 
Summary: Estimating arbitrary subset sums with few probes
Noga Alon
Nick Duffield
Carsten Lund
Mikkel Thorup
School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel
AT&T LabsResearch, 180 Park Avenue, Florham Park, NJ 07932, USA
nogaa@post.tau.ac.il {duffield,lund,mthorup}@research.att.com
ABSTRACT
Suppose we have a large table T of items i, each with a
weight wi, e.g., people and their salary. In a general prepro
cessing step for estimating arbitrary subset sums, we assign
each item a random priority depending on its weight. Sup
pose we want to estimate the sum of an arbitrary subset
I T. For any q > 2, considering only the q highest pri
ority items from I, we obtain an unbiased estimator of the
sum whose relative standard deviation is O(1/
