Optimal Vlsi Circuits for Sorting

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Optimal Vlsi Circuits for Sorting
Richard Cole
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A white marker represents one number and stores the logR/X least significant bits of the number. A white marker has a header bit of 1 to distinguish it from a black marker; its length is thus 1 + logR/X. Again, the numbers are stored in sorted order using these markers. Such a representation takes 0(X\og2R/X) bits.
For R^X, a black marker indicates an increment by one. It is convenient to use a as a header for such a marker as before, but we also reserve logX/R additional bits for use as specif
...ied below. A white marker (1) is bit-sized, and represents X/R instances of a value, rather than just a single instance as before. Thus the number of white markers between two black markers indicate how many multiples of X/R instances of a specific value appear in the data. The number of additional instances of the value is stored in the \ogX/R bits of the black marker following that value. The resulting sequence has bit length 0(Rlog2X/R).
When sorting, it will be convenient to store these encodings in several sequences (packets), each of length 0(T).


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