel, and V. Kumar. ParMetis: Parallel Graph Partitioning and Sparse Matrix Ordering Library, version 1.0. Technical report, Dept. of Computer Science, University of Minnesota, Jul 1997.

....partition. Because of this, the nature and requirements of the application must be considered when determining which graph partitioning algorithm to employ. This report presents an analysis of the algorithms implemented in one of the currently available graph partitioning packages: ParMETIS [10]. ParMETIS, developed by George Karypis, Kirk Schloegel, and Vipin Kumar at the University of Minnesota, operates as a library of graph partitioning functions which may be linked and called from other applications. The rest of this report is arranged as follows: Section 2 presents a formal ....

....[15] Average Processor Degree The Average Processor Degree gives an indication of the number of messages each processor must send. It is determined by summing the degrees of all partitions and dividing this sum by the number of partitions. 15] 3 The ParMETIS Graph Partitioning Package ParMETIS [10] is a package of various MPI based parallel graph partitioning algorithms designed to partition a given graph into a specified number of partitions. These algorithms are based on the multilevel partitioning and fill reducing ordering algorithms implemented in the serial METIS graph partitioning ....

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G. Karypis, K. Schloegel, and V. Kumar. PARMETIS: Parallel graph partitioning and sparse matrix ordering library, version 1.0. Technical report, University of Minnesota, Department of Computer Science, Minneapolis, MN 55455, 1997.

....suitable graph partitioner results in a mesh partitioner based on the DRAMA cost model. Within the current version of the DRAMA library, the subsequent graph partitioning is carried out by calling routines from PARMETIS, the software package developed by Karypis et al. University of Minneapolis ([18,23]) PARMETIS contains several strategies for graph repartitioning; in particular a multilevel method based on diffusing load to adjacent partitions. The idea behind this multilevel technique is that from the originally graph a hierarchy of coarser graphs is generated (by merging graph vertices to ....

G. Karypis, K. Schloegel and V. Kumar, PARMETIS Parallel graph partitioning and sparse matrix ordering library, Version 1.0, Dept. of Computer Science, University of Minnesota, 1997

....contains mesh re partitioning techniques of both types. A meshmigration method is being developed in combination with a parallel re meshing technique [4] Global mesh re partitioning is implemented in DRAMA by interfacing to existing libraries for parallel graph re partitioning, i.e. ParMetis [7] and Jostle [8] Both libraries use multilevel techniques in which the re partitioning of the coarsest graph is based on the diffusion algorithm of Hu Blake [6] which minimizes the Euclidean norm of the data migration based on the processor graph. This diffusion algorithm is synchronous and is ....

G. Karypis, K. Schloegel, and V. Kumar, ParMetis: Parallel Graph Partitioning and Sparse Matrix Ordering Library, version 2.0, Technical Report, Dept. of Computer Science, University of Minnesota.

....a suitable graph partioner results in a mesh partitioner based on the DRAMA cost model. Within the current version of the DRAMA library, the subsequent graph partitioning is carried out by calling routines from PARMETIS, the software package developed by Karypis et al. University of Minneapolis ([13,14]) PARMETIS contains several strategies for graph re partitioning; in particular a multilevel method based on diffusing load to adjacent partitions. The idea behind this multilevel technique is that from the originally graph a hierarchy of coarser graphs is generated (by merging graph vertices ....

G. Karypis, K. Schloegel and V. Kumar, PARMETIS Parallel graph partitioning and sparse matrix ordering library, Version 1.0, Dept. of Computer Science, University of Minnesota, 1997

....program for solving elliptic PDEs. PHAML is written in Fortran 90 and uses MPI for message passing. Adaptive re nement is by newest node bisection of triangles. RTK and RTRB were implemented as part of PHAML. The multilevel di usive method was obtained from version 2. 0 of the ParMETIS library [4]. This C language library is currently the most widely used parallel library for graph partitioning. Most of the methods in the library are better suited for static partitioning, where one is willing to accept long execution times to obtain a higher quality partition. But some are intended for ....

G. Karypis, K. Schloegel, and V. Kumar, ParMETIS: Parallel Graph Partitioning and Sparse Matrix Ordering Library, Version 2.0, http://www.cs.umn.edu/ karypis/metis/metis.html.

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George Karypis and Vipin Kumar. ParMETIS: Parallel graph partitioning and sparse matrix ordering library. Technical Report TR 97-060, Department of Computer Science, University of Minnesota, 1997.

