Finding N bits using O(N/logN) sums

Abstract

The problem we are trying to solve sounds as follows: You are given N bits.Find the value of each bit. We will show a technique which enables finding the values of N bits using O(N/logN) subsequence-sum queries. The algorithm consists of two phases: Constructing the queries for each layer and using the queries for a particular layer to getthe value of every bit. We described the following technique in this blog [1], which wasinspired by this article [2]. It should be noted that this number of queries is indeed theoptimal one for finding all N bits of a binary array, since each subsequence-sum queriesoffers us at most log(2)N bits of information.