Assignment problem

About: Assignment problem is a research topic. Over the lifetime, 7588 publications have been published within this topic receiving 172820 citations. The topic is also known as: marriage problem.

Two-film brachytherapy reconstruction algorithm.

Abstract: We have developed a new isocentric two‐film reconstruction algorithm for brachytherapy seed and needle implants. The algorithm has no requirements that the two films be orthogonal, symmetric, or even be taken in a transverse plane. In addition, there is no requirement that the two films even have the same number of images. We have found removal of these usual constraints useful for head and neck implants where images are often obscured by patient anatomy. The inherent image matching ambiguities associated with traditional two‐film techniques are minimized by considering the image end points, rather than just the image centroids. For two films, the new algorithm, which considers all image combinations at o n e time, matches all the end‐point images on one film with those on the other, and then reconstructs the end‐point positions of the seeds. The algorithm minimizes the difference between the actual images and the projected images from the reconstructed seeds. The new two‐film image matching problem is shown to be equivalent to the well‐known assignment problem. For an implant of N seeds, this equivalence allows the two‐film problem to be solved by an algorithm (ACM algorithm 548) that scales with a polynomial power of N, rather than N! as is usually assumed. An implant of N seeds can be matched and reconstructed in approximately (N/20)2 s on a VAX 11/780.

Lower bounds for the quadratic assignment problem

Abstract: We investigate the classical Gilmore-Lawler lower bound for the quadratic assignment problem We provide evidence of the difficulty of improving the Gilmore-Lawler bound and develop new bounds by means of optimal reduction schemes Computational results are reported indicating that the new lower bounds have advantages over previous bounds and can be used in a branch-and-bound type algorithm for the quadratic assignment problem

A space and time-efficient index for the compacted colored de Bruijn graph

Abstract: Motivation Indexing reference sequences for search-both individual genomes and collections of genomes-is an important building block for many sequence analysis tasks. Much work has been dedicated to developing full-text indices for genomic sequences, based on data structures such as the suffix array, the BWT and the FM-index. However, the de Bruijn graph, commonly used for sequence assembly, has recently been gaining attention as an indexing data structure, due to its natural ability to represent multiple references using a graphical structure, and to collapse highly-repetitive sequence regions. Yet, much less attention has been given as to how to best index such a structure, such that queries can be performed efficiently and memory usage remains practical as the size and number of reference sequences being indexed grows large. Results We present a novel data structure for representing and indexing the compacted colored de Bruijn graph, which allows for efficient pattern matching and retrieval of the reference information associated with each k-mer. As the popularity of the de Bruijn graph as an index has increased over the past few years, so have the number of proposed representations of this structure. Existing structures typically fall into two categories; those that are hashing-based and provide very fast access to the underlying k-mer information, and those that are space-frugal and provide asymptotically efficient but practically slower pattern search. Our representation achieves a compromise between these two extremes. By building upon minimum perfect hashing and making use of succinct representations where applicable, our data structure provides practically fast lookup while greatly reducing the space compared to traditional hashing-based implementations. Further, we describe a sampling scheme for this index, which provides the ability to trade off query speed for a reduction in the index size. We believe this representation strikes a desirable balance between speed and space usage, and allows for fast search on large reference sequences. Finally, we describe an application of this index to the taxonomic read assignment problem. We show that by adopting, essentially, the approach of Kraken, but replacing k-mer presence with coverage by chains of consistent unique maximal matches, we can improve the space, speed and accuracy of taxonomic read assignment. Availability and implementation pufferfish is written in C++11, is open source, and is available at https://github.com/COMBINE-lab/pufferfish. Supplementary information Supplementary data are available at Bioinformatics online.