On Computing Average Common Substring Over Run Length Encoded Sequences

TL;DR

This paper introduces an efficient algorithm to compute the Average Common Substring (ACS) for sequences in run-length encoded format, reducing computational complexity and enabling alignment-free phylogenetic analysis directly on compressed data.

Contribution

The paper presents the first algorithm for computing ACS directly on run-length encoded sequences with improved time complexity.

Findings

ACS can be computed in O(N log N) time on RLE sequences

The algorithm operates in O(N) space, proportional to compressed data size

Enables efficient phylogeny reconstruction from compressed sequences

Abstract

The Average Common Substring (ACS) is a popular alignment-free distance measure for phylogeny reconstruction. The ACS can be computed in O(n) space and time, where n=x+y is the input size. The compressed string matching is the study of string matching problems with the following twist: the input data is in a compressed format and the underling task must be performed with little or no decompression. In this paper, we revisit the ACS problem under this paradigm where the input sequences are given in their run-length encoded format. We present an algorithm to compute ACS(X,Y) in O(Nlog N) time using O(N) space, where N is the total length of sequences after run-length encoding.