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A lower bound for linear approximate compaction
The {\em -approximate compaction} problem is: given an input array of values, each either 0 or 1, place each value in an output array so that all the 1's are in the first array locations, where is the number of 1's in the input. is an accuracy parameter. This problem is of fundamental importance in parallel computation because of its applications to processor allocation and approximate counting. When is a constant, the problem is called {\em Linear Approximate Compaction} (LAC). On the CRCW PRAM model, %there is an algorithm that solves approximate compaction in \order{(\log\log n)^3} time for , using processors. Our main result shows that this is close to the best possible. Specifically, we prove that LAC requires % time using \order{n} processors. We also give a tradeoff between and the processing time. For , and , the time required is