Tagging and navigability

We consider the problem of optimal tagging for navigational purposes in one's own collection. What is the best that a forgetful user can hope for in terms of ease of retrieving a labeled object? We prove that the number of tags has to increase logarithmically in the collection size to maintain a manageable result set. Using Flickr data we then show that users do indeed apply more and more tags as their collection grows and that this is not due to a global increase in tagging activity. However, as the additional terms applied are not statistically independent, users of large collections still have to deal with larger and larger result sets, even when more tags are used as search terms. We pose optimal tag suggestion for navigational purposes as an open problem.