Speeding up the AIFV-2 dynamic programs by two orders of magnitude using Range Minimum Queries

AIFV-2 codes are a new method for constructing lossless memoryless sources that provide better worst-case redundancy than Huffman codes. They do this by using two code trees instead of one and also allowing some bounded delay in the decoding process. Known algorithms AIFV-codes iterative; at each step they replace current tree pair with “better” one. The state art performing replacement is Dynamic Programming (DP) use O(n5) time to fill tables, size O(n3) (where n number different characters source). This paper describes how reduce filling DP tables orders magnitude, down O(n3). It does introducing grouping technique permits separating Θ(n3)-space into Θ(n) groups, O(n2), then Two-Dimensional Range-Minimum Queries (RMQs) group's table entries O(n2) time.