Solving the subset sum problem with a nonideal biological computer

TL;DR

This paper explores solving the NP-complete subset sum problem using a biological computer network of self-propelled agents, analyzing error effects and validating results with simulations.

Contribution

It introduces an approximate analytical framework for error analysis in a biological computing network solving subset sum, with validation through numerical simulations.

Findings

Derived probability distribution for error paths

Estimated minimal number of agents needed for accurate solutions

Validated theoretical predictions with numerical simulations

Abstract

We consider the solution of the subset sum problem based on a parallel computer consisting of self-propelled biological agents moving in a nanostructured network that encodes the NP-complete task in its geometry. We develop an approximate analytical method to analyze the effects of small errors in the nonideal junctions composing the computing network by using a Gaussian confidence interval approximation of the multinomial distribution. We concretely evaluate the probability distribution for error-induced paths and determine the minimal number of agents required to obtain a proper solution. We finally validate our theoretical results with exact numerical simulations of the subset sum problem for different set sizes and error probabilities.