RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Algebra Discrete Math.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Algebra Discrete Math., 2015, Volume 20, Issue 1, Pages 89–114 (Mi adm533)  

RESEARCH ARTICLE

A tabu search approach to the jump number problem

Przemysław Krysztowiak, Maciej M. Sysło

Faculty of Mathematics and Computer Science, Nikolaus Copernicus University, Torun

Abstract: 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.

Keywords: graph theory, poset, jump number, combinatorial optimization, tabu search.

Full text: PDF file (542 kB)
References: PDF file   HTML file

Bibliographic databases:
MSC: 90C27, 90C59
Received: 29.11.2013
Revised: 29.11.2013
Language:

Citation: Przemysław Krysztowiak, Maciej M. Sysło, “A tabu search approach to the jump number problem”, Algebra Discrete Math., 20:1 (2015), 89–114

Citation in format AMSBIB
\Bibitem{KrySys15}
\by Przemys\l aw~Krysztowiak, Maciej~M.~Sys\l o
\paper A tabu search approach to the jump number problem
\jour Algebra Discrete Math.
\yr 2015
\vol 20
\issue 1
\pages 89--114
\mathnet{http://mi.mathnet.ru/adm533}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3431953}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000378728700008}


Linking options:
  • http://mi.mathnet.ru/eng/adm533
  • http://mi.mathnet.ru/eng/adm/v20/i1/p89

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Algebra and Discrete Mathematics
    Number of views:
    This page:85
    Full text:50
    References:24

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020