Abstract
We investigate the problem of finding a total order of a finite set that satisfies various local ordering constraints. Depending on the admitted constraints, we provide an efficient algorithm or prove NP-completeness. We discuss several generalisations and systematically classify the problems.
Please use the following format when citing this chapter: Guttmann, W., Maucher, M., 2006, in International Federation for Information Processing, Volume 209, Fourth IFIP International Conference on Theoretical Computer Science-TCS 2006, eds. Navarro, G., Bertossi, L., Kohayakwa, Y., (Boston: Springer). pp. 77–90.
Chapter PDF
Similar content being viewed by others
Key words
References
M.R. Garey and D.S. Johnson. Computers and Intractability. W.H. Freeman and Company, 1979.
J. Opatrny. Total ordering problem. SIAM Journal on Computing, 8(1):111–114, February 1979.
B. Chor and M. Sudan. A geometric approach to betweenness. SIAM Journal on Discrete Mathematics, 11 (4):511–523, November 1998.
Z. Galil and N. Megiddo. Cyclic ordering is NP-complete. Theoretical Computer Science, 5(2):179–182, October 1977.
A. Isli and A.G. Cohn. A new approach to cyclic ordering of 2D orientations using ternary relation algebras. Artificial Intelligence, 122(1–2):137–187, September 2000.
D.E. Knuth. Fundamental Algorithms, volume 1 of The Art of Computer Programming. Addison-Wesley, third edition, 1997.
W. Guttmann and M. Maucher. Constrained ordering. Technical Report UIB-2005-03, Universität Ulm, December 2005.
Object Management Group, http://www.omg.org/. UML 2.0 Superstructure Specification, August 2005.
M. Fowler. Patterns of Enterprise Application Architecture. Addison-Wesley, 2002.
J.F. Allen. Maintaining knowledge about temporal intervals. Communications of the ACM, 26(11):832–843, November 1983.
B. Nebel and H.-J. Bürckert. Reasoning about temporal relations: A maximal tractable subclass of Allen’s interval algebra. Journal of the ACM, 42(1):43–66, January 1995.
A. Krokhin, P. Jeavons, and P. Jonsson. Reasoning about temporal relations: The tractable subalgebras of Allen’s interval algebra. Journal of the A CM, 50(5):591–640, September 2003.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 International Federation for Information Processing
About this paper
Cite this paper
Guttmann, W., Maucher, M. (2006). Variations on an Ordering Theme with Constraints. In: Navarro, G., Bertossi, L., Kohayakawa, Y. (eds) Fourth IFIP International Conference on Theoretical Computer Science- TCS 2006. IFIP International Federation for Information Processing, vol 209. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-34735-6_10
Download citation
DOI: https://doi.org/10.1007/978-0-387-34735-6_10
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-34633-5
Online ISBN: 978-0-387-34735-6
eBook Packages: Computer ScienceComputer Science (R0)