A tabu search approach to the jump number problem

• Datum: 2015
• Hauptverfasser: Krysztowiak, P., Sysło, M.M.
• Format: Artikel
• Sprache: English
• Veröffentlicht: Інститут прикладної математики і механіки НАН України 2015
• Schriftenreihe: Algebra and Discrete Mathematics
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/154747
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: A tabu search approach to the jump number problem / P. Krysztowiak, M.M. Sysło // Algebra and Discrete Mathematics. — 2015. — Vol. 19, № 2. — С. 89-114 . — Бібліогр.: 28 назв. — англ.

We consider algorithmics for the jump number problem, which is to generate a linear extension of a given poset, minimizing the number of incomparable adjacent pairs. Since this problem is NP-hard on interval orders and open on two-dimensional posets, approximation algorithms or fast exact algorithms are in demand. In this paper, succeeding from the work of the second named author on semi-strongly greedy linear extensions, we develop a metaheuristic algorithm to approximate the jump number with the tabu search paradigm. To benchmark the proposed procedure, we infer from the previous work of Mitas [Order 8 (1991), 115--132] a new fast exact algorithm for the case of interval orders, and from the results of Ceroi [Order 20 (2003), 1--11] a lower bound for the jump number of two-dimensional posets. Moreover, by other techniques we prove an approximation ratio of n/ log(log(n)) for 2D orders.