Department

Computer Science, Mathematics

Document Type

Article

Publication Date

4-2011

Abstract

The fractional weak discrepancy wdF(P) of a poset P=(V,≺) was introduced in Shuchat et al. (2007) [6] as the minimum nonnegative k for which there exists a function f:V→R satisfying (i) if a≺b then f(a)+1≤f(b) and (ii) if a∥b then |f(a)−f(b)|≤k. In this paper we generalize results in Shuchat et al. (2006, 2009) [5] and [7] on the range of wdF for semiorders to the larger class of split semiorders. In particular, we prove that for such posets the range is the set of rationals that can be represented as r/s for which 0≤s−1≤r<2s.

Comments

Post-print version, Nov. 8, 2010. Published version in: Discrete Applied Mathematics, 159(7): 647-660 (2011). doi:10.1016/j.dam.2010.04.014

Version

Post-print

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