Variable-Length Codes for Space-Efficient Grammar-Based Compression

Dictionary is a crucial data structure to implement grammar-based compression algorithms. Such a dictionary should access any codes in O(1) time for an efficient compression. A standard dictionary consisting of fixed-length codes consumes a large amount of memory of 2n log n bits for n variables. We present novel dictionaries consisting of variable-length codes for offline and online grammar-based compression algorithms. In an offline setting, we present a dictionary of at most min{n log n + 2n + o(n), 3n log sigma(1+ o(1))} bits of space where sigma < 2 root n. In an online setting, we present a dictionary of at most 7/4 n log n+4n+o(n) bits of space for a constant alphabet and unknown n. Experiments revealed that memory usage in our dictionary was much smaller than that of state-of-the-art dictionaries.