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Order statistics and estimating cardinalities of massive data sets

Frédéric Giroire 1 
1 MASCOTTE - Algorithms, simulation, combinatorics and optimization for telecommunications
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
Abstract : A new class of algorithms to estimate the cardinality of very large multisets using constant memory and doing only one pass on the data is introduced here. It is based on order statistics rather than on bit patterns in binary representations of numbers. Three families of estimators are analyzed. They attain a standard error of using M units of storage, which places them in the same class as the best known algorithms so far. The algorithms have a very simple internal loop, which gives them an advantage in terms of processing speed. For instance, a memory of only 12 kB and only few seconds are sufficient to process a multiset with several million elements and to build an estimate with accuracy of order 2 percent. The algorithms are validated both by mathematical analysis and by experimentations on real internet traffic., OPTx-editorial-board=yes, OPTx-proceedings=yes, OPTx-international-audience=yes.
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Submitted on : Tuesday, November 29, 2011 - 11:37:07 AM
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  • HAL Id : hal-00646123, version 1



Frédéric Giroire. Order statistics and estimating cardinalities of massive data sets. Discrete Applied Mathematics, 2009, 157 (2), pp.406-427. ⟨hal-00646123⟩



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