A Subsequence-Histogram Method for Generic Vocabulary Recognition over Deletion Channels

TL;DR

This paper introduces a polynomial-time approximation algorithm for recognizing vocabularies from subsequences received over deletion channels, leveraging subsequence-histograms to efficiently distinguish between vocabularies without prior structural assumptions.

Contribution

The paper proposes a novel polynomial approximation algorithm that uses subsequence-histograms for vocabulary recognition, avoiding exponential complexity of MAP solutions and not requiring prior vocabulary structure assumptions.

Findings

Algorithm achieves MAP-like performance in some cases

Demonstrated effectiveness on example datasets

Applicable to bioinformatics, storage, and search systems

Abstract

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.