Abstract
Computing lower bounds to the best-cost extension of a tuple is an ubiquous task in constraint optimization. A particular case of special interest is the computation of lower bounds to all singleton tuples, since it permits domain pruning in Branch and Bound algorithms. In this paper we introduce MCTE(z), a general algorithm which allows the computation of lower bounds to arbitrary sets of tasks. Its time and accuracy grows as a function of z allowing a controlled tradeo. between lower bound accuracy and time and space to fit available resources. Subsequently, a specialization of MCTE(z) called MBTE(z) is tailored to computing lower bounds to singleton tuples. Preliminary experiments on Max-CSP show that using MBTE(z) to guide dynamic variable and value orderings in branch and bound yields a dramatic reduction in the search space and, for some classes of problems, this reduction is highly coste effective producing significant time savings and is competitive against specialized algorithms for Max-CSP.
This work was supported in part by NSF grant IIS-0086529, by MURI ONR award N00014-00-1-0617 and Spanish Cicyt project TAP1999-1086-C03-03
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Dechter, R., Kask, K., Larrosa, J. (2001). A General Scheme for Multiple Lower Bound Computation in Constraint Optimization. In: Walsh, T. (eds) Principles and Practice of Constraint Programming — CP 2001. CP 2001. Lecture Notes in Computer Science, vol 2239. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45578-7_24
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