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We obtain the following results: (1) this problem is NP-hard in a strong sense, and it cannot be approximated within a factor 32−ε in polynomial time for any ε>0; (2) we design three approximation algorithms with different constant factors for this problem; (3) for the version where all intervals have the same weights, we design an optimal algorithm to solve the problem in linear time.
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We believe that the use of -nets can give a better approximation factor for this problem.
Suitable choices of the actions give the first examples of infinite noninjective factors for which this problem has a positive solution.
To elaborate, young age of children, young age of ill parents, low SES of families and long illness duration seem to be risk factors for these problem behaviors.
Still, additional large, prospective studies are needed to confirm our results and also to identify other modifiable prognostic factors for this public health problem.
The best known approximation factor is 3 for this problem (Li et al., 2011).
In this paper, we devise a constant-factor approximation algorithm for this problem based on a random sampling technique.
The best known factor 2 approximation algorithm for this problem runs in O(n2logn) time and takes O(n2) space [1,2].
A simple and practical correction factor cannot be established for this problem because, in a multivariate regression, the standard error for each predictor depends on its correlation with all variables included in the model.
This paper investigates in a quantitative way, how some prominent methods from the literature behave with respect to these critical factors for different problem sizes.
ConclusionsMaternal smoking and cannabis use, early material disadvantage and early-onset persistent conduct problems are important risk factors for adolescent problem cannabis use.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com