Abstract
We devise a theoretical model for dichotomic search algorithms for constrained optimization. We show that, within our model, a certain way of choosing the breaking point minimizes both expected as well as worst case performance in a skewed binary search. Furthermore, we show that our protocol is optimal in the expected and in the worst case. Experimental results illustrate performance gains when our protocols are used within the search strategy by Streeter and Smith.
This work was supported by the National Science Foundation through the Career: Cornflower Project (award number 0644113). We would like to express our thanks to three anonymous reviewers for their helpful comments as well as John Hughes, Anna Lysyanskaya, Claire Mathieu, Steven Smith, and Mathew Streeter for supporting this work and some very insightful discussions.
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Brodal, G.S., Moruz, G.: Skewed Binary Search Trees. In: Azar, Y., Erlebach, T. (eds.) ESA 2006. LNCS, vol. 4168, pp. 708–719. Springer, Heidelberg (2006)
Crawford, J.A., Auton, L.D.: Experimental Results on the Cross-Over Point in Random 3-SAT. Artificial Intelligence 81, 31–57 (1996)
Fahle, T., Schamberger, S., Sellmann, M.: Symmetry Breaking. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 93–107. Springer, Heidelberg (2001)
Ferré, S., King, R.D.: A dichotomic search algorithm for mining and learning in domain-specific logics. Fundamenta Informaticae 66(1–2), 1–32 (2005)
Focacci, F., Lodi, A., Milano, M.: Cost-Based Domain Filtering. In: Jaffar, J. (ed.) CP 1999. LNCS, vol. 1713, pp. 189–203. Springer, Heidelberg (1999)
Focacci, F., Milano, M.: Global Cut Framework for Removing Symmetries. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 77–92. Springer, Heidelberg (2001)
Gomes, C.P., Selman, B., Crato, N., Kautz, H.: Heavy-tailed phenomena in satisfiability and constraint satisfaction problems. Automated Reasoning 24(1–2), 67–100 (2000)
Harvey, W.: Symmetry Breaking and the Social Golfer Problem. In: SymCon. (2001)
Hogg, T., Huberman, B.A., Williams, C.P.: Phase Transitions and Complexity. Artificial Intelligence 81 (1996)
Jussien, N., Lhomme, O.: Dynamic Domain Splitting for Numeric CSPs. In: ECAI, pp. 224–228 (1998)
Kirkpatrick, S., Selman, B.: Critical Behavior in the Satisfiability of Random Boolean Expressions. Science 264, 1297–1301 (1994)
Leong, G.T.: Constraint Programming for the Traveling Tournament Problem. Project Thesis, National University of Singapore (2003)
Lustig, I., Puget, J.-F.: Constraint Programming. Encyclopedia of Operations Research and Management Science, 136–140 (2001)
Monasson, R., Zecchina, R., Kirkpatrick, S., Selman, B., Troyansky, L.: Determining computational complexity from characteristic ‘phase transitions’. Nature 400, 133–137 (1999)
Nievergelt, J., Reingold, E.M.: Binary search trees of bounded balance. In: Annual ACM Symposium on Theory of Computing, pp. 137–142 (1972)
Smith, B.: Reducing Symmetry in a Combinatorial Design Problem. In: CPAIOR, pp. 351–360 (2001)
Streeter, M., Smith, S.F.: Using Decision Procedures Efficiently for Optimization. In: ICAPS, pp. 312–319 (2007)
Wojtaszek, D., Chinneck, J.W.: Faster MIP Solutions via New Node Selection Rules. In: INFORMS (2007)
Wong, C.K., Nievergelt, J.: Upper Bounds for the Total Path Length of Binary Trees. Journal of the ACM 20(1), 1–6 (1973)
Zhang, H.: Specifying Latin Square Problems in Propositional Logic. In: Automated Reasoning and Its Applications. MIT Press, Cambridge (1997)
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Sellmann, M., Kadioglu, S. (2008). Dichotomic Search Protocols for Constrained Optimization. In: Stuckey, P.J. (eds) Principles and Practice of Constraint Programming. CP 2008. Lecture Notes in Computer Science, vol 5202. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85958-1_17
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DOI: https://doi.org/10.1007/978-3-540-85958-1_17
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