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A Geometric Parallel Search Problem Related to Group Testing

Zoltan Firedi 1,2, Nathan Linial3
1Mathematical Institute of the Hungarian Academy of Sciences, P,0, B. 127, Budapest 1364 Hungary
2Department of Mathematics University of Illinois Urbana, IL 61801, USA
3Hebrew University of Jerusalem

Abstract

Given \(n\) real numbers whose sum is zero, find one of the numbers that is non-negative. In the model under consideration, an algorithm is allowed to compute \(p\) linear forms in each time step until it knows an answer. We prove that exactly \(\lceil{\log n}/{\log(p+1)} \rceil\) time steps are required. Some connections with parallel group-testing problems are pointed out.