Miniception

Miniception derives and implements methods to design and analyze practical minimizers for efficient k-mer sampling and density optimization in sequence analysis.

Key Features:

• Minimizer sampling: Samples k-mers from sequences so that similar sequences yield similar sets of sampled k-mers.
• Parameters: Uses the k-mer length (k), window length (w), and an order on k-mers to define minimizers.
• Density analysis: Analyzes minimizer density, the metric that quantifies the sparsity of sampled k-mers, and references the theoretical optimal density of 1/w.
• Asymptotic optimality: Considers asymptotically optimal minimizers characterized by density O(1/w) for given k and w.
• Existence condition: Derives a necessary and sufficient condition for the existence of asymptotically optimal minimizers.
• Randomized algorithm: Introduces a randomized algorithm that provides the best theoretical guarantee to date on achieving low density.
• Construction approach: Design and implementation are akin to constructing and using a random minimizer.
• Resource impact: Aims to improve computational efficiency and reduce memory usage in k-mer–based software and pipelines.
• Scalability: Scales with values of k and w typically employed in contemporary bioinformatics applications.

Scientific Applications:

• Consistent k-mer sampling: Provides consistent k-mer selection to support sequence comparison and related analyses.
• Minimizer optimization: Enables design and analysis of minimizers that approach optimal density behavior for specified k and w.
• Pipeline resource reduction: Reduces sampling density to lower computational cost and memory footprint in k-mer–based pipelines.

Methodology:

Derives a necessary and sufficient condition for asymptotically optimal minimizers and introduces a randomized algorithm, with design and implementation following the construction and use of a random minimizer.