Brief announcement: hashed predecessor patricia trie - a data structure for efficient predecessor queries in peer-to-peer systems

The design of efficient search structures for peer-to-peer systems has attracted a lot of attention in recent years. In this announcement we address the problem of finding the predecessor in a key set and present an efficient data structure called hashed Predecessor Patricia trie. Our hashed Predecessor Patricia trie supports PredecessorSearch(x) and Insert(x) in $\mathcal O(\log \log u)$ and Delete(x) in $\mathcal O(1)$ hash table accesses when u is the size of the universe of the keys. That is the costs only depend on u and not the size of the data structure. One feature of our approach is that it only uses the lookup interface of the hash table and therefore hash table accesses may be realized by any distributed hash table (DHT).