کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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6423496 | 1342396 | 2011 | 6 صفحه PDF | دانلود رایگان |
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)âhL(y)|â¤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)âhW(y)|â¤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.
Journal: Discrete Mathematics - Volume 311, Issue 4, 28 February 2011, Pages 252-257