Minimizing the sum cost in linear extensions of a poset

Minimizing the sum cost in linear extensions of a poset

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Article ID: iaor20111956
Volume: 21
Issue: 2
Start Page Number: 247
End Page Number: 253
Publication Date: Feb 2011
Journal: Journal of Combinatorial Optimization
Authors: , ,
Keywords: greedy algorithms, NP-complete, axioms
Abstract:

A linear extension problem is defined as follows: Given a poset P=(E,≤), we want to find a linear order L such that xy in L whenever xyin P. In this paper, we assign each pair of elements x,yE 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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