Luc Longpré

Computing variance for interval data is NP-hard

When we have only interval ranges [<i>x<inf>i</inf>,</i> <i>x<inf>i</inf></i>] of sample values <i>x</i><inf>1</inf>,…, <i>x<inf>n</inf>,</i> what is the interval [<i>V, V</i>] of possible values for the variance <i>V</i> of these values? We prove that the problem of computing the upper bound <i>V</i> is NP-hard. We provide a feasible (quadratic time) algorithm for computing the lower bound <i>V</i> on the variance of interval data. We also provide a feasible algorithm that computes <i>V</i> under reasonable easily verifiable conditions.

Exact Bounds on Finite Populations of Interval Data

In this paper, we start research into using intervals to bound the impact of bounded measurement errors on the computation of bounds on finite population parameters (“descriptive statistics”). Specifically, we provide a feasible (quadratic time) algorithm for computing the lower bound

Outlier detection under interval uncertainty : Algorithmic solvability and computational complexity

\underline{\sigma^2}

New algorithms for statistical analysis of interval data

on the finite population variance function of interval data. We prove that the problem of computing the upper bound

The Temporal Precedence Problem

\bar{\sigma}^2

Eliminating Duplicates under Interval and Fuzzy Uncertainty: An Asymptotically Optimal Algorithm and Its Geospatial Applications

is, in general, NP-hard. We provide a feasible algorithm that computes