A tabu search approach to the jump number problem

We consider algorithmics for the jump number problem, which isto generate a linear extension of a given poset, minimizing the numberof incomparable adjacent pairs. Since this problem is NP-hardon interval orders and open on two-dimensional posets,approximation algorithms orfast exact algorithms are...

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Bibliographic Details
Date:2015
Main Authors: Krysztowiak, Przemysław, Sysło, Maciej M.
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2015
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Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/101
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Journal Title:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
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Summary:We consider algorithmics for the jump number problem, which isto generate a linear extension of a given poset, minimizing the numberof incomparable adjacent pairs. Since this problem is NP-hardon interval orders and open on two-dimensional posets,approximation algorithms orfast exact algorithms are in demand.In this paper, succeeding from the work of the second named author onsemi-strongly greedylinear extensions, we develop a metaheuristic algorithm to approximatethe jump number with the tabu search paradigm. To benchmarkthe proposed procedure, we infer from the previous work of Mitas[Order 8 (1991), 115--132]a new fast exact algorithm for the case ofinterval orders, and from the results of Ceroi[Order 20 (2003), 1--11]a lower boundfor the jump number of two-dimensional posets.Moreover, by other techniques we provean approximation ratio of \(n / \log\log n\) for 2D orders.