Abstract
It is shown first by Adleman that deoxyribonucleic acid (DNA) strands could be employed towards calculating solution to an instance of the NP-complete Hamiltonian Path Problem (HPP). Lipton also demonstrated that Adleman's techniques could be used to solve the satisfiability (SAT) problem. In this paper, it is demonstrated how the DNA operations presented by Adleman and Lipton can be used to develop the DNA-based algorithm for solving the 0-1 Knapsack Problem.
Highlights
In 1961, Feynman first offered bio-molecular computation, but his idea was not implemented by experiments for a few decades [1]
The knapsack problem proved to be the NP-complete problem by restriction has been solved by a number of different algorithms with exponential time complexity in conventional silicon-based computer [27]
The proposed algorithm for solving the 0-1 knapsack problem is based on basic biological operations
Summary
In 1961, Feynman first offered bio-molecular computation, but his idea was not implemented by experiments for a few decades [1]. DNA-based algorithms had been proposed to solve many computational problems and those consisted of the satisfiability problem [3], the maximal clique [6], three-vertex-coloring [7], the set-splitting problem [8], the set-cover problem and the problem of exact cover by 3-sets [9], the dominating-set [10], the maximum cut problem [11], the binary integer programming problem [12] and the set-partition problem [24]. From [18], DNA-based algorithms for constructing DNA databases are offered.
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