Fast and Near-Optimal Algorithms for Approximating Distributions by Histograms

Histograms are among the most popular structures for the succinct summarization of data in a variety of database applications. In this work, we provide fast and nearoptimal algorithms for approximating arbitrary one dimensional data distributions by histograms. A k-histogram is a piecewise constant function with k pieces. We consider the following natural problem, previously studied by Indyk, Levi, and Rubinfeld [ILR12] in PODS 2012: Given samples from a distribution p over {1, . . . , n}, compute a k-histogram that minimizes the 2-distance from p, up to an additive ε. We design an algorithm for this problem that uses the information– theoretically minimal sample size of m = O(1/ε2 ), runs in sample–linear time O(m), and outputs an O(k)– histogram whose 2-distance from p is at most O(optk)+ , where optk is the minimum 2-distance between p and any k-histogram. Perhaps surprisingly, the sample size and running time of our algorithm are independent of the universe size n. We gene...

• Type: Journal
• Year: 2015
• Where: PODS
• Authors: Jayadev Acharya, Ilias Diakonikolas, Chinmay Hegde, Jerry Zheng Li, Ludwig Schmidt
• Keywords: Database, PODS 2015