On Solving the Multiple Variable Gapped Longest Common Subsequence Problem
Summary: arXiv:2604.18645v1 Announce Type: new
Abstract
This paper addresses the Variable Gapped Longest Common Subsequence (VGLCS) problem, a generalization of the classical LCS problem involving flexible gap constraints between consecutive solutions’ characters. The problem arises in molecular sequence comparison, where structural distance constraints between residues must be respected, and in time-series analysis where events are required to occur within specified temporal delays.
Introduction
The Longest Common Subsequence (LCS) problem has been a cornerstone in computational biology and time-series analysis. However, the classical LCS does not accommodate gaps that may occur due to various biological or temporal constraints. The introduction of the Variable Gapped Longest Common Subsequence (VGLCS) problem offers a more versatile framework for addressing these complexities.
Methodology
To tackle the VGLCS problem, we propose a search framework based on the root-based state graph representation. In this framework, the state space comprises a generally large number of rooted state subgraphs. To address the combinatorial explosion that arises from this complexity, we employ an iterative beam search strategy. This approach dynamically maintains a global pool of promising candidate root nodes, facilitating effective control of diversification across iterations.
Heuristic Integration
To enhance the search for high-quality solutions, our methodology integrates several known heuristics from the LCS literature into the standalone beam search procedure. This integration allows us to leverage existing knowledge while adapting to the requirements of the VGLCS problem.
Experimental Setup
To validate the effectiveness of our approach, we conducted a comprehensive computational study on the VGLCS problem, comprising 320 synthetic instances with up to 10 input sequences and up to 500 characters. This extensive testing not only highlights the robustness of our approach but also establishes a benchmark for future research in this area.
Results
Experimental results demonstrate the robustness of the designed approach over the baseline beam search in comparable runtimes. The iterative beam search showcased significant improvements in identifying high-quality solutions within reasonable time constraints. These findings suggest that our proposed framework is a promising avenue for future research and applications in molecular sequence comparison and time-series analysis.
Conclusion
In summary, the Variable Gapped Longest Common Subsequence problem presents significant challenges that are well-addressed by our proposed search framework. By utilizing a root-based state graph representation and an iterative beam search strategy, we can effectively navigate the complexities of this problem. Future work will explore further enhancements to the search strategy and its applications in real-world scenarios.
Keywords
- Longest Common Subsequence
- Variable Gapped Longest Common Subsequence
- Beam Search
- Molecular Sequence Comparison
- Time-Series Analysis