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On Parallel Hashing and Integer Sorting
, 1991
"... The problem of sorting n integers from a restricted range [1::m], where m is superpolynomial in n, is considered. An o(n log n) randomized algorithm is given. Our algorithm takes O(n log log m) expected time and O(n) space. (Thus, for m = n polylog(n) we have an O(n log log n) algorithm.) The al ..."
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Cited by 25 (9 self)
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The problem of sorting n integers from a restricted range [1::m], where m is superpolynomial in n, is considered. An o(n log n) randomized algorithm is given. Our algorithm takes O(n log log m) expected time and O(n) space. (Thus, for m = n polylog(n) we have an O(n log log n) algorithm.) The algorithm is parallelizable. The resulting parallel algorithm achieves optimal speed up. Some features of the algorithm make us believe that it is relevant for practical applications. A result of independent interest is a parallel hashing technique. The expected construction time is logarithmic using an optimal number of processors, and searching for a value takes O(1) time in the worst case. This technique enables drastic reduction of space requirements for the price of using randomness. Applicability of the technique is demonstrated for the parallel sorting algorithm, and for some parallel string matching algorithms. The parallel sorting algorithm is designed for a strong and non standard mo...
Approximate and Exact Deterministic Parallel Selection
, 1993
"... The selection problem of size n is, given a set of n elements drawn from an ordered universe and an integer k with 1 k n, to identify the kth smallest element in the set. We study approximate and exact selection on deterministic concurrentread concurrentwrite parallel RAMs, where approximate sel ..."
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Cited by 15 (3 self)
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The selection problem of size n is, given a set of n elements drawn from an ordered universe and an integer k with 1 k n, to identify the kth smallest element in the set. We study approximate and exact selection on deterministic concurrentread concurrentwrite parallel RAMs, where approximate selection with relative accuracy ? 0 asks for any element whose true rank differs from k by at most n. Our main results are: (1) Exact selection problems of size n can be solved in O(logn=log log n) time with O(n log log n=logn) processors. This running time is the best possible (using only a polynomial number of processors) , and the number of processors is optimal for the given running time (optimal speedup); the best previous algorithm achieves optimal speedup with a running time of O(logn log n=log log n). (2) For all t (log log n) 4 log n, approximate selection problems of size n can be solved in O(t) time with optimal speedup with relative accuracy 2 \Gammat loglog log n=(log logn) ...
FORK  A HighLevel Language for PRAMs
 Future Generation Computer Systems
, 1994
"... We present a new programming language designed to allow the convenient expression of algorithms for a parallel random access machine (PRAM). The language attempts to satisfy two potentially conflicting goals: On the one hand, it should be simple and clear enough to serve as a vehicle for humantohu ..."
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Cited by 11 (0 self)
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We present a new programming language designed to allow the convenient expression of algorithms for a parallel random access machine (PRAM). The language attempts to satisfy two potentially conflicting goals: On the one hand, it should be simple and clear enough to serve as a vehicle for humantohuman communication of algorithmic ideas. On the other hand, it should be automatically translatable to efficient machine (i.e., PRAM) code, and it should allow precise statements to be made about the amount of resources (primarily time) consumed by a given program. In the sequential setting, both objectives are reasonably well met by the Algollike languages, e.g., with the RAM as the underlying machine model, but we are not aware of any language that allows a satisfactory expression of typical PRAM algorithms. Our contribution should be seen as a modest attempt to fill this gap. Fachbereich 14 Universitat des Saarlandes Im Stadtwald 6600 Saarbrucken 1 Supported by the Deutsche Forschungsge...
On the Power of Some PRAM Models
 Journal of Parallel Algorithms and Applications. Vol
, 1997
"... The focus here is the power of some underexplored CRCW PRAMs, which are strictly more powerful than exclusive write PRAM but strictly less powerful than BSR. We show that some problems can be solved more efficiently in time and/or processor bounds on these models. For example, we show that n linearl ..."
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Cited by 1 (0 self)
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The focus here is the power of some underexplored CRCW PRAMs, which are strictly more powerful than exclusive write PRAM but strictly less powerful than BSR. We show that some problems can be solved more efficiently in time and/or processor bounds on these models. For example, we show that n linearlyranged integers can be sorted in O(log n= log log n) time with optimal linear work on Sum CRCW PRAM. We also show that the maximum gap problem can be solved within the same resource bounds on Maximum CRCW PRAM. Though some models can be shown to be more powerful than others, some of them appear to have incomparable powers. Keywords: PRAM; BSR; time and processor bounds; simulation; sorting. Classification Categories: F.1.1, F.1.2, F.2.2 1 Preliminaries The focus of this work is on some underexplored Concurrent Read Concurrent Write (CRCW) Parallel Random Access Machine (PRAM) models. These PRAM models differ only in the way of resolving write conflicts. Some of them can be shown to be s...