Computing variance for interval data is NP-hard

Authors:
Scott Ferson;Lev Ginzburg;Vladik Kreinovich;Luc Longpré;Monica Aviles
Affiliations:
Applied Biomathematics, Setauket, NY;Applied Biomathematics, Setauket, NY;University of Texas at El Paso, El Paso, TX;University of Texas at El Paso, El Paso, TX;University of Texas at El Paso, El Paso, TX
Venue:
ACM SIGACT News
Year:
2002

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Abstract

When we have only interval ranges [xi, xi] of sample values x1,…, xn, what is the interval [V, V] of possible values for the variance V of these values? We prove that the problem of computing the upper bound V is NP-hard. We provide a feasible (quadratic time) algorithm for computing the lower bound V on the variance of interval data. We also provide a feasible algorithm that computes V under reasonable easily verifiable conditions.