Representing Arc Labels in Dna Algorithms

DNA computing has recently generated much interest as a result of pioneering work by Adleman and Lipton, who described DNA algorithms for solving problems considered NP-hard by computer scientists. Their DNA algorithms worked on graph representations of the problem, but no indication was provided about how information on the arcs between nodes on a graph could be handled. The aim of this paper is extend the basic DNA algorithmic techniques of Adleman and Lipton by demonstrating a method for representing simple arc information | in this case, distances between cities in a simple map. The work described here signiicantly advances our understanding of DNA computational processes and identiies the potential for DNA algorithms for addressing problems in the NP class. 1 Adleman's DNA computing solution for HPP Consider the map presented in Figure 1, which describes the way that ve cities are linked by one-way and two-way roads. Adleman's (1994) approach was to encode each city and each route between two cities in 5 1 2 3 4 Figure 1: A map denoting the one-way and two-way roads between 5 cities. The task is for a travelling salesperson to visit each city once, starting at city 1. The only route is cities 1, 2, 3, 4 and 5. Adleman's (1994) DNA computation (using a slightly diierent version of the problem involving 7 cities and strands for cities of 20 bases in length) took 7 days to perform. DNA strands, and put them into a test-tube. For example, the strand coding for cities 1 and 2 could be AATGCCGG and TTTAAGCC, respectively. A road from city 1 to 2 is encoded in such a way that the rst part is the complementary strand 1 to the second half of strand for city 1, and the second part is 1 What is remarkable is that the DNA are large molecules made up of combinations of only four types of nucleotides | adenine, guanine, thymine and cytosine (called A, G, T, and C, respectively). It is estimated that the DNA in each one of our cells contains about 8 billion nucleotides, spread across 46 chromosomes (discrete molecular structures of DNA), each of