Global roundings of sequences

Authors:
Benjamin Doerr
Affiliations:
Mathematisches Seminar II, Christian-Albrechts-Universität zu Kiel, 24098 Kiel, Germany
Venue:
Information Processing Letters
Year:
2004

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Abstract

For a given sequence a = (a1,...,an) of numbers, a global rounding is an integer sequence b = (b1,...,bn) such that the rounding error |Σi ∈ I(ai - bi)| is less than one in all intervals I ⊆ {1,...,n}. We give a simple characterization of the set of global roundings of a. This allows to compute optimal roundings in time O(n log n) and generate a global rounding uniformly at random in linear time under a non-degeneracy assumption and in time O(n log n) in the general case.