Modified Classical Graph Algorithms for the DNA Fragment Assembly Problem

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.

DNA Paired Fragment Assembly Using Graph Theory

“…Using the overlaps as edges, a directed graph has been obtained, and we could build a set of contigs improving the N50 [8] of the previous release [17]. The interval of the paired fragments was a critical factor in our success.…”

“…Several models have been developed, and these have had variable outcomes with respect to the algorithm's complexity and efficiency and the quality of the results in the assembled DNA. The algorithms based on graph theory include de Bruijn graphs [13], Eulerian paths [10], Hamiltonian paths [10] and Depth-First search (DFS) [17].…”

“…In this publication, taking Mallén et al [17] as a starting point, we developed a new algorithm working with the paired fragments (two records identified by "/1" and "/2", respectively, conforming to an interval of the sequence of DNA) resulting from the sequencing results of the Illumina equipment. In our initial tests, we found some contigs that were not located in the published genome for the same organism, even though these contigs were properly obtained.…”

“…Applying heuristics and algorithms, they obtained optimal solutions for several commonly used benchmarks, and for the first time, a real-world problem was solved by using optimization. Using graph theory and setting the appropriate objective functions, Mallén et al [17] developed a new assembly method from the perspective of a directed graph, looking for the reduction of the algorithm's complexity.…”

“…To obtain the overlaps between DNA fragments, we used a Trie [17]. Using the overlaps as edges, a directed graph has been obtained, and we could build a set of contigs improving the N50 [8] of the previous release [17].…”