A Molecular Solution to the Three-Partition Problem

Abstract

Given a set of numbers, the three-partition problem is to divide them into disjoint triplets that all have the same sum. The problem is NP-complete. This paper presents an algorithm to solve this problem using the biomolecular computing approach. The algorithm uses a distinctive encoding technique that depends on the numbers values which omits the need to an adder to find the sum. The algorithm is explained and an analysis of its complexity in terms of time, the number of strands, number of tubes, and the longest library strand used is presented. A simulation of the algorithm is implemented and tested. This algorithm further proves the ability of molecular computing in solving hard problems.