....the graph into two disconnected subgraphs satisfying some balance criterion. The vertices of the separator are numbered after the vertices in the subgraphs are numbered by following the same strategy recursively. There are two main approaches to parallelizing this algorithm. In the first approach [25, 26], the process of finding the separators is performed in parallel. The advantages of this approach are that a reasonably good speedup on ordering can be obtained and the graphs (both original and the subsequent subgraphs) are stored on multiple nodes, thereby avoiding excessive memory use on any ....

George Karypis and Vipin Kumar. ParMETIS: Parallel graph partitioning and sparse matrix ordering library. Technical Report TR 97-060, Department of Computer Science, University of Minnesota, 1997.

....on Synthetic Data Sets igur s 3 thr ugh 5 show the costs f r m Equation 2 obtained by the Unified Repa rF tioning Algor ithm compar ed to those obtained by the optimized scr tch r map and multilevel di#usion algor ithms, LMSR and Wavefr ont Di#usion [17] as implemented in ParMeTiS, Ver sion 2. 0 [9] on 32, 64, and 128 pr ocessor s of a Cr ay T3E. Specifically, these figur es show thr ee sets ofr esults, onefor each of the gr aphs descr ibed in Table 1. Each set is composed of fifteen pair s of bar s. These pair sr epr esent the aver agedr esultsfr om the eight exper iments (simulating global ....

G. Karypis, K. Schloegel, and V. Kumar. ParMeTiS: Parallel graph partitioning and sparse matri ordering library. Technical report, University of Minnesota, Department of Computer Science and Engineering, 1997.

....vertices) on eight processors is similar to that of partitioning mrng3 (4 million vertices) on 32 processors and mrng4 (7.5 million vertices) on 64 processors. Table 4 gives the run times of the k way single constraint parallel graph partitioning algorithm implemented in the ParMeTiS library [8] on the same graphs used for our experiments. Comparing Tables 3 and 4 shows that computing a three constraint partitioning takes about twice as long as computing a single constraint partitioning. For example, it takes 9.3 seconds to compute a three constraint partitioning and 4.8 seconds to ....

G. Karypis, K. Schloegel, and V. Kumar. ParMeTiS: Parallel graph partitioning and sparse matrix ordering library. Technical report, University of Minnesota, Department of Computer Science and Engineering, 1997.

....of particles. Results on Synthetic Data Sets Figures 3 through 5 show the cost functions obtained by the Unified Repartitioning Algorithm compared to those obtained by the optimized scratch remap and multilevel diffusion algorithms, LMSR and Wavefront Diffusion [17] as implemented in ParMeTiS [9] on up to 128 processors of a Cray T3E. Specifically, these figures show three sets of results, one from each of the graphs described in Table 1. Each set is composed of fifteen pairs of bars. These pairs representtheaveraged results from the eight experiments (simulating global and localized ....

G. Karypis, K. Schloegel, and V. Kumar. ParMeTiS: Parallel graph partitioning and sparse matrix ordering library. Technical report, Univ. of MN, Dept. of Computer Sci. and Engr., 1997. 10

....essentially be used to compute a partitioning for the partitioning algorithm. That is, a rough partitioning of the input graph can be computed by a fast geometric approach. This partitioning can be used to redistribute the graph prior to performing parallel multilevel (or spectral) partitioning [52]. Use of this boot strapping approach significantly increases the parallel efficiency of the more accurate partitioning scheme byproviding it with data locality. Parallel multilevel algorithms for graph partitioning are available in the ParMeTiS [52] and JOSTLE [92] libraries. 0.6 ....

....multilevel (or spectral) partitioning [52] Use of this boot strapping approach significantly increases the parallel efficiency of the more accurate partitioning scheme byproviding it with data locality. Parallel multilevel algorithms for graph partitioning are available in the ParMeTiS [52] and JOSTLE [92] libraries. 0.6 Multi constraint, Multi objective Graph Partitioning In recent years, with advances in the state of the art of scientific simulation, sophisticated classes of computations suchasmulti phase, multi physics, and multi mesh simulations have become commonplace. For ....

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G. Karypis, K. Schloegel, and V. Kumar. ParMeTiS:Parallel graph partitioning and sparse matrix ordering library. Technical report, Dept. of Computer Science and Engineering, Univ. of Minnesota, 1997.

