Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
The Complexity of Some Problems on Subsequences and Supersequences
Journal of the ACM (JACM)
Efficient reconstruction of sequences
IEEE Transactions on Information Theory
On information transmission over a finite buffer channel
IEEE Transactions on Information Theory
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We consider the problem of recognizing a vocabulary-a collection of words (sequences) over a finite alphabet-from a potential subsequence of one of its words. We assume the given subsequence is received through a deletion channel as a result of transmission of a random word from one of the two generic underlying vocabularies. An exact maximum a posterior (MAP) solution for this problem counts the number of ways a given subsequence can be derived from particular subsets of candidate vocabularies, requiring exponential time or space. We present a polynomial approximation algorithm for this problem. The algorithm makes no prior assumption about the rules and patterns governing the structure of vocabularies. Instead, through off-line processing of vocabularies, it extracts data regarding regularity patterns in the subsequences of each vocabulary. In the recognition phase, the algorithm just uses this data, called subsequence-histogram, to decide in favor of one of the vocabularies. We provide examples to demonstrate the performance of the algorithm and show that it can achieve the same performance as MAP in some situations. Potential applications include bioinformatics, storage systems, and search engines.