Abstract
Being a typical NP-complete problem, 0–1 knapsack problem is one of the classical combinatorial optimization problems, the traditional parallel processing techniques can not break through the limitations of the number of processors or the time's exponential increasing. But DNA computing is one of the potential strategies for solving these combinatorial optimization problems availably. In [8], Majid et al solved the problem with exponential O(2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sup> ) DNA chains. In this paper, the objective is to solve the 0–1 knapsack problem with as few DNA chains as possible, for that we apply the divide-and-conquer to the DNA algorithm, and propose the new DNA computer algorithm for solving the 0–1 knapsack problem. This algorithm decreases the number of DNA chains from O(2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sup> ) to sub-exponential O(2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q/2</sup> ). In other words, it can theoretically extend the number of dimension from 60 to 120 when using the DNA computing for solving the 0–1 knapsack problem.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
