Abstract
DNA fragment assembly represents an important challenge to the development of efficient and practical algorithms due to the large number of elements to be assembled. In this study, we present some graph theoretical linear time algorithms to solve the problem. To achieve linear time complexity, a heap with constant time operations was developed, for the special case where the edge weights are integers and do not depend on the problem size. The experiments presented show that modified classical graph theoretical algorithms can solve the DNA fragment assembly problem efficiently.
Highlights
Since its discovery by Watson and Crick [1], the importance of DNA to biology, medicine and human kind has been evident
It is known that the DNA fragment assembly problem is NP-hard (Non-deterministic Polynomial time hard), since it can be reduced from the shortest common superstring problem [14]; in practice, we must only use linear time algorithms, even if by doing so we sacrifice correctness and obtain only an approximate solution
The DNA fragment assembly problem can be transformed into a directed graph: we need to find a sequence of fragments where each one is always the prefix of the one
Summary
Since its discovery by Watson and Crick [1], the importance of DNA to biology, medicine and human kind has been evident. A chain occurs in the real data is much larger than the expected value according to a simple probabilistic model Despite these anomalies and some others, some of the parameters that are used in the assembly of fragments, such as the minimum number of bases that an overlap must have to be considered important, have an empirical basis [5]. If we consider the number of fragments to be sequenced with newer technologies, we need to assemble three to four million fragments to sequence a bacterium, while using long reads, only 50,000 fragments were enough These are really bad news due to the combinatorial nature of the solutions to the problem. The remainder of this paper is organized as follows: Section 2 provides the basic ideas on the use of graph theory for the solution of DNA sequencing problems; Section 3 explains those algorithms that are necessary to tackle the problem; Section 4 illustrates the use of our algorithms on real life problem benchmarks; and, in Section 5, we give our conclusions and future work
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