Abstract
We introduce a parallelized version of tree-decomposition based dynamic programming for solving difficult weighted CSP instances on many cores. A tree decomposition organizes cost functions in a tree of collection of functions called clusters. By processing the tree from the leaves up to the root, we solve each cluster concurrently, for each assignment of its separator, using a state-of-the-art exact sequential algorithm. The grain of parallelism obtained in this way is directly related to the tree decomposition used. We use a dedicated strategy for building suitable decompositions.
We present preliminary results of our prototype running on a cluster with hundreds of cores on different decomposable real problems. This implementation allowed us to solve the last open CELAR radio link frequency assignment instance to optimality.
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.
References
Bertelé, U., Brioshi, F.: Nonserial Dynamic Programming. Academic Press, London (1972)
Cabon, B., de Givry, S., Lobjois, L., Schiex, T., Warners, J.: Radio link frequency assignment. Constraints 4, 79–89 (1999)
Dechter, R.: Bucket elimination: A unifying framework for reasoning. Artificial Intelligence 113(1-2), 41–85 (1999)
Dechter, R., Pearl, J.: Tree clustering for constraint networks. Artificial Intelligence 38, 353–366 (1989)
Kask, K., Dechter, R., Larrosa, J., Dechter, A.: Unifying Cluster-Tree Decompositions for Reasoning in Graphical models. Artificial Intelligence 166(1-2), 165–193 (2005)
Larrosa, J., de Givry, S., Heras, F., Zytnicki, M.: Existential arc consistency: getting closer to full arc consistency in weighted CSPs. In: Proc. of the 19th IJCAI, Edinburgh, Scotland, pp. 84–89 (August 2005)
Lauritzen, S., Spiegelhalter, D.: Local computations with probabilities on graphical structures and their application to expert systems. Journal of the Royal Statistical Society – Series B 50, 157–224 (1988)
Lecoutre, C., Saïs, L., Tabary, S., Vidal, V.: Reasoning from last conflict(s) in constraint programming. Artificial Intelligence 173, 1592–1614 (2009)
Otten, L., Dechter, R.: Towards parallel search for optimization in graphical models. In: Proc. of ISAIM 2010. Fort Lauderdale (FL), USA (2010)
Rose, D.: Tringulated graphs and the elimination process. Journal of Mathematical Analysis and its Applications 32 (1970)
Sanchez, M., Allouche, D., de Givry, S., Schiex, T.: Russian doll search with tree decomposition. In: Proc. IJCAI 2009, San Diego, CA, USA, pp. 603–608 (2009)
Schiex, T., Fargier, H., Verfaillie, G.: Valued constraint satisfaction problems: hard and easy problems. In: Proc. of the 14th IJCAI, Montréal, Canada, pp. 631–637 (August 1995)
Xia, Y., Prasanna, V.: Parallel Exact Inference. In: Bischof, C., Bücker, M., Gibbon, P. (eds.) Parallel Computing 2007. NIC, vol. 38, pp. 185–192. John von Neumann Institute for Computing (September 2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Allouche, D., de Givry, S., Schiex, T. (2010). Towards Parallel Non Serial Dynamic Programming for Solving Hard Weighted CSP. In: Cohen, D. (eds) Principles and Practice of Constraint Programming – CP 2010. CP 2010. Lecture Notes in Computer Science, vol 6308. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15396-9_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-15396-9_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15395-2
Online ISBN: 978-3-642-15396-9
eBook Packages: Computer ScienceComputer Science (R0)