A new light-based solution to the Hamiltonian path problem

• Published in: Future generation computer systems 2013-02, Vol.29 (2), p.520-527
• Main Authors: Sartakhti, Javad Salimi, Jalili, Saeed, Rudi, Ali Gholami
• Format: Article
• Language: English
• Subjects: Hamiltonian path; Light-based computing; NP-complete problem; Optical computing; Unconventional computing
• ISSN: 0167-739X; 1872-7115
• DOI: 10.1016/j.future.2012.07.008

The exponential running time for algorithms designed to solve NP-complete problems in conventional computers, mostly, makes it almost impossible solving large instances of such problems in reasonable time. Unconventional computers may be the answer to this problem. In this paper we use light to solve a Hamiltonian path problem in polynomial time. At first, the solution space of the problem is generated and then invalid solutions are eliminated from it. Our approach is based on filters which remove paths that are not Hamiltonian from the set of possible solutions. We perform polynomial preprocessing steps to produce the filters and find Hamiltonian paths of a graph based on the rays of light passing through them. Finally we report the design of filters and use light to solve the Hamiltonian path problem. ► In this paper we use a light-based way to solve the Hamiltonian path problem. ► Our solution is based on designing filters which remove invalid Hamiltonian paths. ► Totally, our solution is done in two phases preprocessing and processing. ► The time complexity of the solution is polynomial. ► The resource consumption complexity of the solution is still exponential.