Abstract
Randomised algorithms traditionally make stochastic decisions based on the result of sampling from a uniform probability distribution, such as the toss of a fair coin. In this paper, we relax this constraint, and investigate the potential benefits of allowing randomised algorithms to use non-uniform probability distributions. We show that the choice of probability distribution influences the non-functional properties of such algorithms, providing an avenue of optimisation to satisfy non-functional requirements. We use Multi-Objective Optimisation techniques in conjunction with Genetic Algorithms to investigate the possibility of trading-off non-functional properties, by searching the space of probability distributions. Using a randomised self-stabilising token circulation algorithm as a case study, we show that it is possible to find solutions that result in Pareto-optimal trade-offs between non-functional properties, such as self-stabilisation time, service time, and fairness.
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References
Afzal, W., Torkar, R., Feldt, R.: A systematic review of search-based testing for non-functional system properties. Information and Software Technology 51, 957–976 (2009)
Angluin, D.: Local and global properties in networks of processors. In: Proceedings of the Twelfth Annual ACM Symposium on Theory of Computing, pp. 82–93 (1980)
Beauquier, J., Cordier, S., Delaët, S.: Optimum probabilistic self-stabilization on uniform rings. In: Proceedings of the Second Workshop on Self-Stabilizing Systems, pp. 15.1–15.15 (1995)
Beauquier, J., Gradinariu, M., Johnen, C.: Memory space requirements for self-stabilizing leader election protocols. In: Proceedings of the Eighteenth Annual ACM Symposium on Principles of Distributed Computing, pp. 199–207. ACM (1999)
Beauquier, J., Gradinariu, M., Johnen, C.: Randomized self-stabilizing and space optimal leader election under arbitrary scheduler on rings. Distributed Computing 20, 75–93 (2007)
Clarke, E.M.: Model Checking. In: Ramesh, S., Sivakumar, G. (eds.) FST TCS 1997. LNCS, vol. 1346, pp. 54–56. Springer, Heidelberg (1997)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)
Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Communications of the ACM 17, 643–644 (1974)
Dolev, S.: Self-stabilization. The MIT Press (2000)
Harman, M., Mansouri, S., Zhang, Y.: Search Based Software Engineering: A Comprehensive Analysis and Review of Trends Techniques and Applications. Department of Computer Science, Kings College London, Tech. Rep. TR-09-03 (2009)
Herman, T.: Probabilistic Self-stabilization. Information Processing Letters 35(2), 63–67 (1990)
Higham, L., Myers, S.: Self-stabilizing token circulation on anonymous message passing rings. In: OPODIS 1998 Second International Conference on Principles of Distributed Systems (1999)
Johnen, C.: Service Time Optimal Self-stabilizing Token Circulation Protocol on Anonymous Undirectional Rings. In: Proceedings of the 21st IEEE Symposium on Reliable Distributed Systems, pp. 80–89. IEEE (2002)
Johnson, C.G.: Genetic Programming with Fitness Based on Model Checking. In: Ebner, M., O’Neill, M., Ekárt, A., Vanneschi, L., Esparcia-Alcázar, A.I. (eds.) EuroGP 2007. LNCS, vol. 4445, pp. 114–124. Springer, Heidelberg (2007)
Katz, G., Peled, D.: Genetic Programming and Model Checking: Synthesizing New Mutual Exclusion Algorithms. In: Cha, S(S.), Choi, J.-Y., Kim, M., Lee, I., Viswanathan, M. (eds.) ATVA 2008. LNCS, vol. 5311, pp. 33–47. Springer, Heidelberg (2008)
Katz, G., Peled, D.: Model Checking-Based Genetic Programming with an Application to Mutual Exclusion. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 141–156. Springer, Heidelberg (2008)
Katz, G., Peled, D.: Synthesizing Solutions to the Leader Election Problem Using Model Checking and Genetic Programming. In: Namjoshi, K., Zeller, A., Ziv, A. (eds.) HVC 2009. LNCS, vol. 6405, pp. 117–132. Springer, Heidelberg (2011)
Kwiatkowska, M., Norman, G., Parker, D.: PRISM: Probabilistic Symbolic Model Checker. In: Field, T., Harrison, P.G., Bradley, J., Harder, U. (eds.) TOOLS 2002. LNCS, vol. 2324, pp. 200–204. Springer, Heidelberg (2002)
Luke, S.: ECJ, http://cs.gmu.edu/~eclab/projects/ecj/
Motwani, R.: Randomized Algorithms. Cambridge University Press (1995)
Norman, G.: Analysing Randomized Distributed Algorithms. Validation of Stochastic Systems, pp. 384–418 (2004)
Rabin, M.: Probabilistic algorithms. Algorithms and Complexity 21 (1976)
Valmari, A.: The State Explosion Problem. In: Reisig, W., Rozenberg, G. (eds.) APN 1998. LNCS, vol. 1491, pp. 429–528. Springer, Heidelberg (1998)
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Millard, A.G., White, D.R., Clark, J.A. (2012). Searching for Pareto-optimal Randomised Algorithms. In: Fraser, G., Teixeira de Souza, J. (eds) Search Based Software Engineering. SSBSE 2012. Lecture Notes in Computer Science, vol 7515. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33119-0_14
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DOI: https://doi.org/10.1007/978-3-642-33119-0_14
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