We show that a unit-cost RAM with a word length of w bits can sort n integers in the range 0 : : 2 w \Gamma1 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 unit-cost PRAM with a word length of w bits. The first one yields an algorithm that uses O(logn) 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 multiple-precision integers represented in several words. ...

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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, time-processor 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 c-Collision 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 c-Collision 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...

We show that a unit-cost 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 unit-cost 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 multiple-precision integers represented in several words...