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Abstract: We prove that to store n bits x so that each prefix-sum query Sumi :=sum {k < i} x k can be answered by non-adaptively probing q cells of log nbits, one needs memory > n + n-log^{Oq} n. Our bound matches a recent upperbound of n + n-log^{Omegaq} n by Patrascu FOCS 2008, also non-adaptive. Wealso obtain a n + n-log^{2^{Oq}} n lower bound for storing a string ofbalanced brackets so that each Matchi query can be answered by non-adaptivelyprobing q cells. To obtain these bounds we show that a too efficient datastructure allows us to break the correlations between query answers.



Author: Emanuele Viola

Source: https://arxiv.org/



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