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>f</f> one needs to know in order to find a local maximum of <f>f</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. [Copyright &y& Elsevier]