TR09-054 Authors: Emanuele Viola, Emanuele Viola

Publication: 2nd July 2009 11:20

Downloads: 1613

Keywords:

We prove that to store n bits x so that each

prefix-sum query Sum(i) := sum_{k < i} x_k can be answered

by non-adaptively probing q cells of log n bits, one needs

memory > n + n/log^{O(q)} n.

Our bound matches a recent upper bound of n +

n/log^{Omega(q)} n by Patrascu (FOCS 2008), also

non-adaptive.

We also obtain a n + n/log^{2^{O(q)}} n lower bound for

storing a string of balanced brackets so that each

Match(i) query can be answered by non-adaptively probing q

cells. To obtain these bounds we show that a too efficient

data structure allows us to break the correlations between

query answers.