Pattern matching through Chaos Game Representation: bridging numerical and discrete data structures for biological sequence analysis

The exploratory analysis described here consisted of selecting foundational string problems and refactoring them using CGR-based algorithms. We found that CGR can take the role of suffix trees and emulate sophisticated string algorithms, efficiently solving exact and approximate string matching problems such as finding all palindromes and tandem repeats, and matching with mismatches. The common feature of these problems is that they use longest common extension (LCE) queries as subtasks of their procedures, which we show to have a constant time solution with CGR. Additionally, we show that CGR can be used as a rolling hash function within the Rabin-Karp algorithm.The analysis of biological sequences relies on algorithmic foundations facing mounting challenges, both logistic (performance) and analytical (lack of unifying mathematical framework). CGR is found to provide the latter and to promise the former: graph-based data structures for sequence analysis operations are entailed by numerical-based data structures produced by CGR maps, providing a unifying analytical framework for a diversity of pattern matching problems.Biological sequence analysis remains a central problem in bioinformatics, boosted in recent years by the emergence of new generation sequencing high-throughput techniques [1,2]. With the advances of new technologies, the need for efficient algorithms for string representation and processing is increasing continuously.Sequence representation plays a particular role in this regard, being the first step that both enables and conditions subsequent data processing, and has been the object of several analytical approaches over the last years [3]. The development of string processing algorithms based on different data structures, particularly suffix trees and suffix arrays, has been increasing steadily [1,4]. The classical version of these structures enhances the functionality of the underlying sequence by efficiently supporting several look-up procedures [4