F. Manne and T. S#revik, Optimal partitioning of sequences, Tech. Rep. CS92 -62, University of Bergen, Norway, 1992.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....horizontal stripes are performed in parallel. Optimal Jagged Decomposition ( OJD) The OJD algorithms presented in this section are based on the optimal semi generalized block partitioning algorithm proposed by Manne and Srevik [17] Their algorithm extends the dynamic programming based 1D CCP [16] to OJD. They perform a p way CCP on the rows of the workload array. The cost of a subchain in a p way rowwise partition is found by applying a q way CCP on the columns of that stripe and taking the bottleneck value of the columnwise partition as the cost of the subchain. The complexity of their ....

F. Manne and T. Srevik. Optimal partitioning of sequences. J. Algorithms, 19:235--249, 1995.

....array partitioning problems. Here we briefly describe the application context for each; further details of modeling will be discussed in the journal version. One dimensional case under F . This problem was abstracted for load balancing in pipelined, parallel environments in [B88] and studied in [OM95, AF91, HL92, MS95, M93, CN91, HNC92, N91] etc. Two dimensional case under F . This problem arises in balanced data distribution as implemented in the Superb environment [ZBG86] and HPF2 [HPF] High Performance Fortran) See [M93, CM 95] for more applications to particlein cell computations and sparse matrix computations. Two ....

....extensively researched. We summarize the previous work and our results in the table below, providing all citations where identical bounds were obtained independently. Reference Bound Bokhari [B88] O(n 3 p) Anily Federgruen [AF91] O(n 2 p) Hansen Liu [HL92] O(n 2 p) Manne Sorevik [MS95] O(np log p) Choi Narahari [CN91] O(np) Olstad Manne [OM95] O(np) Nicol [N91] O(n p 2 log 2 n) Charikar, Chekuri Motwani [CCM96] O(n p 2 log 2 n) Han, Narahari Choi [HNC92] O(n p 1 ffl ) ffl 1 This paper O(n log n) Our result relies on a binary search over a space ....

F. Manne and T. Sorevik. Optimal partitioning of sequences. Journal of Algorithms, 19, 235 -- 249, 1995.

....This work is partially supported by ONR award 400x116yip01 and NSF Grant CCR 9625669. Abstract. We consider the problem of partitioning an array of n items into p intervals so that the maximum weight of the intervals is minimized. The currently best known bound for this problem is O(np) [MS95]. In this paper, we present two improved algorithms for this problem: one runs in time O(n p 2 (log n) 2 ) and the other runs in time O(n log n) The former is optimal whenever p p n= log n, and the latter is nearoptimal for arbitrary p. We consider the natural generalization of this ....

....of size n into p intervals such that the maximum number of nonzero elements in any interval is minimized. This gives our 1D p partition problem under F . Further details on the application of the 1D p partition problem under F for load balancing in pipelined, parallel environments can be found in [B88, OM95, AF91, HL92, MS95, M93, MH95]. Two dimensional case under F . For data stored in two dimensional arrays, several high performance computing languages allow the user to specify a partitioning and distribution of data onto a logical set of processors. An example of such a scheme is what is known as the generalized block ....

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F. Manne and T. Sorevik. Optimal partitioning of sequences. Journal of Algorithms, 19, 235 -- 249, 1995.

....Olstad and Manne [27] introduced asymptotically faster O(MK) time, and O( M Gamma K)K) time DP based algorithms, respectively. Iterative refinement approach starts with a partition and iteratively tries to improve the solution. The O( M GammaK)K lg K) time algorithm proposed by Manne and S revik [22] falls into this class. The probe approach relies on repeated investigations for the existence of a partitionwith a bottleneck value no greater than a given value. Such a probing takes (M ) time since every task has to be examined. Since probing needs to be performed repeatedly, an individual ....

....to O(K lg wmax lg K K lg wmax lg(w max=w avg ) K lg M ) together with the initial cost of O(K lg M ) for setting the SL p and SH p values. 3.1. 2 Bidding Algorithm In this work, we propose an iterative refinement scheme which is much more effective than the one proposed by Manne and S revik [22]. The proposed algorithm, namely the BIDDING algorithm, is presented in Fig. 3. In this algorithm, we dynamically increase the bottleneck value BIDDING(T; K) sp 0 for p 0; 1; K Gamma 1; and sK M ; Perform prefix sum on T [0 : M ] with T [0] 0; BIDS[0] B W tot T [M ] B W tot ....

