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New models and algorithms for RNA pseudoknot order assignment

Zok Tomasz, Badura Jan, Swat Sylwester, Figurski Kacper, Popenda Mariusz, Antczak Maciej

International Journal of Applied Mathematics and Computer Science

2020

Vol. 30, no. 2

315--324

The pseudoknot is a specific motif of the RNA structure that highly influences the overall shape and stability of a molecule. It occurs when nucleotides of two disjoint single-stranded fragments of the same chain, separated by a helical fragment, interact with each other and form base pairs. Pseudoknots are characterized by great topological diversity, and their systematic description is still a challenge. In our previous work, we have introduced the pseudoknot order: a new coefficient representing the topological complexity of the pseudoknotted RNA structure. It is defined as the minimum number of base pair set decompositions, aimed to obtain the unknotted RNA structure. We have suggested how it can be useful in the interpretation and understanding of a hierarchy of RNA folding. However, it is not trivial to unambiguously identify pseudoknots and determine their orders in an RNA structure. Therefore, since the introduction of this coefficient, we have worked on the method to reliably assign pseudoknot orders in correspondence to the mechanisms that control the biological process leading to their formation in the molecule. Here, we introduce a novel graph coloring-based model for the problem of pseudoknot order assignment. We show a specialized heuristic operating on the proposed model and an alternative integer programming algorithm. The performance of both approaches is compared with that of state-of-the-art algorithms which so far have been most efficient in solving the problem in question. We summarize the results of computational experiments that evaluate our new methods in terms of classification quality on a representative data set originating from the non-redundant RNA 3D structure repository.

On-line maximum independent set in chordal graphs

Christodoulou G., Zissimopoulos V.

Foundations of Computing and Decision Sciences

2005

Vol. 30, No. 4

283-296

In this paper we deal with the on-line maximum independent set and we propose a probabilistic O(logn)-competitive algorithm for chordal and interval graphs, proving that the same ratio is a lower bound of the problem. The relation of the on-line maximum independent set with the on-line admission control, allows us to obtain as particular case, an O(logn)-competitive algorithm for the on-line admission control in trees and lines. In addition to that, we propose a competitive algorithm for the on-line call admission of subtrees in trees.