Minimizing the sum cost in linear extensions of a poset

Longcheng Liu (), Biao Wu and Enyu Yao
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Longcheng Liu: Xiamen University
Biao Wu: Zhejiang University
Enyu Yao: Zhejiang University

Journal of Combinatorial Optimization, 2011, vol. 21, issue 2, No 6, 247-253

Abstract: 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.

Keywords: Partially ordered set; Linear extension; Polynomial algorithm; Approximation (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10878-009-9237-6

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