Sorting algorithms based on the odd-even transposition sort and the shearsort with DNA strands

In recent works for high performance computing, computation with DNA molecules, that is, DNA computing, has considerable attention as one of non-silicon based computing. In this paper, we propose two procedures for sorting with DNA strands. An input of the algorithms is a set of binary numbers of bits, which are denoted by kinds of DNA strands. We first propose a procedure for the compare-and-exchange operation, which is a basic operation for the sorting algorithms. We next propose two sorting algorithms, which are based on the odd-even transposition sort and the shearsort. The first algorithm runs in steps using DNA strands, and the second algorithm runs in steps using DNA strands.