This paper presents a deterministic sorting algorithm, called Sharesort, that sorts n records on an n processor hypercube, shuffle-exchange or cube-connected cycles in O(log n(log log n) 2 ) time in the worst case. The algorithm requires only a constant amount of storage at each processor. The fastest previous deterministic algorithm for this problem was bitonic sort , which runs in O(log 2 n) time. 1 Introduction Given n records distributed uniformly over the n processors of some fixed interconnection network, the sorting problem is to route the record with the ith largest associated key to processor i, 0 i ! n. One of the earliest parallel sorting algorithms is Batcher's bitonic sort , which runs in O(log 2 n) time on the hypercube, shuffle-exchange (SE)  and cube-connected cycles (CCC) . More recently, Leighton  exhibited a bounded-degree, O(log n) time sorting network based on the O(logn) depth sorting circuit of Ajtai, Koml'os and Szemer'edi . Howe..
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