Abstract. Most DNA computing algorithms for mathematical problems start with combinatorial generation of an initial pool. Several methods for initialpool generation have been proposed, including hybridization/ligation and mix/split methods. Here, we implement and compare parallel overlap assembly with the hybridization/ligation method. We applied these methods to the molecular algorithm to solve an instance of the graph problem with weighted edges. Our experimental results show that parallel overlap assembly is a better choice in terms of generation speed and material consumption than the hybridization/ligation method. Simulation of parallel overlap assembly was performed to investigate the potential and the limitation of the method. 1

Bio-molecular or DNA computing has emerged as an interdisciplinary field that draws together chemistry, molecular biology, computer science, and mathematics. From DNA computing point of view, it has been proven that it is possible to solve weighted graph problems such as Traveling Salesman Problem (TSP) and shortest path problem by exploiting some characteristics of DNA. Those characteristics are length, concentration, and melting temperature of DNA. In this work, we present an alternative length-based DNA computing approach whereby the cost of each path is encoded by the length of the oligonucleotides in a proportional way. The advantage is such that, after an initial pool generation and amplification, gel electrophoresis can be performed to separate the respective DNA duplex according to their length which directly decodes the results. For initial pool generation, parallel overlap assembly method and hybridization/ligation method are reviewed. Moreover, it is found that the parallel overlap assembly method should be employed instead of hybridization/ligation method for an efficient initial pool generation of direct-proportional length-based DNA computing. 1.

Abstract—Molecular computing has proved its possibility to solve weighted graph problem such as Hamiltonian Path Problem (HPP), Traveling Salesman Problem (TSP)

Previously, direct-proportional length-based DNA computing (DPLB-DNAC) for solving weighted graph problems has been reported. The proposed DPLB-DNAC has been successfully applied to solve the shortest path problem, which is an instance of weighted graph problems. The design and development of DPLB-DNAC is important in order to extend the capability of DNA computing for solving numerical optimization problem. According to DPLB-DNAC, after the initial pool generation, the initial solution is subjected to amplification by polymerase chain reaction and, finally, the output of the computation is visualized by gel electrophoresis. In this paper, however, we give more attention to the initial pool generation of DPLB-DNAC. For this purpose, two kinds of initial pool generation methods, which are generally used for solving weighted graph problems, are evaluated. Those methods are hybridization-ligation and parallel overlap assembly (POA). It is found that for DPLB-DNAC, POA is better than that of the hybridization-ligation method, in terms of population size, generation time, material usage, and efficiency, as supported by the results of actual experiments.