A randomized competitive algorithm for evaluating priced AND/OR trees

Recently, Charikar et al. investigated the problem of evaluating AND/OR trees, with non-uniform costs on its leaves, from the perspective of the competitive analysis. For an AND/OR tree T they presented a @m(T)-competitive deterministic polynomial time algorithm, where @m(T) is the number of leaves that must be read, in the worst case, in order to determine the value of T. Furthermore, they proved that @m(T) is a lower bound on the deterministic competitiveness, which assures the optimality of their algorithm. The power of randomization in this context has remained as an open question. Here, we take a step towards solving this problem by presenting a 56@m(T)-competitive randomized polynomial time algorithm. This contrasts with the best known lower bound @m(T)/2.

[1]  Yoshiharu Kohayakawa,et al.  Querying Priced Information in Databases: The Conjunctive Case , 2004, LATIN.

[2]  Joseph M. Hellerstein,et al.  Optimization techniques for queries with expensive methods , 1998, TODS.

[3]  Ojas Parekh,et al.  Randomized Approximation Algorithms for Query Optimization Problems on Two Processors , 2002, ESA.

[4]  Yanjun Zhang.  On the Optimality of Randomized alpha-beta Search , 1995, SIAM J. Comput..

[5]  Eduardo Sany.  A Randomized Competitive Algorithm for Evaluating Priced AND/OR Trees , 2004 .

[6]  Russ Bubley,et al.  Randomized algorithms , 1995, CSUR.

[7]  Luc Bouganim,et al.  Processing queries with expensive functions and large objects in distributed mediator systems , 2001, Proceedings 17th International Conference on Data Engineering.

[8]  Venkatesan Guruswami,et al.  Query strategies for priced information (extended abstract) , 2000, STOC '00.

[9]  Judea Pearl,et al.  The solution for the branching factor of the alpha-beta pruning algorithm and its optimality , 1982, CACM.

[10]  Donald E. Knuth,et al.  The Solution for the Branching Factor of the Alpha-Beta Pruning Algorithm , 1981, ICALP.

[11]  Michael Tarsi,et al.  Optimal Search on Some Game Trees , 1983, JACM.

[12]  Allan Borodin,et al.  Online computation and competitive analysis , 1998 .

[13]  Kyuseok Shim,et al.  Query Optimization in the Presence of Foreign Functions , 1993, VLDB.

[14]  Michael E. Saks,et al.  Probabilistic Boolean decision trees and the complexity of evaluating game trees , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[15]  Marc Snir,et al.  Lower Bounds on Probabilistic Linear Decision Trees , 1985, Theor. Comput. Sci..