Input Sensitive Optimal Parallel Randomized Algorithms for Addition And Identif

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Input Sensitive Optimal Parallel Randomized Algorithms for Addition And Identif
Paul G Spirakis
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We give tne algorithm in two parts : Procedure ADDITION (m') actually performs the addition, assuming an estimate m'= cm +d, (c, d > 1 constants) known. Function ESTIMATION produces such an estimate. So, the whole algorithm has the following high level description : begin m' ^ ESTIMATION ADDITION (m') end We provide the description of ESTIMATION first. In ESTIMATION, each Pi with x-^'o produces k estimates of m (k is a constant) through a probabilistic technique, and then does a variance-reduct...ion process to get the final estimate. The actual . /. . -4- value of k is determined in the analysis. Function ESTIMATION procedure PRODUCE -AN -ESTIMATE begin stage 1 (Initialization) Processor P, initializes a special shared memory location (CLOCK) to zero. Them, each P. Executes TIME. -6- o. 1 stage 2 (Estimate) Processor P. 1 if X. ^ o then begin (1) Flip a fair coin (two-sided) (2) If the autcome is 'tail 'then begin (2a) TIME^- : -r-TIMEj +1 (2b) CLOCK . 1. The rest is a relatively easy calculation, since Prob [ CLOCK o, if we choose k ^ 4/6 then, with probability at least 1-5, we have (1) iE - logml ^ 2 and (2) The total running time of ESTIMATION is 4 ( -5- .

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