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Abstract

Counting in general, and estimating the cardinality of (multi-) sets in particular, is highly desirable for a large variety of applications, representing a foundational block for the efficient deployment and access of emerging internetscale information systems. Examples of such applications range from optimizing query access plans in internet-scale databases, to evaluating the significance (rank/score) of various data items in information retrieval applications. The key constraints that any acceptable solution must satisfy are: (i) efficiency: the number of nodes that need be contacted for counting purposes must be small in order to enjoy small latency and bandwidth requirements; (ii) scalability, seemingly contradicting the efficiency goal: arbitrarily large numbers of nodes nay need to add elements to a (multi-) set, which dictates the need for a highly distributed solution, avoiding server-based scalability, bottleneck, and availability problems; (iii) access and storage load balancing: counting and related overhead chores should be distributed fairly to the nodes of the network; (iv) accuracy: tunable, robust (in the presence of dynamics and failures) and highly accurate cardinality estimation; (v) simplicity and ease of integration: special, solution-specific indexing structures should be avoided. In this paper, first we contribute a highly-distributed, scalable, efficient, and accurate (multi-) set cardinality estimator. Subsequently, we show how to use our solution to build and maintain histograms, which have been a basic building block for query optimization for centralized databases, facilitating their porting into the realm of internet-scale data networks.