Abstract
A linear extension problem is defined as follows: Given a poset P=(E,≤), we want to find a linear order L such that x≤y in L whenever x≤yin P. In this paper, we assign each pair of elements x,y∈E with a cost, and to find a linear extension of P with the minimum sum cost. For the general case, it is NP-complete and we present a greedy approximation algorithm which can be finished in polynomial time. Also we consider a special case which can be solved in polynomial time.
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This research is supported by National Nature Science Foundation of China (grant 10671177) and Zhejiang Provincial Natural Science Foundation of China (Y607079).
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Liu, L., Wu, B. & Yao, E. Minimizing the sum cost in linear extensions of a poset. J Comb Optim 21, 247–253 (2011). https://doi.org/10.1007/s10878-009-9237-6
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DOI: https://doi.org/10.1007/s10878-009-9237-6