We show that several versions of Floyd and Rivest’s improved algorithm Select for finding the kth smallest of n elements require at most n + min{k, n − k} + O(n1/2 ln n) comparisons on average and with high probability. This rectifies the analysis of Floyd and Rivest, and extends it to the case of nondistinct elements. Encouraging computational results on large median-finding problems are repor...

In this paper we address the problem of estimating the number of stations in a wireless network. Under the assumption that each station can detect collisions, we show that it is possible to estimate the number stations in the network within a factor 2 from the correct value in time O(log n log log n). We further show that if no station can detect collisions, the same task can be accomplished wi...

Consider an election between k candidates in which each voter votes randomly (but not necessarily independently) and suppose that there is a single candidate that every voter prefers (in the sense that each voter is more likely to vote for this special candidate than any other candidate). Suppose we have a voting rule that takes all of the votes and produces a single outcome and suppose that ea...

Let p be an unknown and arbitrary probability distribution over [0, 1). We consider the problem of density estimation, in which a learning algorithm is given i.i.d. draws from p and must (with high probability) output a hypothesis distribution that is close to p. The main contribution of this paper is a highly efficient density estimation algorithm for learning using a variable-width histogram,...