Krishna P. Belkhale and Prithviraj Banerjee. Recursive partitions on multiprocessors. In Q. F. Stout D. W. Walker, editor, The Fifth Distributed Memory Computing Conference, volume 2, pages 930--938, April 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....we have encountered during the parallelization has been the allocation of a three dimensional world on a set of processors. A study on decomposition techniques available which maintain locality of data as well as a good scheme of communication for load balancing purpose has been developed ( SS90] [BB90], Hin90] No general 3D algorithm has yet been proposed. The necessity to keep neighborhood locality and to adopt a load balancing strategy lead us to choose an allocation where processors are connected in a linear network fashion, and where the 3D world is distributed along an axis, called ....

Krishna P. Belkhale and Prithviraj Banerjee. Recursive partitions on multiprocessors. In Q. F. Stout D. W. Walker, editor, The Fifth Distributed Memory Computing Conference, volume 2, pages 930--938, April 1990.

....might still require a certain minimal set of strategies to be always available [Han89, PSC93a] Note also that the user may not select a specific strategy for distributing data explicitly, as shown in Figure 2.3. In this case the compiler chooses a default strategy, such as recursive bisection [BP90] or spacefilling curves [PB94] Furthermore, since the default number of dimensions is one and some key words are optional, the DISTRIBUTE atomD(VALUE(DIM=1, VALS=x, WEIGHT=inb) could be abbreviated as DISTRIBUTE atomD(VALUE(x,inb) 22 DistDirective is DISTRIBUTE ValMapping AlignDirective is ....

K. P. Belkhale and P. Prithviraj. Recursive partitions on multiprocessors. In Proceedings of the 5th Distributed Memory Computing Conference, pages 930--938, 1990.

....partition algorithm was developed by Berger Bokhari in 1985 [3, 4] as a means for partitioning non uniform domains. It was inspired by Bentley s work on k dimensional search trees [2] This approach permits a very fast solution to the partitioning problem and has found many applications [1, 9, 17]. The key idea behind this algorithm is to make a series of bisections, along orthogonal directions, minimizing the load imbalance at each step. This algorithm does not take into consideration the perimeter, surface area, or aspect ratio of the subregions being generated and can yield ....

....finding algorithm[5, 6] The sorting step is eliminated and we are left with O(dn) time. However the constants involved in the linear time median finding algorithm are large and this method remains of theoretical interest only. Although binary dissection has found many applications, for example [1, 9, 17], it partitions only on the basis of numbers of points. It is insensitive to the distribution of points in space. As a result, in its attempt to equalize the number of points at each bisection, it can yield partitions which have poor aspect ratio (the ratio of largest to smallest sides) This ....

Krishan Belkhale and Prithviraj Banerjee. Recursive partitions on multiprocessors. In The Fifth Distributed Memory Computing Conference, pages 930--938, April 1990.

....work has been done on parallel machines with uniform computational power. For these machines, decomposition of arrays is relatively simple. The array is partitioned equally along one or more dimensions. This is reflected in the BLOCK directive of High Performance Fortran [1] Belkhale and Banerjee [5] have proposed methods for partitioning a nonuniform grid. Grid problems with varying resource demands have been studied by Nicol and Saltz [13] Nicol [12] has described the decomposition of unstructured grids into perfectly rectilinear partitions. There has been very little work done on ....

Krishna P. Belkhale and Prithviraj Banerjee. "Recursive partitions on multiprocessors. "Proceedings of the Fifth Distributed Memory Computing Conference, pp. 930--938, April 1990.

....of processors, network speed, and communication pattern. Bounds are established on the costs of these partitioning schemes. These may be used to make better decomposition decisions. Data partitioning in multiprocessors and distributed systems has received substantial treatment in the literature [1, 2, 4, 5, 9, 10, 12, 14, 15], but only recently has decomposition in the heterogeneous environment been explored. A number of systems for parallel computing in the heterogeneous workstation cluster have recently become available. PVM [8] the p4 [3] and Dataparallel C [11] are examples of these The increasing interest in ....

Krishna P. Belkhale and Prithviraj Banerjee. Recursive partitions on multiprocessors. In Proceedings of the Fifth Distributed Memory Computing Conference, pages 930--938, April 1991.

