P. Berthome, A. Ferreira, B.M. Maggs, S. Perennes, and C.G. Plaxton. Sorting-Based Selection Algorithms for Hypercubic Networks. In Proceedings of the 7th International Parallel Processing Symposium, pages 89-95, Newport Beach, CA, April 1993. IEEE Computer Society Press.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....with k = 2 . In previous work, we have designed deterministic and ecient parallel algorithms for the selection problem on current parallel machines [4, 5, 3] In this paper, we discuss a new UltraFast Randomized algorithm for the selection problem which, unlike previous research (for example, [10, 11, 14, 7, 13, 12, 15, 18, 17, 16]) is not dependent on network topology or limited to the PRAM model which does not assign a realistic cost for communication. In addition, our randomized algorithm improves upon previous implementations on current parallel platforms, for example, Al Furaih et al. 2] implement both our ....

P. Berthome, A. Ferreira, B.M. Maggs, S. Perennes, and C.G. Plaxton. Sorting-Based Selection Algorithms for Hypercubic Networks. In Proceedings of the 7th International Parallel Processing Symposium, pages 89-95, Newport Beach, CA, April 1993. IEEE Computer Society Press.

....general problem is that of selection; namely, we have to find the element of rank i, for a given parameter i, 1 i n. Parallel sorting trivially solves the selection problem, but sorting is known to be computationally harder than selection. Previous parallel algorithms for selection (e.g. [10, 20, 28, 22]) tend to be network dependent or assume the PRAM model, and thus, are not efficient or portable to current parallel machines. In this paper, we present algorithms that are shown to be scalable and efficient across a number of different platforms. 2. The Block Distributed Memory Model We use ....

....when p does not divide n evenly, the last processor will receive less than q elements. We refer to this as Method A. Figure 2 shows a dynamic data redistribution example for Method A. This is a simple example for 8 processors and 63 elements, with an arbitrary initial distribution of N = [10,3,2200,14,6,8]. Here, qj = 1 = 8, for 0 j 6, while q7: 7, since 3 7 receives the remainder of elements when p does not divide the total number of elements evenly. An algorithm for Method A first calls the concat communication primitive and assigns it to array N t, a p x p shared array. Another p ....

R BerthomE, A. Ferreira, B. Maggs, S. Perennes,and C. Plaxton. Sorting-Based Selection Algorithms for Hypercubic Networks. In Proceedings of the 7th International Parallel Processing Symposium, pages 89-95, Newport Beach, CA, April 1993. IEEE Computer Society Press. 300

....U.S. Government, The University of New Mexico, or the Maui High Performance Computing Center. ALENEX00: Second Workshop on Algorithm Engineering and Experiments 116 D.A. Bader which, unlike previous research (for example, Hao et al. 1992; Krizanc and Narayanan 1992; Rajasekaran and Reif 1993; Berthome et al. 1993; Rajasekaran et al. 1994; Rajasekaran 1996; Rajasekaran and Sahni 1997; Sarnath and He 1997; Rajasekaran and Wei 1997; Rajasekaran and Sahni 1998] is not dependent on network topology or limited to the PRAM model which does not assign a realistic cost for communication. In addition, our ....

BERTHOM E, P., FERREIRA, A., MAGGS, B. M., PERENNES, S., AND PLAXTON, C. G. 1993. Sorting-Based Selection Algorithms for Hypercubic Networks. In Proceedings of the 7th International Parallel Processing Symposium (Newport Beach, CA, April 1993), pp. 89--95. IEEE Computer Society Press.

....(unshuffled) then the rank of a packet can be estimated by comparing its value with the other packets in its submesh. In this paper we reintroduce splitters in deterministic sorting algorithms. By reducing their number to a minimum, applying a variant of successive sampling (term used in [3], see Section 5 for a description of the method) handling and comparing the packets with them is considerably cheaper than before. In the context of selection and ranking, comparable splitter selection methods have been used before. The idea originates with Cole and Yap. In [8] they give a ....

....selection and ranking, comparable splitter selection methods have been used before. The idea originates with Cole and Yap. In [8] they give a parallel comparison model algorithm for finding the median based on successive sampling. For selection on a hypercube it has been applied by Berthom e ea. [3]; for selection on a PRAM by Chaudhuri, Hagerup and Raman [4] Our variant turns out to resemble most the application in [3] Application of successive sampling for meshes requires specific adaptation to the features of the network. It appears that we are the first to apply it for sorting. 1.3 ....

