Multipath greedy algorithm for canonical representation of numbers in the double base number system

The double base number system (DBNS) has been used in applications such as cryptography and digital filters. Two important properties of this type of representation are high redundancy and sparseness, which are key in eliminating carry propagation in basic arithmetic operations. High redundancy poses challenges in determining the canonical double base number representation (CDBNR) of an algebraic value. An exhaustive search for this representation can be computationally intensive, even for relatively small values. The greedy algorithm is very fast and simple to implement, but only allows for a single near canonical double base number representation (NCDBNR). The multipath greedy (MG) algorithm discussed in this paper is much faster than exhaustive search and gives better performance since it dramatically increases the likelihood of finding canonical representations. Since multiple starting points are used, this algorithm is able to find more than one NCDBNR in a single run.