F. Manne, andT. Sørevik, "Optimal Partitioning of Sequences," J. Algorithms, Vol. 19, 1995, pp. 235--249.

....results for sparse matrix vector multiplication on a SIMD machine. For sparse Cholesky factorization it gave worse results than the simple Cut Stack. We tried to improve the method by balancing the load on each processor based on the amount of work in each matrix column after the randomization [24]. This was slightly better, but still did not beat Cut Stack. While the numeric Cholesky factorization ran on a parallel computer in this implementation, all the preprocessing was done sequentially. On the larger test matrices this preprocessing, which included preordering and symbolic ....

F. Manne and T. S#revik, Optimal partitioning of sequences, Tech. Rep. CS92 -62, University of Bergen, Norway, 1992.

....matrix, dense vector multiplication on a SIMD computer. In the final section we summarize and point to areas of future work. 2 A partitioning problem We will in this section give a formal definition of the main partitioning problem and also recapitulate previous work. The problem as stated in [10] is as follows: Let the two integers p n be given and let foe 0 ; oe 1 ; oe n Gamma1 g be a finite ordered set of bounded real numbers. Let R = fr 0 ; r 1 ; r p g be a set of integers such that r 0 = 0 r 1 : r p Gamma1 r p = n. Then R defines a partition of foe 0 ; oe 1 ; oe ....

....to the MinMax problem that we are aware of is by Bokhari [4] who presented an O(n 3 p) algorithm using a bottleneck path algorithm. Anily and Federgruen [2] and Hansen and Lih [9] independently presented the same dynamic programming algorithm with time complexity O(n 2 p) Manne and S revik [10] then presented an O(p(n Gamma p) log p) algorithm based on iteratively improving a given partition. They also described a bisection method for finding an approximate solution which runs in time O(n log(f(0; n Gamma 1) ffl) where ffl is the desired precision. In the next section we show how ....

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F. Manne and T. Sørevik, Optimal partitioning of sequences, Tech. Report CS-92-62, University of Bergen, Norway, 1992.

....partitioning problem is described and solved in Section 4. In the final section we summarize and point to areas of future work. 2 A partitioning problem We will in this section give a formal definition of the main partitioning problem and also recapitulate previous work. The problem as stated in [11] is as follows: Let the two integers p n be given and let foe 0 ; oe 1 ; oe n Gamma1 g be a finite ordered set of bounded real numbers. Let R = fr 0 ; r 1 ; r p g be a set of integers such that r 0 = 0 r 1 : r p Gamma1 r p = n. Then R defines a partition of foe 0 ; oe 1 ; oe ....

....0 ; oe n Gamma1 g. Bokhari [3] presents the MinMax problem and gives an O(n 3 p) algorithm using a bottleneck path algorithm. Anily and Federgruen [2] and Hansen and Lih [8] independently presented the same dynamic programming algorithm with time complexity O(n 2 p) Manne and S revik [11] then presented an O(p(n Gamma p) log p) algorithm based on iteratively improving a given partition. They also described a bisection method based on a simple O(n) feasibility test for finding an approximate solution which runs in time O(n log(f(0; n Gamma 1) ffl) where ffl is the desired ....

[Article contains additional citation context not shown here]

F. Manne and T. Sørevik, Optimal partitioning of sequences, Tech. Report CS-92-62, University of Bergen, Norway, 1992.

....results for sparse matrix vector multiplication on a SIMD machine. For sparse Cholesky factorization it gave worse results than the simple Cut Stack. We tried to improve the method by balancing the load on each processor based on the amount of work in each matrix column after the randomization [23]. This was slightly better, but still did not beat Cut Stack. While the numeric Cholesky factorization ran on a parallel computer in this implementation, all the preprocessing was done sequentially. On the larger test matrices this preprocessing, which included preordering and symbolic ....

F. Manne and T. Sørevik, Optimal partitioning of sequences, Tech. Report CS-92-62, University of Bergen, Norway, 1992.

....show how an optimal semi generalized block distribution can be found. The performance of these algorithms are compared with other orderings such as the uniform block distribution and the binary recursive decomposition [1, 3] The algorithms presented extend earlier work for one dimensional arrays [13, 14]. The paper is organized as follows: Section 2 gives formal definitions of the different partitioning schemes and relate these to each other. Section 3 presents new algorithms for computing the different distributions and Section 4 reports on the performance of these. Finally, in Section 5 we ....

F. Manne and T. Sørevik, Optimal partitioning of sequences, J. Alg., 19 (1995), pp. 235--249.

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