Scaffold Filling Research Articles

Algorithms and Hardness for Scaffold Filling to Maximize Increased Duo-Preservations.

Scaffold filling is a critical step in DNA assembly. Its basic task is to fill the missing genes (fragments) into an incomplete genome (scaffold) to make it similar to the reference genome. There have been a lot of work under distinct measurements in the literature of genome comparison. For genomes with gene duplications, common string partition reveals the similarity more precisely, since it constructs a one-to-one correspondence between the same segments in the two genomes. In this paper, we adopt duo-preservation as the measurement, which is the complement of common string partition, i.e., the number of duo-preservations added to the number of common strings is exactly the length of a genome. Towards a proper scaffold filling, we just focus on the increased duo-preservations. This problem is called scaffold filling to maximize increased duo-preservations (abbr. SF-MIDP). We show that SF-MIDP is solvable in linear time for a simple version where all the genes of the scaffold are matched in a block-matching, but MAX SNP-complete for the general version, and cannot be approximated within [Formula: see text]. Moreover, we present a basic approximation algorithm of factor 2, by which the optimal solution can be described in a new way, and then, improve the approximation factor to [Formula: see text] via a greedy method.

On the solution bound of two-sided scaffold filling

In this paper, we propose an algorithm which approximates the Two-Sided Scaffold Filling problem to a performance ratio 1.4+ε. This is achieved through a deep investigation of the optimal solution structure of Two-Sided Scaffold Filling. We make use of a relevant graph aiming at a solution of a Two-Sided Scaffold Filling instance, and evaluate the optimal solution value by the number of connected components in this graph. We show that an arbitrary optimal solution can be transformed into one whose relevant graph admits connected components that are available to compare with the solution of our algorithm in terms of their values. The performance ratio 1.4+ε is obtained by comparing the bound of such an optimal solution with the solution of our algorithm.

A new approximation algorithm for contig-based genomic scaffold filling

Genomic Scaffold Filling problem forms an important class of problems, and has been paid lots of attention in the literature. In this paper, we study one of the Genomic Scaffold Filling problems, called One-sided-GSF-max-BC problem. In this paper, we give a new approximation algorithm for the problem. For any given instance of the One-sided-GSF-max-BC problem, auxiliary graphs are constructed based on the given instance and the relation between maximum matching in auxiliary graphs and optimal solution is studied, which results in an approximation algorithm with ratio 2.57.

A 1.5-Approximation Algorithm for Two-Sided Scaffold Filling

The scaffold filling problem aims to set up the whole genomes by filling those missing genes into the scaffolds to optimize a similarity measure of genomes. A typical and frequently used measure for the similarity of two genomes is the number of common adjacencies. One-sided scaffold filling is given by a scaffold and a whole genome, and asks to fill the missing genes into that scaffold to result in such a genome that the number of common adjacencies between it and the given genome is maximized. Two-sided scaffold filling is given by two scaffolds, and asks to fill the missing genes into those two scaffolds respectively to result in such two genomes that the number of common adjacencies between them is maximized. One-sided scaffold filling can be approximated to $$\frac{5}{4}$$54 by now. However, the algorithmic progress for two-sided scaffold filling seems rare. What we know for two-sided scaffold filling is a 2-approximation algorithm by now. In this paper, we propose a new algorithm for two-sided scaffold filling which can achieve a performance ratio of $$\frac{3}{2}$$32 in $$O(N^3)$$O(N3) time, where $$N$$N is the number of genes in an output genome. An example can be given to show that the performance ratio $$\frac{3}{2}$$32 for this algorithm is actually tight.

An Improved Approximation Algorithm for Scaffold Filling to Maximize the Common Adjacencies

Scaffold filling is a new combinatorial optimization problem in genome sequencing. The one-sided scaffold filling problem can be described as given an incomplete genome I and a complete (reference) genome G, fill the missing genes into I such that the number of common (string) adjacencies between the resulting genome I' and G is maximized. This problem is NP-complete for genome with duplicated genes and the best known approximation factor is 1.33, which uses a greedy strategy. In this paper, we prove a better lower bound of the optimal solution, and devise a new algorithm by exploiting the maximum matching method and a local improvement technique, which improves the approximation factor to 1.25. For genome with gene repetitions, this is the only known NP-complete problem which admits an approximation with a small constant factor (less than 1.5).

Scaffold Filling under the Breakpoint and Related Distances

Motivated by the trend of genome sequencing without completing the sequence of the whole genomes, a problem on filling an incomplete multichromosomal genome (or scaffold) I with respect to a complete target genome G was studied. The objective is to minimize the resulting genomic distance between I' and G, where I' is the corresponding filled scaffold. We call this problem the onesided scaffold filling problem. In this paper, we conduct a systematic study for the scaffold filling problem under the breakpoint distance and its variants, for both unichromosomal and multichromosomal genomes (with and without gene repetitions). When the input genome contains no gene repetition (i.e., is a fragment of a permutation), we show that the two-sided scaffold filling problem (i.e., G is also incomplete) is polynomially solvable for unichromosomal genomes under the breakpoint distance and for multichromosomal genomes under the genomic (or DCJ--Double-Cut-and-Join) distance. However, when the input genome contains some repeated genes, even the one-sided scaffold filling problem becomes NP-complete when the similarity measure is the maximum number of adjacencies between two sequences. For this problem, we also present efficient constant-factor approximation algorithms: factor-2 for the general case and factor 1.33 for the one-sided case.