Random Sampling from a Search Engine's Index
We revisit a problem introduced by Bharat and Broder almost a decade ago: how to sample random pages from a search engine's index using only the search engine's public interface? Such a primitive is particularly useful in creating objective benchmarks for search engines.
The technique of Bharat and Broder suffers from two well recorded biases: It favors long documents and highly ranked documents. We introduce two novel sampling techniques: a lexicon-based technique and a random walk technique. Our methods produce biased sample documents, but each sample is accompanied by a corresponding ``weight'', which represents the probability of this document to be selected in the sample. The samples, in conjunction with the weights, are then used to simulate near-uniform samples. To this end, we resort to four well known Monte Carlo simulation methods: rejection sampling, importance sampling, the Metropolis-Hastings algorithm, and the maximum degree method.
We analyze our methods rigorously and prove that under plausible assumptions, our techniques are guaranteed to produce near-uniform samples from the search engine's index. Experiments on a corpus of 2.4 million documents substantiate our analytical findings and show that our algorithms do not have significant bias towards long or highly ranked documents. We use our algorithms to collect fresh data about the relative sizes of Google, MSN Search, and Yahoo!.
Joint work with Maxim Gurevich.