Upper and Lower Bounds for the Dictionary Problem (Abstract)

Martin Dietzfelbinger, Kurt Mehlhorn, Friedhelm Meyer auf der Heide, Hans Rohnert

Abstract: We give a randomized algorithm for the dictionary problem with O(1) worst case time for lookup and O(1) expected amortized time for insertion and deletion. We also prove an Ω(log n) lower bound on the amortized worst case time complexity of any deterministic algorithm based on hashing. Furthermore, if the worst case lookup time is restricted to k, then the lower bound becomes Ω(k·.n 1/k ).