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The Average Common Substring (ACS) is a popular alignment-free distancemeasure for phylogeny reconstruction. The ACS can be computed in O(n) space andtime, where n=x+y is the input size. The compressed string matching is thestudy of string matching problems with the following twist: the input data isin a compressed format and the underling task must be performed with little orno decompression. In this paper, we revisit the ACS problem under this paradigmwhere the input sequences are given in their run-length encoded format. Wepresent 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.

On Computing Average Common Substring Over Run Length Encoded Sequences