Online Linear Discrepancy of Partially Ordered Sets
نویسندگان
چکیده
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 linear discrepancy of P is k. This inequality is best possible, even for the class of interval orders. Furthermore, if the poset P is a semiorder, then the inequality is improved to |hL(x)− hL(y)| ≤ 2k. Again, this result is best possible.
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