....multicomputers and multiprocessors [5, 6, 7, 13, 20, 21, 23, 29] While the N4 general quadrilateral affords a finer grained load balance than those methods that preserve rectangularity, a greater number of communications between processors may be generated in the worst case. Belkhale and Banerjee [4] propose two dynamic recursive partitioning schemes for a non homogeneous grid problem space. The slice partitioning technique divides the domain into vertical slices so that each section has approximately the same number of points. The rectangular method first divides the domain across the x ....

K. P. Belkhale and P. Banerjee. Recursive partitions on multiprocessors. In Proceedings of the Fifth Distributed Memory Computing Conference, pages 930--938, April 1990.

....to the compiler to achieve a static workload balance. Nicol and Saltz [12] examine grid problems with varying resource demands. Nicol [11] deals with the decomposition of irregular grids into perfectly rectilinear partitions to facilitate their mapping to mesh networks. Belkale and Banerjee [3] propose recursive slice and rectangular methods for partitioning a nonhomogeneous grid. The investigation of problem partitioning in the face of non uniform processors has only recently begun. Nedeljkovi c and Quinn address heterogeneity in the workstation cluster, and they present a dynamic load ....

Krishna P. Belkhale and Prithviraj Banerjee. Recursive partitions on multiprocessors. In Proceedings of the Fifth Distributed Memory Computing Conference, pages 930--938, April 1991.

....this class. Most previous data decomposition research has been concerned with partitioning a problem across the homogeneous grouping of processors found in traditional parallel computers. Some of the previous work deals with partitioning a heterogeneous problem space across homogeneous processors [2, 3, 17, 20]. The grid points in these problems do not have equal computational requirements, or the grid is sparse. Decomposition reduces to the problem of assigning equal computational effort to each processor. Block decomposition has specifically been addressed by [2, 3, 8, 9, 15, 18] and data ....

....homogeneous processors [2, 3, 17, 20] The grid points in these problems do not have equal computational requirements, or the grid is sparse. Decomposition reduces to the problem of assigning equal computational effort to each processor. Block decomposition has specifically been addressed by [2, 3, 8, 9, 15, 18], and data decomposition across heterogeneous processors has been discussed in [4, 10, 16] A number of systems to facilitate parallel processing on workstation clusters have recently appeared. PVM (Parallel Virtual Machine) which is freely available, supports parallel computing across a wide ....

Krishna P. Belkhale and Prithviraj Banerjee. Recursive partitions on multiprocessors. In Proceedings of the Fifth Distributed Memory Computing Conference, pages 930--938, April 1991.

....and grid squares are equal. Previous work in data decomposition has addressed the partitioning of non uniform problems across homogeneous processors, and of uniform problems across heterogeneous processors. Berger and Bokhari [3] propose a Binary Dissection method, and Belkhale and Banerjee [2] present a Recursive Partitioning (RP) scheme for dividing a non uniform grid for homogeneous processors so that each processor is assigned an equal share of workload. Bokhari et al. 4] develop a Parametric Binary Dissection technique that considers load and shape, where load is defined as the ....

Krishna P. Belkhale and Prithviraj Banerjee. Recursive partitions on multiprocessors. In Proceedings of the Fifth Distributed Memory Computing Conference, pages 930--938, April 1990.

....Section 5 describes each of the four partitioning schemes and Section 6 compares the mathematical characterizations and draws conclusions regarding the relative costs. 2 Related Work Data partitioning in multiprocessors and distributed systems has received substantial treatment in the literature [2, 4, 7, 8, 12, 14, 16, 18, 19]. Little of this work, however, is specific to the heterogeneous, high communication cost environment of the workstation network. With the increased popularity of clustered parallel programming, there has been increased exploration of these issues. Cheung and Reeves examine data distribution of ....

Krishna P. Belkhale and Prithviraj Banerjee. Recursive partitions on multiprocessors. In Proceedings of the Fifth Distributed Memory Computing Conference, pages 930--938, April 1991.

....and grid squares are equal. Previous work in data decomposition has addressed the partitioning of non uniform problems across homogeneous processors, and of uniform problems across heterogeneous processors. Berger and Bokhari [2] propose a Binary Dissection method, and Belkhale and Banerjee [1] present a Recursive Partitioning (RP) scheme for dividing a non uniform grid for homogeneous processors so that each processor is assigned an equal share of workload. Bokhari et al. 3] develop a Parametric Binary Dissection technique that considers load and shape, where load is defined as the ....

