DNA Algorithm Based on Reverse Complement Alignment for 0/1 Knapsack Problem

By means of reverse complement alignments of DNA sequences, this paper gives a DNA encoding method and DNA algorithm for the 0/1 knapsack problem. For any instance of the 0/1 knapsack problem, it uses DNA strand s_i = s_i\´s_pis_i" to encode item ui, where the length of si is wi and the length of s_pi is p_i. And then it computes the reverse complement alignment r_pi of s_pi, and let l_pi be the reversal of the lower strand of r_pi. Next, it computes the reverse complement alignment r_i" and r_j\´ of s_i" and s_j\´, and adds DNA strand a_ij = l_i"+l_j\´ as additional code, where l_i" and l_j\´ are the reversals of the lower strands of r_i" and r_j\´, respectively. The DNA encoding method can obtain the optimal solutions more easily than the formers, and it has the characteristics of low error rate.