@inproceedings{5a5c706f1ab44169b7f9f4b4c06995e9,

title = "On the variance of subset sum estimation",

abstract = "For high volume data streams and large data warehouses, sampling is used for efficient approximate answers to aggregate queries over selected subsets. We are dealing with a possibly heavy-tailed set of weighted items. We address the question: Which sampling scheme should we use to get the most accurate subset sum estimates? We present a simple theorem on the variance of subset sum estimation and use it to prove optimality and near-optimality of different known sampling schemes. The performance measure suggested in this paper is the average variance over all subsets of any given size. By optimal we mean there is no set of input weights for which any sampling scheme can have a better average variance. For example, we show that appropriately weighted systematic sampling is simultaneously optimal for all subset sizes. More standard schemes such as uniform sampling and probability-proportional-to-size sampling with replacement can be arbitrarily bad. Knowing the variance optimality of different sampling schemes can help deciding which sampling scheme to apply in a given context.",

author = "Mario Szegedy and Mikkel Thorup",

year = "2007",

doi = "10.1007/978-3-540-75520-3_9",

language = "English (US)",

isbn = "9783540755197",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "75--86",

booktitle = "Algorithms - ESA 2007 - 15th Annual European Symposium, Proceedings",

address = "Germany",

note = "15th Annual European Symposium on Algorithms, ESA 2007 ; Conference date: 08-10-2007 Through 10-10-2007",

}