Partitioning a weighted partial order

Linda S. Moonen () and Frits C. R. Spieksma ()
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Linda S. Moonen: Katholieke Universiteit Leuven
Frits C. R. Spieksma: Katholieke Universiteit Leuven

Journal of Combinatorial Optimization, 2008, vol. 15, issue 4, No 3, 342-356

Abstract: Abstract The problem of partitioning a partially ordered set into a minimum number of chains is a well-known problem. In this paper we study a generalization of this problem, where we not only assume that the chains have bounded size, but also that a weight w i is given for each element i in the partial order such that w i ≤w j if i ≺ j. The problem is then to partition the partial order into a minimum-weight set of chains of bounded size, where the weight of a chain equals the weight of the heaviest element in the chain. We prove that this problem is $\mathcal{APX}$ -hard, and we propose and analyze lower bounds for this problem. Based on these lower bounds, we exhibit a 2-approximation algorithm, and show that it is tight. We report computational results for a number of real-world and randomly generated problem instances.

Keywords: Partially ordered sets; Chain decomposition; Approximation algorithms (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/s10878-007-9086-0

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