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Berthom'e, P., A. Ferreira, B.M. Maggs, S. Perennes, C.G. Plaxton, `Sorting-Based Selection Algorithms for Hypercubic Networks,

....allows to decouple the routing from the rank estimation. As routing can be performed with a smaller lower order term than the conventional sorting algorithms, this may be profitable. The number of splitters is reduced to a minimum, by applying a variant of successive sampling (term used in [2]) handling them and comparing the packets with them is cheaper than before. In the context of selection and ranking, comparable splitter selection methods have been used before. In [4] Cole and Yap give an algorithm for finding the median based on successive sampling. For selection on a hypercube ....

....with them is cheaper than before. In the context of selection and ranking, comparable splitter selection methods have been used before. In [4] Cole and Yap give an algorithm for finding the median based on successive sampling. For selection on a hypercube it has been applied by Berthome ea. [2]; for selection on a PRAM by Chaudhuri, Hagerup and Raman [3] Our variant resembles most the application in [2] Application of successive sampling for meshes requires specific adaptation to the features of the network. It appears that we are the first to apply it for sorting. Contents. We start ....

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Berthome, P., A. Ferreira, B.M. Maggs, S. Perennes, C.G. Plaxton, `Sorting-Based Selection Algorithms for Hypercubic Networks,' Proc. 7th IPPS, pp. 89--95, IEEE, 1993.

....(unshuffled) then the rank of a packet can be estimated by comparing its value with the other packets in its submesh. In this paper we reintroduce splitters in deterministic sorting algorithms. By reducing their number to a minimum, applying a variant of successive sampling (term used in [3], see Section 5 for a description of the method) handling and comparing the packets with them is cheaper than before. In the context of selection and ranking, comparable splitter selection methods have been used before. In [8] Cole and Yap give an algorithm for finding the median based on ....

....with them is cheaper than before. In the context of selection and ranking, comparable splitter selection methods have been used before. In [8] Cole and Yap give an algorithm for finding the median based on successive sampling. For selection on a hypercube it has been applied by Berthom e ea. [3]; for selection on a PRAM by Chaudhuri, Hagerup and Raman [4] Our variant resembles most the application in [3] Application of successive sampling for meshes requires specific adaptation to the features of the network. It appears that we are the first to apply it for sorting. 1.3 Contents We ....

[Article contains additional citation context not shown here]

Berthom'e, P., A. Ferreira, B.M. Maggs, S. Perennes, C.G. Plaxton, `Sorting-Based Selection Algorithms for Hypercubic Networks, ' 7th Proc. International Parallel Processing Symp., pp. 89--95, IEEE, 1993.

....computation time and O(log n log p log log p) communication time, and relies on Cypher and Plaxton s theoretical hypercube sorting algorithm [6] We call this the RCY algorithm. The best fine grain weak hypercube algorithm (i.e. n = Theta(p) for the selection problem is due to Berthome et al. [3], who give an O(log p log p) time solution based on the theoretical hypercube sorting algorithm [6] We refer to [3] as the BFMPP algorithm. In this paper, we present efficient solutions for several selection related problems on coarse grain and fine grain hypercubes. Our results for the ....

....sorting algorithm [6] We call this the RCY algorithm. The best fine grain weak hypercube algorithm (i.e. n = Theta(p) for the selection problem is due to Berthome et al. 3] who give an O(log p log p) time solution based on the theoretical hypercube sorting algorithm [6] We refer to [3] as the BFMPP algorithm. In this paper, we present efficient solutions for several selection related problems on coarse grain and fine grain hypercubes. Our results for the weighted selection problem are summarized in Table 1. In this table, the function g(n; p) is defined to be minflog n p ; ....

P. Berthome, A. Ferreira, B. M. Maggs, S. Perennes, and C. G. Plaxton. Sorting-based selection algorithms for hypercubic networks. In the Proceedings of the 7 th International Parallel Processing Symposium, pages 89--95, 1993.

....time with high probability. Though the same result is implied by the sorting algorithm of Reif and Valiant [13] our algorithm is very simple and has a smaller underlying constant in the time bound. Therefore, in practice, our selection algorithm is likely to be faster. Recently Berthom e et al. [2] have presented a deterministic selection algorithm for p = n which runs in O(log n log n) time. Table I summarizes the best known selection algorithms on the hypercube. In this table [ p ] refers to results presented in this paper. L.B. stands for lower bound. All the bounds mentioned in ....

