An Efficient Algorithm For Chinese Postman Walk on Bi-directed de Bruijn Graphs

Sequence assembly from short reads is an important problem in biology. It is known that solving the sequence assembly problem exactly on a bi-directed de Bruijn graph or a string graph is intractable. However finding a Shortest Double stranded DNA string (SDDNA) containing all the k-long words in the reads seems to be a good heuristic to get close to the original genome. This problem is equivalent to finding a cyclic Chinese Postman (CP) walk on the underlying un-weighted bi-directed de Bruijn graph built from the reads. The Chinese Postman walk Problem (CPP) is solved by reducing it to a general bi-directed flow on this graph which runs in O(|E|2 log2(|V |)) time. In this paper we show that the cyclic CPP on bi-directed graphs can be solved without reducing it to bi-directed flow. We present a ?(p(|V | + |E|) log(|V |) + (dmaxp)3) time algorithm to solve the cyclic CPP on a weighted bi-directed de Bruijn graph, where p = max{|{v|din(v) - dout(v) > 0}|, |{v|din(v) - dout(v) < 0}|} and dmax = max{|din(v) - dout(v)}. Our algorithm performs asymptotically better than the bidirected flow algorithm when the number of imbalanced nodes p is much less than the nodes in the bi-directed graph. From our experimental results on various datasets, we have noticed that the value of p/|V | lies between 0.08% and 0.13% with 95% probability

Assessing the benefits of using mate-pairs to resolve repeats in de novo short-read prokaryotic assemblies

<p>Abstract</p> <p>Background</p> <p>Next-generation sequencing technologies allow genomes to be sequenced more quickly and less expensively than ever before. However, as sequencing technology has improved, the difficulty of <it>de novo </it>genome assembly has increased, due in large part to the shorter reads generated by the new technologies. The use of mated sequences (referred to as mate-pairs) is a standard means of disambiguating assemblies to obtain a more complete picture of the genome without resorting to manual finishing. Here, we examine the effectiveness of mate-pair information in resolving repeated sequences in the DNA (a paramount issue to overcome). While it has been empirically accepted that mate-pairs improve assemblies, and a variety of assemblers use mate-pairs in the context of repeat resolution, the effectiveness of mate-pairs in this context has not been systematically evaluated in previous literature.</p> <p>Results</p> <p>We show that, in high-coverage prokaryotic assemblies, libraries of short mate-pairs (about 4-6 times the read-length) more effectively disambiguate repeat regions than the libraries that are commonly constructed in current genome projects. We also demonstrate that the best assemblies can be obtained by 'tuning' mate-pair libraries to accommodate the specific repeat structure of the genome being assembled - information that can be obtained through an initial assembly using unpaired reads. These results are shown across 360 simulations on 'ideal' prokaryotic data as well as assembly of 8 bacterial genomes using SOAPdenovo. The simulation results provide an upper-bound on the potential value of mate-pairs for resolving repeated sequences in real prokaryotic data sets. The assembly results show that our method of tuning mate-pairs exploits fundamental properties of these genomes, leading to better assemblies even when using an off -the-shelf assembler in the presence of base-call errors.</p> <p>Conclusions</p> <p>Our results demonstrate that dramatic improvements in prokaryotic genome assembly quality can be achieved by tuning mate-pair sizes to the actual repeat structure of a genome, suggesting the possible need to change the way sequencing projects are designed. We propose that a two-tiered approach - first generate an assembly of the genome with unpaired reads in order to evaluate the repeat structure of the genome; then generate the mate-pair libraries that provide most information towards the resolution of repeats in the genome being assembled - is not only possible, but likely also more cost-effective as it will significantly reduce downstream manual finishing costs. In future work we intend to address the question of whether this result can be extended to larger eukaryotic genomes, where repeat structure can be quite different.</p