Analysis on Yu et al.’s dynamic algorithm for canonic DBC

Recently, Yu et al. presented an algorithm for a canonic DBC of a positive integer n by solving certain subproblems recursively and it requires O((logn)²loglogn) bit operations and O((logn)²) bits of memory. This is currently the most efficient recoding type algorithm for canonic DBCs when balanced computing power and memory are available. In this paper, we present a memory efficient algorithm to compute a nearly DBC from the idea of Yu et al. We present a simple overview of Yu et al.’s algorithm focusing on canonic DBC and refine Yu et al.’s proof for range of the leading term of canonic DBCs. By using the refined range, we suggest how to improve the efficiency of Yu et al.’s algorithm computationally and present an algorithm for nearly canonic DBC with memory requirement O(logn). We also present experimental comparison on the Hamming weights of Yu et al.’s algorithm, tree based algorithm, the classic greedy DBC algorithm, and our memory efficient algorithm.