The fractional weak discrepancy of a partially ordered set
نویسندگان
چکیده
منابع مشابه
The fractional weak discrepancy of a partially ordered set
In this paper we introduce the notion of the fractional weak discrepancy of a poset, building on previous work on weak discrepancy in [5, 8, 9]. The fractional weak discrepancy wdF (P ) of a poset P = (V,≺) is the minimum nonnegative k for which there exists a function f : V → R satisfying (1) if a ≺ b then f(a) + 1 ≤ f(b) and (2) if a ‖ b then |f(a)− f(b)| ≤ k. We formulate the fractional weak...
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We define the total weak discrepancy of a poset P as the minimum nonnegative integer k for which there exists a function f : V → Z satisfying (i) if a ≺ b then f(a) + 1 ≤ f(b) and (ii) ∑ |f(a)− f(b)| ≤ k, where the sum is taken over all unordered pairs {a, b} of incomparable elements. If we allow k and f to take real values, we call the minimum k the fractional total weak discrepancy of P . The...
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In this paper we describe the range of values that can be taken by the fractional weak discrepancy of a poset and characterize semiorders in terms of these values. In [6], we defined the fractional weak discrepancy wdF (P ) of a poset P = (V,≺) to be the minimum nonnegative k for which there exists a function f : V → R satisfying (1) if a ≺ b then f(a) + 1 ≤ f(b) and (2) if a ‖ b then |f(a) − f...
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The linear discrepancy of a poset P is the least k for which there is a linear extension L of P such that if x and y are incomparable in P, then |hL(x) − hL(y)| ≤ k, where hL(x) is the height of x in L. In this paper, we consider linear discrepancy in an online setting and devise an online algorithm that constructs a linear extension L of a poset P so that |hL(x) − hL(y)| ≤ 3k − 1, when the lin...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2007
ISSN: 0166-218X
DOI: 10.1016/j.dam.2007.05.032