Abstract
In this paper we show how the problem of computing the irregularity strength of a graph can be expressed in terms of CP(FD) programming methodology and solved by parallel computations in the Mozart system. We formulate this problem as an optimization task and apply the branch-and-bound method and iterative best-solution search in order to solve it. Both of these approaches have been evaluated in experiments. We also estimate the speedup obtained by parallel processing.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Apt, K.R.: Principles of Constraint Programming. Cambridge University Press, Cambridge (2003)
Aigner, M., Triesch, E.: Irregular assignments of trees and forests. SIAM J. Discrete Math. 3(4), 439–449 (1990)
Chartrand, G., Jacobson, M.S., Lehel, J., Oellermann, O.R., Ruiz, S., Saba, F.: Irregular networks. Congressus Numerantium 64, 187–192 (1988)
Meissner, A., Zwierzyński, K.: Vertex-magic Total labeling of a Graph by Distributed Constraint Solving in the Mozart System. In: Wyrzykowski, R., Dongarra, J., Meyer, N., Waśniewski, J. (eds.) PPAM 2005. LNCS, vol. 3911, pp. 952–959. Springer, Heidelberg (2006)
Meissner, A., Niwińska, M.A., Zwierzyński, K.: Computing an irregularity strength of selected graphs. El. Notes in Discrete Mathematics 24, 137–144 (2006)
Schulte, Ch.: Programming Constraint Services, PhD thesis. University of Saarlandes (2000)
Smolka, G.: The Oz Programming Model. In: van Leeuwen, J. (ed.) Computer Science Today. LNCS, vol. 1000, pp. 324–343. Springer, Heidelberg (1995)
The Mozart Programming System (2004), http://www.mozart-oz.org
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Meissner, A., Niwińska, M., Zwierzyński, K. (2008). Computing the Irregularity Strength of Connected Graphs by Parallel Constraint Solving in the Mozart System. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Wasniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2007. Lecture Notes in Computer Science, vol 4967. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68111-3_116
Download citation
DOI: https://doi.org/10.1007/978-3-540-68111-3_116
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-68105-2
Online ISBN: 978-3-540-68111-3
eBook Packages: Computer ScienceComputer Science (R0)