Simple Worst-Case Optimal Adaptive Prefix-Free Coding

Abstract: We give a new and simple worst-case optimal algorithm for adaptive prefix-free coding that matches Gagie and Nekrich's bounds except for lower-order terms, and uses no data structures more complicated than a lookup table. Moreover, when Gagie and Nekrich's algorithm is modified for adaptive alphabetic prefix-free coding its decoding time slows down to $O (\log \log n)$ per character, but ours can be modified for this problem with no asymptotic slowdown. As far as we know, this gives the first algorithm for this alphabetic problem that is simultaneously worst-case optimal in terms of encoding and decoding time and of encoding length.