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

Abstract: 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 Ò binary numbers of Ñ bits, which are denoted by Ç ÑÒ 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 Ç Ò steps using Ç ÑÒ DNA strands, and the second algorithm runs in Ç Ô Ò ÐÓ � Ò steps using Ç ÑÒ DNA strands