Efficient Implementation & Application of Maximal String Covering Algorithm

Abstract

This thesis describes the development and application of the new software MAXCOVER that computes maximal covers and non-extendible repeats (a.k.a. “maximal repeats”).

A string is a finite array x[1..n] of elements chosen from a set of totally ordered symbols called an alphabet. A repeat is a substring that occurs at least twice in x. A repeat is left/right extendible if every occurrence is preceded/followed by the same symbol; otherwise, it is non-left/non-right extendible (NLE/NRE). A non-extendible (NE) repeat is both NLE and NRE. A repeat covers a position i if x[i] lies within the repeat. A maximal cover (a.k.a. “optimal cover”) is a repeat that covers the most positions in x.

For simplicity, we first describe a quadratic O(n2) implementation of MAXCOVER to compute all maximal covers of a given string based on the pseudocode given in [1]. Then, we consider the logarithmic O(n log n) pseudocode in [1], in which we identify several errors. We leave a complete correction and implementation for future work. Instead, we propose two improved quadratic algorithms that, shown through experiments, will execute in linear time for the average case.

We perform a benchmark evaluation of MAXCOVER’s performance and demonstrate its value to biologists in the protein context [2]. To do so, we develop an extension of MAXCOVER for the closely related task of computing NE repeats. Then, we compare MAXCOVER to the repeat-match feature of the well-known MUMmer software [3] (600+ citations). We determine that MAXCOVER is an order-of-magnitude faster than MUMmer with much lower space requirements. We also show that MAXCOVER produces a more compact, exact, and user-friendly output that specifies the repeats.

Availability: Open source code, binaries, and test data are available on Github at https://github.com/hollykoponen/MAXCOVER. Currently runs on Linux, untested on other OS.