A modified dna computing approach to tackle the exponential solution space of the graph coloring problem

TL;DR

This paper introduces a modified DNA computing method based on the Adleman-Lipton model that sequentially colors graph vertices, reducing the exponential solution space and improving efficiency in solving large graph coloring problems.

Contribution

It proposes a novel DNA computing approach that colors vertices sequentially, addressing the exponential solution space challenge in large graph coloring problems.

Findings

Significant reduction in DNA strands used during coloring

Effective handling of large graph coloring problems

Simulation results demonstrate improved efficiency

Abstract

Although it has been evidenced that DNA computing is able to solve the graph coloring problem in a polynomial time complexity, but the exponential solution space is still a restrictive factor in applying this technique for solving really large problems. In this paper a modified DNA computing approach based on Adleman-Lipton model is proposed which tackles the mentioned restriction by coloring the vertices one by one. In each step, it expands the DNA strands encoding promising solutions and discards those which encode infeasible ones. A sample graph is colored by simulating the proposed approach and shows a notable reduction in the number of DNA strands used.