(wh)-Density Global Alignment Algorithm for Molecular Sequences
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Solution Overview
Problem
Existing computational techniques for global alignment of molecular sequences are not adequately efficient for biological applications, particularly in sequencing data, as they do not effectively handle stringent density constraints.
Innovation Solution
A constrained version of the pairwise global alignment problem, termed the (wh)-density global alignment problem, is defined, where cells in a grid representing partial alignments are tested against initialization and extension conditions, eliminating unfeasible cells and ensuring only optimal solutions are computed, thereby reducing computational complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional dynamic programming is used for global alignment, then all possible alignments are computed, but computational complexity increases significantly
Solution Approach 1:
The patent applies preliminary action by performing initialization conditions on grid cells before the main dynamic programming computation. Cells are pre-screened using conditions that check whether they can possibly satisfy the (wh)-density constraint, eliminating infeasible cells beforehand. This preliminary filtering reduces the number of cells that require full DP computation, thereby reducing overall computational complexity while maintaining reliability of finding optimal solutions.
2Reliability
If all grid cells are examined in dynamic programming, then optimal solutions are ensured, but running time increases
Solution Approach 1:
The patent extracts and removes infeasible grid cells from the computation set by applying initialization and extension conditions. These conditions identify and eliminate cells that cannot possibly lead to optimal (wh)-density alignments. By taking out these unnecessary cells before main computation, the algorithm maintains optimality guarantees for remaining cells while significantly reducing running time.
Solution Approach 2:
The patent performs preliminary screening of grid cells using initialization conditions that check basic feasibility criteria before committing to full dynamic programming computation. This preliminary action filters out cells that violate density constraints or other necessary conditions, ensuring that only potentially optimal cells undergo expensive computation, thus reducing overall running time while preserving optimality.
3Manufacturing precision
If density constraints are made more stringent, then alignment quality improves, but number of cells requiring computation increases
Solution Approach 1:
The patent applies preliminary action by establishing initialization conditions that pre-screen grid cells based on stringent density constraints. Rather than applying these constraints during the main computation (which would increase computational burden), the algorithm evaluates cells against necessary conditions beforehand. This allows stringent quality requirements to be maintained while actually reducing the number of cells that need full computation, as infeasible cells are eliminated early.
Solution Approach 2:
The patent segments the grid computation into multiple stages: initialization condition evaluation, extension condition evaluation, and main dynamic programming. By segmenting the computation this way, stringent density constraints can be enforced through initialization conditions that divide and conquer the problem space, allowing high-quality alignment requirements to be met without proportionally increasing overall computational complexity.
Data Source
AI summary
To determine optimal alignment of two molecules, an alignment space of two strings representing element sequences of the molecules is conceived as a grid of cells, where each cell represents alignments between substrings of the two strings. The cells are tested against conditions that are framed, in the context of the (wh)-density global alignment problem. Two such conditions do not require an examination of the actual characters of the strings, and are hence computed with relative speed. A third condition, which involves examination of the characters in the string further prunes the cells that are to be considered.