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Partitioning Posets

13 years 3 months ago
Partitioning Posets
Given a poset P = (X, ), a partition X1, . . . , Xk of X is called an ordered partition of P if, whenever x Xi and y Xj with x y, then i j. In this paper, we show that for every poset P = (X, ) and every integer k 2, there exists an ordered partition of P into k parts such that the total number of comparable pairs within the parts is at most (m - 1)/k, where m 1 is the total number of edges in the comparability graph of P. We show that this bound is best possible for k = 2, but we give an improved bound, m/k - c(k) m, for k 3, where c(k) is a constant depending only on k. We also show that, given a poset P = (X, ), we can find an ordered partition of P that minimises the total number of comparable pairs within parts in polynomial time. We prove more general, weighted versions of these results.
Viresh Patel
Added 14 Dec 2010
Updated 14 Dec 2010
Type Journal
Year 2008
Where ORDER
Authors Viresh Patel
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