QuateXelero : an accelerated exact network motif detection algorithm

Finding motifs in biological, social, technological, and other types of networks has become a widespread method to gain more knowledge about these networks’ structure and function. However, this task is very computationally demanding, because it is highly associated with the graph isomorphism which is an NP problem (not known to belong to P or NP-complete subsets yet). Accordingly, this research is endeavoring to decrease the need to call NAUTY isomorphism detection method, which is the most time-consuming step in many existing algorithms. The work provides an extremely fast motif detection algorithm called QuateXelero, which has a Quaternary Tree data structure in the heart. The proposed algorithm is based on the well-known ESU (FANMOD) motif detection algorithm. The results of experiments on some standard model networks approve the overal superiority of the proposed algorithm, namely QuateXelero, compared with two of the fastest existing algorithms, G-Tries and Kavosh. QuateXelero is especially fastest in constructing the central data structure of the algorithm from scratch based on the input network

The concept of Equality Point.

<p>Positive and negative equality points are illustrated respectively in the left and the right charts. The vertical axis <i>t</i> indicates the total time of algorithms and the horizontal axis <i>r</i> shows the number of random networks used for motif detection.</p

Searching a sample quaternary tree for input string “321”.

<p>Searching starts at the root of the tree. After respectively visiting children 3 and 2 throughout the path, the search finishes in a newly added leaf, corresponding to number 1.</p

Trends of random network census time ratio (left) and Equality Point (right) for undirected networks.

<p>The ratio in the left chart indicates the ratio of average time spent by QuateXelero for census on random networks to the same time required for G-Tries.</p

Experimental Datasets.

<p>Experimental Datasets.</p

Experimental Limitations.

<p>Experimental Limitations.</p

Steps taken during classifying a subgraph which has reached a previously existing leaf in the quaternary tree.

<p>1) The quaternary tree is searched and the corresponding leaf is identified 2) Using the identified leaf’s pointer to the corresponding leaf from binary tree, the latter’s counter is augmented.</p

Algorithm 1.

<p>Algorithm 1.</p

QuateXelero (QX) vs. G-Tries in larger motifs.

<p>5 random networks were used in all experiments. Bolded italic values for Yeast network are estimated with respect to the results in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0068073#pone-0068073-t005" target="_blank">Table 5</a>.</p

Algorithm 2.

<p>Algorithm 2.</p