Abstract
We present a general step-by-step extending approach to parallel execution of enumeration of combinatorial objects (ECO). The methodology extends a famous enumeration algorithm, OrderlyGeneration, which allows concurrently generating all objects of size nā+ā1 from all objects of size n. To the best of our knowledge, this is the first time there is an attempt to plug parallel computing into OrderlyGeneration algorithm for ECO problem. The potential impact of this general approach could be applied for many different servants of ECO problem on scientific computing areas in the future. Our work has applied this strategy to enumerate Orthogonal Array (OA) of strength t, a typical kind of combinatorial objects by using a implementation with MPI paradigm. Several initial results in relation to speedup time of the implementation have been analyzed and given significant efficiency of the proposed approach.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Avis, D., Fukuda, K.: Reverse search for enumeration. Discrete Applied MathematicsĀ 65, 21ā46 (1993)
Agrawal, R., Srikant, R.: Fast algorithms for mining association rules. In: APriori, pp. 487ā499 (1994)
Brinkmann, G., Caporossi, G., Hansen, P.: A survey and new results on computer enumeration of polyhex and fusene hydrocarbons. Journal of Chemical Information and Computer SciencesĀ 43(3), 842ā851 (2003)
Berenbrink, P., Friedetzky, T.: The natural work-stealing algorithm is stable. In: FOCS 2001: Proceedings of the 42nd IEEE symposium on Foundations of Computer Science, Washington, DC, USA, p. 178. IEEE Computer Society, Los Alamitos (2001)
Chen, Y., Crippen, G.M.: A novel approach to structural alignment using realistic structural and environmental information. Protein ScienceĀ 14(12), 2935ā2946 (2005)
Dinan, J., Larkins, D.B., Sadayappan, P., Krishnamoorthy, S., Nieplocha, J.: Scalable work stealing. In: SC 2009: Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis, pp. 1ā11. ACM, New York (2009)
Faradzev, I.A.: Constructive enumeration of combinatorial objects. problemes combinatoires et theorie des graphes collogue interat. CNRSĀ 260, 131ā135 (1978)
Grner, T., Laue, R., Meringer, M., Bayreuth, U.: Algorithms for group actions: Homomorphism principle and orderly generation applied to graphs. In: DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pp. 113ā122. American Mathematical Society, Providence (1996)
Kumar, V., Grama, A.Y., Rao, V.N.: Scalable load balancing techniques for parallel computers. Journal of Parallel and Distributed computing, 60ā79 (1994)
Kaski, P., Ostergard, P.R.J.: Classification algorithms for codes and designs. Algorithms and Computation in MathematicsĀ 15 (2006)
Khosrovshahi, G.B., Tayfeh-Rezaie, B.: Classification of simple 2-(11,3,3) designs. Discrete MathematicsĀ 309(3), 515ā520 (2009); International Workshop on Design Theory, Graph Theory, and Computational Methods - IPM Combinatorics II, International Workshop on Design Theory, Graph Theory, and Computational Methods
Lazic, L., Mastorakis, N.: Orthogonal array application for optimal combination of software defect detection techniques choices. W. Trans. on Comp.Ā 7(8), 1319ā1336 (2008)
Lee, K.-H., Yi, J.-W., Park, J.-S., Park, G.-J.: An optimization algorithm using orthogonal arrays in discrete design space for structures. Finite Elements in Analysis and DesignĀ 40(1), 121ā135 (2003)
McKay, B.D.: Isomorph-free exhaustive generation. J. AlgorithmsĀ 26(2), 306ā324 (1998)
Message-Passing Interface Forum. MPI-2.0: Extensions to the Message-Passing Interface, ch. 9. MPI Forum (June 1997)
Moura, L., Stojmenovic, I.: Backtracking and isomorph-free generation of polyhexes. In: Nayak, A., Stojmenovic, I. (eds.) Handbook of Applied Algorithms: Solving Scientic, Engineering, and Practical Problems, pp. 39ā83. John Wiley & Sons, Chichester (2008)
Nguyen, M.: Computer-algebraic methods for the construction of designs of experiments. Ph.D. Thesis, Technische Universiteit Eindhoven (2005)
Nguyen, M.V.M.: Some new constructions of strength 3 mixed orthogonal arrays. Journal of Statistical Planning and InferenceĀ 138(1), 220ā233 (2008)
Park, B.-H., Samatova, N.F., Karpinets, T., Jallouk, A., Molony, S., Horton, S., Arcangeli, S.: Data-driven, data-intensive computing for modelling and analysis of biological networks: application to bioethanol production. Journal of Physics: Conference SeriesĀ 78, 012061 (6p.) (2007)
Read, R.C.: Every one a winner. Ann Discrete Math., 107ā120 (1979)
Schoen, E.D., Eendebak, P.T., Nguyen, M.V.M.: Complete enumeration of pure-level and mixed-level orthogonal array. Journal of Combinatorial DesignsĀ 18(2), 123ā140 (2010)
Walker, R.J.: An enumerative technique for a class of combinatorial problems. In: Proc. Sympos. Appl. Math., vol.Ā 10. American Mathematical Society, Providence (1960)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
Ā© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Phan, H., Soh, B., Nguyen, M. (2010). A Step-by-Step Extending Parallelism Approach for Enumeration of Combinatorial Objects. In: Hsu, CH., Yang, L.T., Park, J.H., Yeo, SS. (eds) Algorithms and Architectures for Parallel Processing. ICA3PP 2010. Lecture Notes in Computer Science, vol 6081. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13119-6_40
Download citation
DOI: https://doi.org/10.1007/978-3-642-13119-6_40
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13118-9
Online ISBN: 978-3-642-13119-6
eBook Packages: Computer ScienceComputer Science (R0)