# On Algorithmic Complexity of Biomolecular Sequence Assembly Problem

In twitter, we noticed this paper with the same title as of this post. It is written by G. Narzisi, Bud Mishra and Michael Schatz and is accepted by 1st International Conference on Algorithms for Computational Biology, AlCoB 2014 to be held in Tarragona, Spain. Michael Schatz is an expert in genome assembly and we covered his work several times.

The paper can be best described as a review or synthesis of existing ideas on sequence assembly.

Because of its connection to the well-known NP-complete shortest superstring combinatorial optimization problem, the Sequence Assembly Problem (SAP) has been formulated in simple and sometimes unrealistic string and graph-theoretic frameworks. This paper revisits this problem by re-examining the relationship between the most common formulations of the SAP and their computational tractability under different theoretical frameworks. For each formulation we show examples of logically-consistent candidate solutions which are nevertheless unfeasible in the context of the underlying biological problem. This material is hoped to be valuable to theoreticians as they develop new formulations of SAP as well as of guidance to developers of new pipelines and algorithms for sequence assembly and variant detection.

It discusses shortest superstring problem, de Bruijn graph and overlap graph. That is along the line of traditional way to discuss genome assembly algorithms. Unfortunately, we do not like the paper for two reasons.

(a) The paper fails to cover the fourth chain of developments starting from Batzoglou’s MIT thesis, going into ARACHNE and later integrated into R. Li’s human paper and SPAdes, and that is the incorporation of mate pairs. Incorporation of paired reads increases the effective read length and thus allows easier resolution of repeats. In fact, R. Li’s human paper nicely discussed statistical analysis of distance between repeats in human genome and that analysis is possibly the reason behind BGI’s subsequent experimental strategy of building longer and longer mate pairs. Similarly, Pevzner made significant conceptual improvement in his de Bruijn graph (Euler) methodology, when his SPAdes group came up with rectangular graphs to incorporate mate pairs. Without having that conceptual block being added, the readers are getting incomplete picture of algorithmic development so far.

(b) The paper fails to cover the statistical aspect of sequence assembly (maximum likelihood estimation in Kececioglu’s thesis and or distance statistics in SPAdes paper) and presents the assembly problem in purely computer science terms (NP-complete). The abstract says -

For each formulation we show examples of logically-consistent candidate solutions which are nevertheless unfeasible in the context of the underlying biological problem.

“Logically-consistent” is code-word for mathematically neat but practically unrealistic solution. For example, a mathematically neat quadratic equation can find that a person weighs negative. In the same vein, an elegant computer algorithm (mathematical construct) can obtain hundreds of cool and unrealistic solution.

The reason we say all these is because we believe the authors wrote the paper for a computer science audience and tried to pose the problem in terms of what is known by such an audience and moving outward. In our opinion, they would have done their audience justice by first presenting all experimental tools and limitations (i.e. (i) what a typical genome is like, (ii) the sequencing methods) and then posing various algorithmic ways to approximate that reality.

As always, we encourage our readers to present their thoughts and express disagreement with us.