A tabu search approach to the jump number problem
We consider algorithmics for the jump numberproblem, which is to generate a linear extension of a given poset,minimizing the number of incomparable adjacent pairs. Since thisproblem is NP-hard on interval orders and open on two-dimensionalposets, approximation algorithms or fast exact algorithms are...
Збережено в:
| Дата: | 2015 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2015
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/158002 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | A tabu search approach to the jump number problem / P. Krysztowiak, M.M. Sysło // Algebra and Discrete Mathematics. — 2015. — Vol. 20, № 1. — С. 89–114. — Бібліогр.: 28 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | We consider algorithmics for the jump numberproblem, which is to generate a linear extension of a given poset,minimizing the number of incomparable adjacent pairs. Since thisproblem is NP-hard on interval orders and open on two-dimensionalposets, approximation algorithms or fast exact algorithms are indemand.In this paper, succeeding from the work of the second namedauthor on semi-strongly greedy linear extensions, we develop ametaheuristic algorithm to approximate the jump number with thetabu search paradigm. To benchmark the proposed procedure, weinfer from the previous work of Mitas [Order 8 (1991), 115–132] anew fast exact algorithm for the case of interval orders, and from theresults of Ceroi [Order 20 (2003), 1–11] a lower bound for the jumpnumber of two-dimensional posets. Moreover, by other techniqueswe prove an approximation ratio ofn/log lognfor 2D orders. |
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