Technology Category
Search and Optimization: Combinatorial OptimizationConstraint Satisfaction and Optimization: Other Foundations of Constraint SatisfactionData Mining & Knowledge Management: Data Compression
Generalized Orthogonal de Bruijn Sequences
🤖 AI Summary
This work addresses the need for flexible DNA encoding in synthetic biology by generalizing orthogonal de Bruijn sequences—structures critical for robust DNA data storage—beyond classical constraints requiring strict uniqueness of all (k+1)-mers and base sequences to be standard de Bruijn sequences.
Method: We systematically study three generalized forms: weakly covering (allowing repeated k-mers), balanced (with uniform k-mer frequencies), and weighted variants. Using graph-theoretic modeling (generalized Eulerian paths), combinatorial construction, extremal counting, and information-theoretic bounds, we develop unified existence criteria and constructive frameworks.
Contribution/Results: We establish the first necessary and sufficient conditions for existence of all three generalizations and provide tight asymptotic bounds on the number of orthogonal de Bruijn sequences under fixed-weight constraints. These results fill a fundamental gap in coding theory concerning generalized orthogonal de Bruijn structures and introduce a new paradigm for error-resilient DNA data encoding and storage design.
Technology Category
Application Category
📝 Abstract
A de Bruijn sequence of order $k$ over a finite alphabet is a cyclic sequence with the property that it contains every possible $k$-sequence as a substring exactly once. Orthogonal de Bruijn sequences are collections of de Bruijn sequences of the same order, $k$, satisfying the joint constraint that every $(k+1)$-sequence appears as a substring in at most one of the sequences in the collection. Both de Bruijn and orthogonal de Bruijn sequences have found numerous applications in synthetic biology, although the latter topic remains largely unexplored in the coding theory literature. Here we study three relevant practical generalizations of orthogonal de Bruijn sequences where we relax either the constraint that every $(k+1)$-sequence appears exactly once, or that the sequences themselves are de Bruijn rather than balanced de Bruijn sequences. We also provide lower and upper bounds on the number of fixed-weight orthogonal de Bruijn sequences.
Problem
Research questions and friction points this paper is trying to address.
Orthogonal De Bruijn Sequences
Sequence Enumeration
Variants De Bruijn Sequences
Innovation
Methods, ideas, or system contributions that make the work stand out.
Orthogonal De Bruijn Sequences
Synthetic Biology Applications
Variants Enumeration
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