When Linear and Weak Discrepancy are Equal
BibTeX
@MISC{B_whenlinear,
author = {David M. Howard B and Stephen J. Young B and Stephen J. Young and David M. Howard B and Stephen J. Young B},
title = {When Linear and Weak Discrepancy are Equal},
year = {}
}
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Abstract
The linear discrepancy of a poset P is the least k such that there is a linear extension L of P such that if x and y are incomparable, then |hL(x) − hL(y) | ≤ k. Whereas the weak discrepancy is the least k such that there is a weak extension W of P such that if x and y are incomparable, then |hW (x) − hW (y) | ≤ k. This paper resolves a question of Tanenbaum, Trenk, and Fishburn on characterizing when the weak and linear discrepancy of a poset are equal. Although it is shown that determining whether a poset has equal weak and linear discrepancy is NP-complete, this paper provides a complete characterization of the minimal posets with equal weak and linear discrepancy. Further, these minimal posets can be completely described as a family of interval orders.
Citations
| 36 | Intransitive indifference with unequal indifference intervals - Fishburn - 1970 |
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| 7 | Irreducible posets of linear discrepancy 1 and 2 - Chae, Cheong, et al. - 2006 |
| 7 | On the weakness of an ordered set - Gimbel, Trenk - 1998 |
| 7 | A characterization of partially ordered sets with linear discrepancy equal to 2 - Howard, Keller, et al. |
| 5 | Irreducible width 2 posets of linear discrepancy 3 - Howard, Chae, et al. |
| 5 | The fractional weak discrepancy of a partially ordered set - Shuchat, Shull, et al. - 2007 |
| 3 | Linear discrepancy and bandwidth, Order 18 (3 - Fishburn, Tanenbaum, et al. - 2001 |
| 3 | Can transitive orientation make sandwich problems easier? Disc - Habib, Kelly, et al. |
| 2 | Forbidden subposets for fractional weak discrepancy at most k - Choi, West |
