On the complexity of finding a local maximum of functions on discrete planar subsets

We study how many values of an unknown integer-valued function f one needs to know in order to find a local maximum of f. We consider functions defined on finite subsets of discrete plane. We prove upper bounds for functions defined on rectangles and present lower bounds for functions defined on arbitrary domains in terms of the size of the domain and the size of its border.

[1]  Gábor Tardos,et al.  Query complexity, or why is it difficult to separateNPA∩coNPA fromPA by random oraclesA? , 1989, Comb..

[2]  Moni Naor,et al.  Search problems in the decision tree model , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.

[3]  Pierluigi Crescenzi,et al.  Sperner's lemma and robust machines , 1993, [1993] Proceedings of the Eigth Annual Structure in Complexity Theory Conference.

[4]  Da-Lun Wang,et al.  Discrete Isoperimetric Problems , 1977 .

[5]  Lev D. Beklemishev,et al.  On the induction schema for decidable predicates , 2000, Journal of Symbolic Logic.

[6]  Manuel Blum,et al.  Generic oracles and oracle classes , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[7]  Miklos Santha.  On the Monte Carlo Boolean decision tree complexity of read-once formulae , 1991, [1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference.

[8]  Lev D. Beklemishev,et al.  On the query complexity of finding a local maximum point , 2000, Inf. Process. Lett..

[9]  J. Kiefer,et al.  Sequential minimax search for a maximum , 1953 .

[10]  Moni Naor,et al.  Decision trees and downward closures , 1988, [1988] Proceedings. Structure in Complexity Theory Third Annual Conference.