Online Sorting via Searching and Selection

In this paper, we present a framework based on a simple data structure and parameterized algorithms for the problems of finding items in an unsorted list of linearly ordered items based on their rank (selection) or value (search). As a side-effect of answering these online selection and search queries, we progressively sort the list. Our algorithms are based on Hoare's Quickselect, and are parameterized based on the pivot selection method. For example, if we choose the pivot as the last item in a subinterval, our framework yields algorithms that will answer q<=n unique selection and/or search queries in a total of O(n log q) average time. After q=\Omega(n) queries the list is sorted. Each repeated selection query takes constant time, and each repeated search query takes O(log n) time. The two query types can be interleaved freely. By plugging different pivot selection methods into our framework, these results can, for example, become randomized expected time or deterministic worst-case time. Our methods are easy to implement, and we show they perform well in practice

Fast computation of trimmed means

We present two methods of calculating trimmed means without sorting the data in O(n) time. The existing method implemented in major statistical packages relies on sorting, which takes O(n log n) time. The proposed algorithm is based on the quickselect algorithm for calculating order statistics with O(n) expected running time. It is an order of magnitude faster than the existing method for large data sets

Comment: Monitoring Networked Applications With Incremental Quantile Estimation

Our comments are in two parts. First, we make some observations regarding the methodology in Chambers et al. [arXiv:0708.0302]. Second, we briefly describe another interesting network monitoring problem that arises in the context of assessing quality of service, such as loss rates and delay distributions, in packet-switched networks.Comment: Published at http://dx.doi.org/10.1214/088342306000000600 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org