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

 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
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}