Query strategies for priced information (extended abstract)

We consider a class of problems in which an algorithm seeks to compute a function over a set of inputs, where each input has an associatedprice. The algorithm queries inputs sequentially, trying to learn the value of the function for the minimum cost. We app ly the competitive analysis of algorithms to this framework, d esigning algorithms that incur large cost only when the cost of the che apest “proof” for the value of is also large. We provide algorithms that achieve the optimal competitive ratio for functions th at include arbitrary Boolean AND/OR trees, and for the problem of searc hing in a sorted array. We also investigate a model for pricing in t h s framework, constructing a set of prices for any AND/OR tree t hat satisfies a very strong type of equilibrium property.