Synthesizing Minimal Tile Sets for Patterned DNA Self-Assembly

TL;DR

This paper presents an exact branch-and-bound algorithm for synthesizing minimal tile sets that self-assemble into specified patterns, improving over previous heuristics in efficiency and optimality.

Contribution

The paper introduces an exhaustive algorithm for minimal tile set synthesis in DNA self-assembly, utilizing a novel search and pruning strategy for optimal solutions.

Findings

Algorithm efficiently finds minimal tile sets

Outperforms previous heuristic methods

Demonstrates practical applicability on pattern sizes

Abstract

The Pattern self-Assembly Tile set Synthesis (PATS) problem is to determine a set of coloured tiles that self-assemble to implement a given rectangular colour pattern. We give an exhaustive branch-and-bound algorithm to find tile sets of minimum cardinality for the PATS problem. Our algorithm makes use of a search tree in the lattice of partitions of the ambient rectangular grid, and an efficient bounding function to prune this search tree. Empirical data on the performance of the algorithm shows that it compares favourably to previously presented heuristic solutions to the problem.