Some applications of the McCreight-Meyer algorithm in abstract complexity theory

AbstractThe McCreight-Meyer algorithm is a priority-queue construction from abstract recursion theory which was designed for the proof of the so-called Naming or Honesty theorem. We explain the ideas behind the algorithm, pointing at its behaviour as a “closure operator” and obtaining various known and new results as corollaties of more general assertions

Prospects and limitations of full-text index structures in genome analysis

The combination of incessant advances in sequencing technology producing large amounts of data and innovative bioinformatics approaches, designed to cope with this data flood, has led to new interesting results in the life sciences. Given the magnitude of sequence data to be processed, many bioinformatics tools rely on efficient solutions to a variety of complex string problems. These solutions include fast heuristic algorithms and advanced data structures, generally referred to as index structures. Although the importance of index structures is generally known to the bioinformatics community, the design and potency of these data structures, as well as their properties and limitations, are less understood. Moreover, the last decade has seen a boom in the number of variant index structures featuring complex and diverse memory-time trade-offs. This article brings a comprehensive state-of-the-art overview of the most popular index structures and their recently developed variants. Their features, interrelationships, the trade-offs they impose, but also their practical limitations, are explained and compared

External-Memory Dictionaries with Worst-Case Update Cost

The Bϵ-tree [Brodal and Fagerberg 2003] is a simple I/O-efficient external-memory-model data structure that supports updates orders of magnitude faster than B-tree with a query performance comparable to the B-tree: for any positive constant ϵ \u3c 1 insertions and deletions take O(B11-ϵ logB N) time (rather than O(logB N) time for the classic B-tree), queries take O(logB N) time and range queries returning k items take O(logB N + Bk) time. Although the Bϵ-tree has an optimal update/query tradeoff, the runtimes are amortized. Another structure, the write-optimized skip list, introduced by Bender et al. [PODS 2017], has the same performance as the Bϵ-tree but with runtimes that are randomized rather than amortized. In this paper, we present a variant of the Bϵ-tree with deterministic worst-case running times that are identical to the original’s amortized running times

Data structures

We discuss data structures and their methods of analysis. In particular, we treat the unweighted and weighted dictionary problem, self-organizing data structures, persistent data structures, the union-find-split problem, priority queues, the nearest common ancestor problem, the selection and merging problem, and dynamization techniques. The methods of analysis are worst, average and amortized case

ecoPrimers: inference of new DNA barcode markers from whole genome sequence analysis

Using non-conventional markers, DNA metabarcoding allows biodiversity assessment from complex substrates. In this article, we present ecoPrimers, a software for identifying new barcode markers and their associated PCR primers. ecoPrimers scans whole genomes to find such markers without a priori knowledge. ecoPrimers optimizes two quality indices measuring taxonomical range and discrimination to select the most efficient markers from a set of reference sequences, according to specific experimental constraints such as marker length or specifically targeted taxa. The key step of the algorithm is the identification of conserved regions among reference sequences for anchoring primers. We propose an efficient algorithm based on data mining, that allows the analysis of huge sets of sequences. We evaluate the efficiency of ecoPrimers by running it on three different sequence sets: mitochondrial, chloroplast and bacterial genomes. Identified barcode markers correspond either to barcode regions already in use for plants or animals, or to new potential barcodes. Results from empirical experiments carried out on a promising new barcode for analyzing vertebrate diversity fully agree with expectations based on bioinformatics analysis. These tests demonstrate the efficiency of ecoPrimers for inferring new barcodes fitting with diverse experimental contexts. ecoPrimers is available as an open source project at: http://www.grenoble.prabi.fr/trac/ecoPrimers