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...
Saved in:
| Date: | 2015 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2015
|
| Series: | Algebra and Discrete Mathematics |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/158002 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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. |
|---|