Efficient Synthesis for Two-Dimensional Strand Arrays with Row Constraints

2026-01-12

AI Summary

This study addresses the scheduling problem in large-scale DNA synthesis involving two-dimensional chain arrays under row constraints—where at most one strand per row can be synthesized per round—with a focus on the single-row, two-strand setting. By modeling the process as a Markov chain and employing stochastic analysis, the work establishes the first analytical upper and lower bounds on the expected completion time, characterizes the performance limits of non-lookahead online strategies, and demonstrates that a single-symbol lookahead can improve performance in the binary case. The authors propose a “laggard-first” online policy achieving an asymptotic expected time of $(q+3)L/2$, design a single-symbol lookahead strategy for binary sequences attaining $7L/3$, and present a dynamic programming algorithm that computes the optimal offline schedule for any fixed pair of sequences.

Technology Category

• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

We study the theoretical problem of synthesizing multiple DNA strands under spatial constraints, motivated by large-scale DNA synthesis technologies. In this setting, strands are arranged in an array and synthesized according to a fixed global synthesis sequence, with the restriction that at most one strand per row may be synthesized in any synthesis cycle. We focus on the basic case of two strands in a single row and analyze the expected completion time under this row-constrained model. By decomposing the process into a Markov chain, we derive analytical upper and lower bounds on the expected synthesis time. We show that a simple laggard-first policy achieves an asymptotic expected completion time of (q+3)L/2 for any alphabet of size q, and that no online policy without look-ahead can asymptotically outperform this bound. For the binary case, we show that allowing a single-symbol look-ahead strictly improves performance, yielding an asymptotic expected completion time of 7L/3. Finally, we present a dynamic programming algorithm that computes the optimal offline schedule for any fixed pair of sequences. Together, these results provide the first analytical bounds for synthesis under spatial constraints and lay the groundwork for future studies of optimal synthesis policies in such settings.

Problem

• DNA synthesis
• spatial constraints
• strand arrays
• synthesis scheduling
• row constraints

Innovation

• row-constrained synthesis
• DNA strand scheduling
• Markov chain analysis
• laggard-first policy
• dynamic programming