Contig assembly is the first stage that most assemblers solve when reconstructing a genome from a set of reads. Its output consists of contigs -- a set of strings that are promised to appear in any genome that could have generated the reads. From the introduction of contigs 20 years ago, assemblers have tried to obtain longer and longer contigs, but the following question was never solved: given a genome graph @math (e.g. a de Bruijn, or a string graph), what are all the strings that can be safely reported from @math as contigs? In this paper we finally answer this question, and also give a polynomial time algorithm to find them. Our experiments show that these strings, which we call omnitigs, are 66 to 82 longer on average than the popular unitigs, and 29 of dbSNP locations have more neighbors in omnitigs than in unitigs.
Abstract In recent years, a flurry of new DNA sequencing technologies have altered the landscape of genomics, providing a vast amount of sequence information at a fraction of the costs that were previously feasible. The task of assembling these sequences into a genome has, however, still remained an algorithmic challenge that is in practice answered by heuristic solutions. In order to design better assembly algorithms and exploit the characteristics of sequence data from new technologies, we need an improved understanding of the parametric complexity of the assembly problem. In this article, we provide a first theoretical study in this direction, exploring the connections between repeat complexity, read lengths, overlap lengths and coverage in determining the “hard” instances of the assembly problem. Our work suggests at least two ways in which existing assemblers can be extended in a rigorous fashion, in addition to delineating directions for future theoretical investigations. Abstract An accurate genome sequence of a desired species is now a pre-requisite for genome research. An important step in obtaining a high-quality genome sequence is to correctly assemble short reads into longer sequences accurately representing contiguous genomic regions. Current sequencing technologies continue to offer increases in throughput, and corresponding reductions in cost and time. Unfortunately, the benefit of obtaining a large number of reads is complicated by sequencing errors, with different biases being observed with each platform. Although software are available to assemble reads for each individual system, no procedure has been proposed for high-quality simultaneous assembly based on reads from a mix of different technologies. In this paper, we describe a parallel short-read assembler, called Ray, which has been developed to assemble reads obtained from a combination of sequencing platforms. We compared its performance to other assemblers on simulated and real datasets. We used a combin... Preface Introduction Molecular Biology Mathematics, Statistics, and Computer Science Some Molecular Biology DNA and Proteins The Central Dogma The Genetic Code Transfer RNA and Protein Sequences Genes Are Not Simple Biological Chemistry Restriction Maps Introduction Graphs Interval Graphs Measuring Fragment Sizes Multiple Maps Double Digest Problem Classifying Multiple Solutions Algorithms for DDP Algorithms and Complexity DDP is N P-Complete Approaches to DDP Simulated Annealing: TSP and DDP Mapping with Real Data Cloning and Clone Libraries A Finite Number of Random Clones Libraries by Complete Digestion Libraries by Partial Digestion Genomes per Microgram Physical Genome Maps: Oceans, Islands, and Anchors Mapping by Fingerprinting Mapping by Anchoring An Overview of Clone Overlap Putting It Together Sequence Assembly Shotgun Sequencing Sequencing by Hybridization Shotgun Sequencing Revisited Databases and Rapid Sequence Analysis DNA and Protein Sequence Databases A Tree Representation of a Sequence Hashing a Sequence Repeats in a Sequence Sequence Comparison by Hashing Sequence Comparison with at most l Mismatches Sequence Comparison by Statistical Content Dynamic Programming Alignment of Two Sequences The Number of Alignments Shortest and Longest Paths in a Network Global Distance Alignment Global Similarity Alignment Fitting One Sequence into Another Local Alignment and Clumps Linear Space Algorithms Tracebacks Inversions Map Alignment Parametric Sequence Comparisons Multiple Sequence Alignment The Cystic Fibrosis Gene Dynamic Programming in r-Dimensions Weighted-Average Sequences Profile Analysis Alignment by Hidden Markov Models Consensus Word Analysis Probability and Statistics for Sequence Alignment Global Alignment Local Alignment Extreme Value Distributions The Chein-Stein Method Poisson Approximation and Long Matches Sequence Alignment with Scores Probability and Statistics for Sequence Patterns A Central Limit Theorem Nonoverlapping Pattern Counts Poisson Approximation Site Distributions RNA Secondary Structure Combinatorics Minimum Free-energy Structures Consensus folding Trees and Sequences Trees Distance Parsimony Maximum Likelihood Trees Sources and Perspectives Molecular Biology Physical Maps and Clone Libraries Sequence Assembly Sequence Comparisons Probability and Statistics RNA Secondary Structure Trees and Sequences References Problem Solutions and Hints Mathematical Notation Algorithm Index Author Index Subject Index