We present a simple dictionary with worst case constant lookup time, equaling the theoretical performance of the classic dynamic perfect hashing scheme of Dietzfelbinger et al. (Dynamic perfect hashing: Upper and lower bounds. SIAM J. Comput., 23(4):738–761, 1994). The space usage is similar to that of binary search trees, i.e., three words per key on average. Besides being conceptually much simpler than previous dynamic dictionaries with worst case constant lookup time, our data structure is interesting in that it does not use perfect hashing, but rather a variant of open addressing where keys can be moved back in their probe sequences. An implementation inspired by our algorithm, but using weaker hash functions, is found to be quite practical. It is competitive with the best known dictionaries having an average case (but no nontrivial worst case) guarantee. Key Words: data structures, dictionaries, information retrieval, searching, hashing, experiments * Partially supported by the Future and Emerging Technologies programme of the EU

We have examined the tradeoffs in applying regular and Compressed Bloom filters to the name query problem in distributed file systems and developed and tested a novel mechanism for scaling queries as the network grows large. Filters greatly reduced query messages when using Fan's "Summary Cache" in web cache hierarchies[6], a similar albeit smaller, searching problem. We have implemented a testbed that models a distributed file system and run experiments that test various configurations of the system to see if Bloom filters could provide the same kind of improvements. In a realistic system, where the chance that a randomly queried node holds the file being searched for is low, we show that filters always provide lower bandwidth /search and faster time/search, as long as the rates of change of the files stored at the nodes is not extremely high relative to the number of searches. In other words, we confirm the intuition that keeping some state about the contents of the rest of the system will aid in searching as long as acquiring this state is not overly costly and it does not expire too quickly.