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 computing 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, and discuss the scalability of the nonideal problem using realistic experimental error probabilities.
Highlights
Solving complex problems requires high-performance computing methods
The network consists of a grid of channels which can be traversed by cytoskeletal filaments from top to bottom
The grid is made of two types of junctions: pass junctions that allow an agent to continue on its previous path and split junctions that allow an agent to switch lanes, or not, with equal probability
Summary
Solving complex problems requires high-performance computing methods. Since the number of computing steps typically increases exponentially with the size of a problem, multi-processor parallel algorithms are better suited to solve such tasks than single-processor serial algorithms [1, 2]. In particular, the probability distribution for error-induced paths, taking into account errors both in pass and split junctions, and introduce a procedure with which the minimal number of agents required to obtain a correct solution of the problem may be determined. Both issues are essential for the successful experimental implementation of the biological computation strategy [15]. We compare our theoretical results with exact numerical simulations of the subset sum problem for different set sizes and error probabilities
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