Fast Probabilistic Techniques for Dynamic Parallel Addition Parallel Counting a
Fast Probabilistic Techniques for Dynamic Parallel Addition Parallel Counting a
Paul G Spirakis
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En after the m rounds, we call L an m-algorithm for the processor identification problem. (We allow unrestricted local memory per processor. ) An obvious L (which would take 0(n) parallel time) is that consisting of n^i's with €i[j] = 0, jVi and €i(i)= 1 (IrsirSn). Erdos and Renyi [ER, 63] considered a very closely related problem, the "coin-weight" problem. Using their techniques, we show that the m needed is 9(n/logn) and that L is constructive (in fact, there is an easy probabilistic way to ...find L). Let us view L as an mX n matrix of O's and I's. Lemma 2 (see also [ER, 63] ). A matrix L, mXn, of O's and I's is an m- algorithm for the processor identification problem iff: For each pair c, c' of subsets of the set C of columns of L, such that c^^c', if we form the row- sums of the submatrices L(c) and L(c') (consisting of the selected columns) and denote by V^andV*^. The column-vectors, consisting of these row-sums, then ^c^^v Proof sketch: After m-rounds, each processor has a row-sum vector, V, of L.
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