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.
The number of related assembly papers is vast, and we refer the reader to some surveys @cite_23 @cite_32 . For an empirical evaluation of the correctness of several state-of-the-art assemblers, see @cite_25 . Here, we discuss work on the theoretical underpinnings of assembly.
@cite_25 @cite_32 @cite_23
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Assembly planning and evaluation is an important component of the product design process in which details about how parts of a new product will be put together are formalized. A well designed assembly process should take into account various factors such as optimum assembly time and sequence, tooling and fixture requirements, ergonomics, operator safety, and accessibility, among others. Existing computer-based tools to support virtual assembly either concentrate solely on representation of the geometry of parts and fixtures and evaluation of clearances and tolerances or use simulated human mannequins to approximate human interaction in the assembly process. Virtual reality technology has the potential to support integration of natural human motions into the computer aided assembly planning environment ( in Proc I MECH E Part B J Eng 213(5):461–474, 1999). This would allow evaluations of an assembler’s ability to manipulate and assemble parts and result in reduced time and cost for product design. This paper provides a review of the research in virtual assembly and categorizes the different approaches. Finally, critical requirements and directions for future research are presented. Abstract In which order can a product be assembled or disassembled? How many hands are required? How many degrees of freedom? What parts should be withdrawn to allow the removal of a specified subassembly? To answer such questions automatically, important theoretical issues in geometric reasoning must be addressed. This paper investigates the planning of assembly algorithms specifying (dis) assembly operations on the components of a product and the ordering of these operations. It also presents measures to evaluate the complexity of these algorithms and techniques to estimate the inherent complexity of a product. The central concept underlying these planning and complexity evaluation techniques is that of a “non-directional blocking graph”, a qualitative representation of the internal structure of an assembly product. This representation describes the combinatorial set of parts interactions in polynomial space. It is obtained by identifying physical criticalities where geometric interferences among parts change. It is generated from an input geometric description of the product. The main application considered in the paper is the creation of smart environments to help designers create products that are easier to manufacture and service. Other possible applications include planning for rapid prototyping and autonomous robots. High-level assembly planning systems generate plans for the automated assembly of mechanical products by robots. The sequences to be generated underlie several physical and geometrical constraints, and in addition have to be efficient to increase productivity. The challenges still facing the field are to develop efficient and robust analysis tools, and to develop planners capable of finding optimal or near-optimal sequences rather than just feasible sequences. The presented high level assembly planning system High LAP automatically considers physical and geometrical constraints to generate and to evaluate stable assembly sequences. In this paper we propose a relational assembly model including a CAD description and the specification of features and relations of the assembly components. We use an optional specification of an arbitrary hierarchy of assemblies to speed up and guide the generation of sequences. High LAP evaluates all feasible assembly sequences considering several criteria like separability and manipulability of the generated (sub)assemblies. Furthermore, the necessity of reorientation for a mating operation and parallelism during plan execution are considered. Another important criterion is the stability of the generated (sub)assemblies. Most of the assembly planners developed up to date use heuristical or user-defined criteria to determine assembly stability for plan evaluation. The presented system is the first assembly planning system which automatically determines the range of all stable orientations of an assembly for plan evaluation. Therefore, we introduce a stability metric and an algorithm to calculate all stable orientations of an assembly considering friction. Experimental results are presented to demonstrate the efficiency of our assembly planning system. Abstract This paper presents the application of geometric reasoning to the automatic construction of an assembly partial order from an attributed liaison graph representation of an assembly. The construction is based on the principle of assembly by disassembly and on the extraction of preferred subassemblies. On the basis of accessibility and manipulability criteria, the system first decomposes the given assembly into clusters of mutually inseparable parts. An abstract liaison graph is then generated wherein each cluster of mutually inseparable parts is represented as a supernode. A set of subassemblies is then generated by decomposing the abstract liaison graph into subgraphs, verifying the disassemblability of individual subgraphs, and applying the criteria for selecting preferred subassemblies to the disassemblable subgraphs. The recursive application of this process to the selected subassemblies results in a Hierarchical Partial-Order Graph (HPOG). A HPOG not only provides the precedence relations among assembly operations but also presents the temporal and spatial parallelism for implementing distributed and cooperative assembly. The system is organized under the “cooperative problem solving (CPS)” paradigm.