Molecular Solutions for the Set-Partition Problem on Dna-Based Computing

Abstract

Consider that the every element in a finite set S having q elements is a positive integer. The set-partition problem is to determine whether there is a subset T ⊆ S such thatwhere T = {x| x ∈ S and x ∉ T}. This research demonstrates that molecular operations can be applied to solve the set-partition problem. In order to perform this goal, we offer two DNA-based algorithms, an unsigned parallel adder and a parallel Exclusive-OR (XOR) operation, that formally demonstrate our designed molecular solutions for solving the set-partition problem.

A Molecular Solution to the Three-Partition Problem

“…The algorithm used mathematical calculations to find the subsets sum. Another algorithm that was also based on mathematical operations was presented in (Tsai et al, 2008). Two DNA-based algorithms, an unsigned parallel adder and a parallel exclusive-OR (XOR) operation were presented to solve the set partition problem.…”