Probably Approximately Correct Search

We consider the problem of searching a document collection using a set of independent computers. That is, the computers do not cooperate with one another either (i) to acquire their local index of documents or (ii) during the retrieval of a document. During the acquisition phase, each computer is assumed to randomly sample a subset of the entire collection. During retrieval, the query is issued to a random subset of computers, each of which returns its results to the query-issuer, who consolidates the results. We examine how the number of computers, and the fraction of the collection that each computer indexes, affects performance in comparison to a traditional deterministic configuration. We provide analytic formulae that, given the number of computers and the fraction of the collection each computer indexes, provide the probability of an approximately correct search, where a “correct search” is defined to be the result of a deterministic search on the entire collection. We show that the randomized distributed search algorithm can have acceptable performance under a range of parameters settings. Simulation results confirm our analysis.