Krishna P. Belkhale and Prithviraj Banerjee. Recursive partitions on multiprocessors. In Proceedings of the Fifth Distributed Memory Computing Conference, pages 930--938, April 1990.

.... (ORB) scheme for solving the N body problem [16] and [17] Cybenko has reported on a scheme for recursive decomposition of workload in a multiprocessor [18] Belkhale and Banerjee have proposed an alternate recursive partitioning algorithm for partitioning a set of points on a multiprocessor [19], and have reported implementations of this scheme in the context of a parallel circuit extractor [20] and [21] All of the above partitioning methods are fairly complex to implement efficiently. ProperDRC utilizes a data partitioning strategy based on a scheme proposed by Ramkumar and Banerjee ....

K. P. Belkhale and P. Banerjee, "Recursive partitions on multiprocessors," in Proc. 5th Distributed Memory Computing Conf., Apr. 1990.

....al. 91, Raine et al. 89, Rapaport 91, Smith 91] 3.2 Application Induced Load Balancing 3.2.1 Automatic Data Partitioning Much research has been done on parallel schemes for partitioning spatial data. One part of this work deals with the schemes for partitioning the space into rectangular regions [Belkhale Banerjee 90, Berger Bokhari 87, Bokhari et al. 93, Cybenko Allen, Nicol 91] while the other looks at non rectangular regions [Hinz 90, Pilkington Baden 94, Reed et al. 87, Weaver Schnabel 92, Williams 92] Specialized runtime systems such as the DIME [Williams 91a] Voxel Database [Williams 92] and ....

....methods of estimating the load distribution and partitioning the space into regions of approximately equal load. 7.2.1 Sorting vs. Discretization There are two general schemes for partitioning the space into regions of equal load: one uses the list of objects sorted by their spatial coordinates [Belkhale Banerjee 90] and the other discretizes the space into rectangular slots and uses the load estimate in each slot. We describe the sorting method for a simple case where the space is partitioned along just one dimension, say along the X axis. Let the processors P 1 ; PN manage consecutive regions of ....

K. P. Belkhale and P. Banerjee. Recursive Partitions on Multiprocessors. Proceedings of the 4th Distributed Memory Computing Conference, pages 930--938, April 1990.

.... Bisection (ORB) scheme for solving the N body problem [25, 26] Cybenko has reported on a scheme for recursive decomposition of workload in a multiprocessor [27] Belkhale and Banerjee have proposed an alternate recursive partitioning algorithm for partitioning a set of points on a multiprocessor [28], and have reported implementations of this scheme in the context of a parallel circuit extractor [29, 30] All of the above partitioning methods are fairly complex to implement efficiently. ProperDRC utilizes a data partitioning strategy based on a scheme proposed by Ramkumar and Banerjee [6] ....

K. P. Belkhale and P. Banerjee, "Recursive partitions on multiprocessors," in Proc. 5th Distributed Memory Computing Conf., Apr. 1990.

....for every batch. Addition or deletion of points from the data structure involves restructuring the partitions so that the resulting regions have the same number of points. We have obtained an efficient algorithm for this problem for the case of a general recursive partition. This is described in [27]. The main idea in the algorithm is to recursively decompose an addition deletion operation on a region R into addition deletion operations on its subregions, at the immediate lower level, so that the sub regions are balanced. In PACE we have applied this algorithm for the special case of slice ....

K. P. Belkhale and P. Banerjee, "Recursive Partitions on Multiprocessors," Proc. 5th Distributed Memory Computing Conf., pp. 930-938, Apr. 1990.

....to a multiprocessor environment. Recently, researchers have started to investigate parallel algorithms for various CAD applications on commercially available general purpose multiprocessors [3] Example applications include logic simulation [4] switch level simulation [5] circuit simulation [6], testing and fault simulation [7] cell placement [8, 9] wire routing [10] design rule checking [11, 12, 13] and circuit extraction [14, 15, 16] In this thesis, we will describe parallel algorithms for one particular CAD application, namely VLSI circuit extraction. General purpose ....

K. P. Belkhale, P. Banerjee, "Recursive Partitions on Multiprocessors", Proc. 5th Distributed Memory Computing Conf, April 1990.

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