Solving the maximal matching problem with DNA molecules in Adleman–Lipton model

Abstract

The maximal matching problem (MMP) is to find maximal edge subsets in a given undirected graph, that no pair of edges are adjacent in the subsets. It is a vitally important NP-complete problem in graph theory and applied mathematics, having numerous real life applications in optimal combination and linear programming fields. It can be difficultly solved by the electronic computer in exponential level time. Meanwhile in previous studies deoxyribonucleic acid (DNA) molecular operations usually were used to solve NP-complete continuous path search problems, e.g. HPP, traveling salesman problem, rarely for NP-hard problems with discrete vertices or edges solutions, such as the minimum vertex cover problem, graph coloring problem and so on. In this paper, we present a DNA algorithm for solving the MMP with DNA molecular operations. For an undirected graph with [Formula: see text] vertices and [Formula: see text] edges, we reasonably design fixed length DNA strands representing vertices and edges of the graph, take appropriate steps and get the solutions of the MMP in proper length range using [Formula: see text] time. We extend the application of DNA molecular operations and simultaneously simplify the complexity of the computation.

A new parallel algorithm to solve one classic water resources optimal allocation problem based on inspired computational model

“…and Append-tail (T,y) [19][20][21][22]. Meanwhile, the complexity of these operations is O(1) [23][24][25].…”

Fast Parallel Molecular Solution for Longest and Shortest Paths with Forbidden Pairs

“…A DNA (deoxyribonucleic acid) is a polymer, which is strung together from monomers called deoxyribonucleotides [14]. Distinct nucleotides are detected only with their bases [13].…”

“…Lipton [5] solved the second NP hard problem with those operations. Some other NP-hard problems which have been solved [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. In this paper, the DNA operations proposed by Adleman [1] and Lipton [5] are used to solve Longest path with forbidden pairs.…”