Approximate medians and other quantiles in one pass and with limited memory
SIGMOD '98 Proceedings of the 1998 ACM SIGMOD international conference on Management of data
SIGMOD '99 Proceedings of the 1999 ACM SIGMOD international conference on Management of data
A Unified Lower Bound for Selection and Set Partitioning Problems
Journal of the ACM (JACM)
New upper bounds for selection
Communications of the ACM
Journal of Computer and System Sciences
An Ω(1/ε log 1/ε) space lower bound for finding ε-approximate quantiles in a data stream
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
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Let V (n) be the minimum number of binary comparisons that are required to determine the i-th largest of n elements drawn from a totally ordered set. In this thesis we use adversary strategies to prove lower bounds on V (n). For i = 3, our lower bounds determine V (n) precisely for infinitely many values of n, and determine V (n) to within 2 for all n. For a general fixed i, our lower bound has the asymptotic form n + (i-1)log n -0(log(log n)) where log n is a very slowly growing function. As a result, the asymptotic behavior of V (n) is determined to within 0(log(log n)). A more general problem is raised in which one wants to find an element which is (i,j)-mediocre, i.e. smaller than at least i elements and greater than at least j elements. For i = 1, it is shown that the best algorithm is to select the i + 1st largest of any subset of i + j + 1 elements. It is an interesting question whether for general i this procedure is also optimal for finding an (i,J)-mediocre element. An affirmative answer to this question would imply V (n) 3n. {PB 230-950/AS}