....in this table are asymptotic. Model Processors Run Time L.B. Det. Rand. Reference Sequential p n p log log p log 2 p log( n p ) n p log log p log p Det. 8] Sequential p n p log log p log p log log p n p log log p log p Rand. p ] Sequential n log n log n log n Det. [2] Sequential n log n log n Rand. 13] p ] Weak Parallel p n p log p log log p n p log p Det. 8] Weak Parallel p n p log p n p log p Rand. p ] Table I: Best Known Selection Algorithms 2 Preliminary Facts 2.1 Packet Routing Definitions. Let B(n; p) stand for a binomial ....

P. Berthom'e, A. Ferreira, B.M. Maggs, S. Perennes, and C.G. Plaxton, SortingBased Selection Algorithms for Hypercubic Networks, Proc. International Parallel Processing Symposium, 1993, pp. 89-95.

....sets, parallel graph partitioning and parallel construction of multidimensional binary search trees. Many parallel algorithms for selection have been designed for the PRAM model [2, 3, 4, 9, 14] and for various network models including trees, meshes, hypercubes and reconfigurable architectures [6, 7, 13, 16, 22]. More recently, Bader et.al. 5] implement a parallel deterministic selection algorithm on several distributed memory machines including CM 5, IBM SP 2 and INTEL Paragon. In this paper, we consider and evaluate parallel selection algorithms for coarse grained distributed memory parallel ....

Berthomi, A. Ferreira, B.M. Maggs, S. Perennes, and C.G. Plaxton, Sorting-based selection algorithms for hypercubic networks, Proc. 7 th International Parallel Processing Symposium (1993) 89-95.

....A more general problem is that of selection; namely, we have to find the element of rank i, for a given parameter i, 1 i n. Parallel sorting trivially solves the selection problem, but sorting is known to be computationally harder than selection. Previous parallel algorithms for selection ([9], 23] 31] 25] and data redistribution ( 28] 34] tend to be network dependent or assume the PRAM model, and thus, are not efficient or portable to current parallel machines. In this paper, we present algorithms that are shown to be scalable and efficient across a number of different ....

P. Berthom'e, A. Ferreira, B.M. Maggs, S. Perennes, and C.G. Plaxton. Sorting-Based Selection Algorithms for Hypercubic Networks. In Proceedings of the 7th International Parallel Processing Symposium, pages 89--95, Newport Beach, CA, April 1993. IEEE Computer Society Press.

....data sets, parallel graph partitioning and parallel construction of multidimensional binary search trees. Many parallel algorithms for selection have been designed for the PRAM model and for various network models including trees, meshes, hypercubes and reconfigurable architectures [BFMP93] More recently, Bader et.al. BJ95] implement a parallel deterministic selection algorithm on several distributed memory machines. In this chapter, we consider and evaluate parallel selection algorithms for coarsegrained distributed memory parallel computers. 3.1 Parallel Algorithms for ....

A. Berthomi, B.M. Ferreira, S. Maggs, and C.G. Plaxton. Sorting-based selection algorithms for hypercubic networks. In Proc. 7 th International Parallel Processing Symposium, pages 89--95, 1993.

....e O(n 1=6 ) RAND. Table 8: Selection on a Mesh with Fixed Buses Model Run Time Lower Bound Ref. Sequential O( n p log log p log 2 p log( n p ) n p log log p log p [46] Sequential e O( n p log log p log p log log p) n p log log p log p [48] Sequential O(log n log n) log n [6] Sequential e O(log n) log n [57, 48] Weak Parallel O( n p log p log log p) n p log p [46] Weak Parallel e O( n p log p) n p log p [48] Table 9: Selection on the Hypercube [48] s algorithm has been implemented on CM 2 and empirical results are promising [51] The best known ....

.... Parallel O( n p log p log log p) n p log p [46] Weak Parallel e O( n p log p) n p log p [48] Table 9: Selection on the Hypercube [48] s algorithm has been implemented on CM 2 and empirical results are promising [51] The best known deterministic algorithm is due to Berthom e, et al. [6] and has a run time of O(log n log n) For the case of p 6= n, refer to Table 9 for a summary of the best known algorithms. All the algorithms in this Table use the technique of sampling (either deterministic or randomized) A slightly better deterministic algorithm can be obtained using ....

P. Berthom'e, A. Ferreira, B.M. Maggs, S. Perennes, and C.G. Plaxton, Sorting-Based Selection Algorithms for Hypercubic Networks, Proc. International Parallel Processing Symposium, 1993, pp. 89-95.

