Abstract
This paper describes the design of a linear time DNA algorithm for the Hamiltonian Path Problem (HPP) suited for parallel implementation using a microfluidic system. This bioalgorithm was inspired by the algorithm contained in [16] within the tissue P systems model. The algorithm is not based on the usual brute force generate/test technique, but builds the space solution gradually. The possible solutions/paths are built step by step by exploring the graph according to a breadth-first search so that only the paths that represent permutations of the set of vertices, and which, therefore, do not have repeated vertices (a vertex is only added to a path if this vertex is not already present) are extended. This simple distributed DNA algorithm has only two operations: concatenation (append) and sequence separation (filter). The HPP is resolved autonomously by the system, without the need for external control or manipulation. In this paper, we also note other possible bioalgorithms and the relationship of the implicit model used to solve the HPP to other abstract theoretical distributed DNA computing models (test tube distributed systems, grammar systems, parallel automata).
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Ledesma, L., Pazos, J., Rodríguez-Patón, A. (2003). A DNA Algorithm for the Hamiltonian Path Problem Using Microfluidic Systems. In: Jonoska, N., Păun, G., Rozenberg, G. (eds) Aspects of Molecular Computing. Lecture Notes in Computer Science, vol 2950. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24635-0_21
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