....vertices) on eight processors is similar to that of partitioning mrng3 (4 million vertices) on 32 processors and mrng4 (7.5 million vertices) on 64 processors. Table 4 gives the run times of the k way single constraint parallel graph partitioning algorithm implemented in the ParMeTiS library [9] on the same graphs used for our experiments. Comparing 18 Graph 8 processors 16 processors 32 processors 64 processors 128 processors time efficiency time efficiency time efficiency time efficiency time efficiency mrng2 9.8 100 5.3 92 3.5 70 2.5 49 3.1 20 mrng3 31.8 100 16.9 94 9.3 85 ....

G. Karypis, K. Schloegel, and V. Kumar. ParMeTiS: Parallel graph partitioning and sparse matrix ordering library. Technical report, University of Minnesota, Department of Computer Science and Engineering, 1997.

....criterion. The vertices of the separator are numbered after the vertices in the subgraphs are numbered by following the same strategy recursively. There are two main approaches to parallelizing this algorithm. In the first approach, the process of finding the separators is performed in parallel [10]. The advantages of this approach are that a reasonably good speedup on ordering can be obtained and the graphs (both original and the subsequent subgraphs) are stored on multiple nodes, thereby avoiding excessive memory use on any single node in a distributed memory environment. A disadvantage of ....

George Karypis and Vipin Kumar. Parmetis: Parallel graph partitioning and sparse matrix ordering library. Technical Report TR 97-060, Department of Computer Science, University of Minnesota, 1997.

....true for slightly to moderately imbalanced graphs. The above results are consistent with those presented by Oliker and Biswas in [13] They show that remapping is more effective for partitionings computed from scratch by the parallel k way multilevel graph partitioner implemented in ParMeTiS [8, 12] than by the serial k way multilevel graph partitioner implemented in MeTiS [9, 10] The ParMeTiS graph partitioner utilizes a matching scheme that favors local matching over global matching, 1 while the MeTiS graph partitioner utilizes global matching. 1 ParMeTiS allows non local matchings ....

....algorithm while computing high quality, well balanced partitionings. 6.1.2 WD vs. LMSR vs. MLDD Figures 15, 16, and 17 compare the TotalV, edge cut, and MaxV results obtained by the multilevel directed diffusion algorithm (MLDD) described in [15] and implemented as PARDAMETIS in ParMeTiS [12], with our LMSR and Wavefront Diffusion algorithms. In these figures, the results from MLDD and Wavefront Diffusion are normalized against those obtained from our LMSR algorithm. Hence, a bar below the 1.0 index line indicates that the LMSR algorithm obtained worse results than the indicated ....

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G. Karypis, K. Schloegel, and V. Kumar. ParMeTiS: Parallel graph partitioning and sparse matrix ordering library. Technical report, University of Minnesota, Department of Computer Science and Engineering, 1997.

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Karypis, G., Schloegel, K., and Kumar, V.: ParMetis Parallel Graph Partitioning and Sparse Matrix Ordering Library, Version 3.1. University of Minnesota Department of Computer Science and Engineering, and Army HPC Research Center, Minneapolis, (2003). Open-source software distributed at http://www-users.cs.umn.edu/~karypis/metis.

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G. Karypis, V. Kumar, ParMETIS: Parallel graph partitioning and sparse matrix ordering library, Tech. Rep. 97-060, Department of Computer Science, University of Minnesota, available on the WWW at URL http://www.cs.umn.edu/~metis (1997).

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G. Karypis, K. Schloegel, and V. Kumar, "ParMetiS: Parallel graph partitioning and sparse matrix ordering library," Technical report 97-060, Dept. of Computer Science, University of Minnesota, Minneapolis, 1997.

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Karypis, G., Schloegel, K., and Kumar, V, ParMETIS: Parallel Graph Partitioning and Sparse Matrix Ordering Library Version 1.0. University of Minnesota, Department of Computer Science, Minneapolis, MN 55455, July 1997. 10

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G. Karypis, K. Schloegel, and V. Kumar. PARMETIS -- parallel graph partitioning and sparse matrix ordering library, Version 2.0. University of Minnesota, Minneapolis, MN, 1998.

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G. Karypis, K. Schloegel, and V. Kumar. ParMETIS: Parallel Graph Partitioning and Sparse Matrix Ordering Library, Version 2.0. Department of Computer Science, University of Minnesota (1998): 3-8.

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G. Karypis, K. Schloegel and V. Kumar, PARMETIS: Parallel Graph Partitioning and Sparse Matrix Ordering Library, July 1997.

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George Karypis, Kirk Schloegel, and Vipin Kumar. Parmetis: Parallel graph partitioning and sparse matrix ordering library version 2.0, June 1998. Scalable Instrumentation and Program Database 19

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