....in practice than its deterministic counterpart due to the low constant associated with the algorithm. Many parallel algorithms for selection have been designed for the PRAM model [2, 3, 4, 9, 14] and for various network models including trees, meshes, hypercubes and reconfigurable architectures [6, 7, 13, 16, 21]. More recently, Bader et.al. 5] implement a parallel deterministic selection algorithm on several distributed memory machines including CM 5, IBM SP 2 and INTEL Paragon. In this paper, we consider and evaluate parallel selection algorithms for coarse grained distributed memory parallel ....

Berthom, A. Ferreira, B.M. Maggs, S. Perennes, and C.G. Plaxton, Sorting-based selection algorithms for hypercubic networks, Proc. 7 th International Parallel Processing Symposium (1993) 89-95.

....(a; b; c) selection game lead to new upper and lower bounds for selection on bounded degree hypercubic machines for what is arguably the most interesting range of the parameters n and p. Previous work on this problem has addressed the following two extreme cases: ffl For n p, Berthom e et al. [1] have proven that Cole s EREW PRAM algorithm [4] can be adapted to obtain a normal hypercube algorithm running in O( log n) Delta log n) time. This upper bound holds for any hypercubic machine. While this algorithm is not work optimal, it comes within a log n factor of the trivial diameterbased ....

P. Berthom'e, A. Ferreira, B. M. Maggs, S. Perennes, and C. G. Plaxton. Sorting-based selection algorithms for hypercubic networks. In Proceedings of the 7th International Parallel Processing Symposium, pages 89--95, April 1993.

No context found.

P. Berthom'e, A. Ferreira, B. M. Maggs, S. Perennes, and C. G. Plaxton. Sortingbased selection algorithms for hypercubic networks. In Proceedings of the 7th International Parallel Processing Symposium, pages 89--95, April 1993.

.... solved on an N node butterfly (or multibutterfly) in O(log N ) time using the randomized Flashsort algorithm of Reif and Valiant [21, 34] Prior to this work, the fastest deterministic selection algorithm for multibutterflies was the algorithm of Berthom e, Ferreira, Maggs, Perennes, and Plaxton [5]. This algorithm selects the kth largest element from among N elements on an N node butterfly (or any other hypercubic network) in O(logN log N ) time. Like the Sharesort algorithm, this algorithm does not make use of expansion when run on a multibutterfly. Since the selection problem can be ....

P. Berthom'e, A. Ferreira, B. M. Maggs, S. Perennes, and C. G. Plaxton. Sorting-based selection algorithms for hypercubic networks. In Proceedings of the 7th International Parallel Processing Symposium, pages 89--95, April 1993.

No context found.

P. Berthome, A. Ferreira, B. M. Maggs, S. Perennes, and C. G. Plaxton. Sorting-based selection algorithms for hypercubic networks. In Proceedings of the 7th International Parallel Processing Symposium, pages 89--95, April 1993.

.... be solved on an N node butterfly (or multibutterfly) in O(log N) time using the randomized Flashsort algorithm of Reif and Valiant [21, 34] Prior to this work, the fastest deterministic selection algorithm for multibutterflies was the algorithm of Berthom e, Ferreira, Maggs, Perennes, and Plaxton [5]. This algorithm selects the kth largest element from among N elements on an N node butterfly (or any other hypercubic network) in O(log N log N) time. Like the Sharesort algorithm, this algorithm does not make use of expansion when run on a multibutterfly. Since the selection problem can be ....

P. Berthom'e, A. Ferreira, B. M. Maggs, S. Perennes, and C. G. Plaxton. Sorting-based selection algorithms for hypercubic networks. In Proceedings of the 7th International Parallel Processing Symposium, pages 89--95, April 1993.

.... solved on an N node butterfly (or multibutterfly) in O(log N ) time using the randomized Flashsort algorithm of Reif and Valiant [30, 49] Prior to this work, the fastest deterministic selection algorithm for multibutterflies was the algorithm of Berthom e, Ferreira, Maggs, Perennes, and Plaxton [7]. This algorithm selects the kth largest item from among N items on an N node butterfly (or any other hypercubic network) in O(logN log N ) time. Like the Sharesort algorithm, this algorithm does not make use of expansion when run on a multibutterfly. Since the selection problem can be solved ....

P. Berthom'e, A. Ferreira, B. M. Maggs, S. Perennes, and C. G. Plaxton. Sorting-based selection algorithms for hypercubic networks. In Proceedings of the 7th International Parallel Processing Symposium, pages 89--95, April 1993.

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