Greedy online histograms applied to deterministic sampling

Motivated by quantizing a continuous distribution for the purpose of sampling, we develop a new cost function for histograms and give two algorithms which approximate the optimal cost. Our algorithms are greedy and have optimality guarantees. The second is an adaption of the first in the context of data streams. In this context, we show that the histogram becomes stable fast, in any case; in addition, convergence is much faster under a hypothesis of random order of arrival. To our knowledge, this has not been studied for classical types of histograms. Our experimental results confirm these results in practice and quantify the good behavior of our histogram algorithms, for both our new cost function, and formerly studied cost functions.