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Optimal parallel selection
 In Proceedings of the fourteenth annual ACMSIAM symposium on Discrete algorithms
, 2003
"... Dear Professors: I would like to submit this paper to FOCS'02 for your consideration for publication. This paper presents a parallel selection result which closes this problem. As final result on an important problem is usually highly evaluated, I urge your support of this result. Your suport will b ..."
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Dear Professors: I would like to submit this paper to FOCS'02 for your consideration for publication. This paper presents a parallel selection result which closes this problem. As final result on an important problem is usually highly evaluated, I urge your support of this result. Your suport will be very much appreciated.
Hashing Strategies for Simulating Shared Memory on Distributed Memory Machines
, 1992
"... . We survey shared memory simulations on distributed memory machines (DMMs), that use universal hashing to distribute the shared memory cells over the memory modules of the DMM. We measure their quality in terms of delay, timeprocessor efficiency, memory contention (how many requests have to be sat ..."
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. We survey shared memory simulations on distributed memory machines (DMMs), that use universal hashing to distribute the shared memory cells over the memory modules of the DMM. We measure their quality in terms of delay, timeprocessor efficiency, memory contention (how many requests have to be satisfied by one memory module per simulated step) and simplicity. Further we take into consideration different access conflict rules to the modules of the DMM, in particular the cCollision rule motivated by the idea of communicating between processors and modules using an optical crossbar. It turns out that simulations with very small delay require more than one hash function. Further, simple simulations on DMMs with the cCollision rule are only known if more than one hash function is allowed. 1 Introduction Parallel machines that communicate via a shared memory, so called parallel random access machines (PRAMs) represent the most powerful parallel computation model considered in the theor...
Arne Andersson
"... We show that a unitcost RAM with a word length of w bits can sort n integers in the range 0 : : 2 w \Gamma 1 in O(n log log n) time, for arbitrary w log n, a significant improvement over the bound of O(n p log n) achieved by the fusion trees of Fredman and Willard. Provided that w (log n) 2+ ..."
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We show that a unitcost RAM with a word length of w bits can sort n integers in the range 0 : : 2 w \Gamma 1 in O(n log log n) time, for arbitrary w log n, a significant improvement over the bound of O(n p log n) achieved by the fusion trees of Fredman and Willard. Provided that w (log n) 2+ffl for some fixed ffl ? 0, the sorting can even be accomplished in linear expected time with a randomized algorithm. Both of our algorithms parallelize without loss on a unitcost PRAM with a word length of w bits. The first one yields an algorithm that uses O(log n) time and O(n log log n) operations on a deterministic CRCW PRAM. The second one yields an algorithm that uses O(log n) expected time and O(n) expected operations on a randomized EREW PRAM, provided that w (log n) 2+ffl for some fixed ffl ? 0. Our deterministic and randomized sequential and parallel algorithms generalize to the lexicographic sorting problem of sorting multipleprecision integers represented in several words...