Lightweight compositional analysis of metagenomes with FracMinHash and minimum metagenome covers

The identification of reference genomes and taxonomic labels from metagenome data underlies many microbiome studies. Here we describe two algorithms for compositional analysis of metagenome sequencing data. We first investigate the FracMinHash sketching technique, a derivative of modulo hash that supports Jaccard containment estimation between sets of different sizes. We implement FracMinHash in the sourmash software, evaluate its accuracy, and demonstrate large-scale containment searches of metagenomes using 700,000 microbial reference genomes. We next frame shotgun metagenome compositional analysis as the problem of finding a minimum collection of reference genomes that "cover" the known k-mers in a metagenome, a minimum set cover problem. We implement a greedy approximate solution using FracMinHash sketches, and evaluate its accuracy for taxonomic assignment using a CAMI community benchmark. Finally, we show that the minimum metagenome cover can be used to guide the selection of reference genomes for read mapping. sourmash is available as open source software under the BSD 3-Clause license at github.com/dib-lab/sourmash/.

On the VC-dimension of half-spaces with respect to convex sets

A family S of convex sets in the plane defines a hypergraph H = (S, E) as follows. Every subfamily S' of S defines a hyperedge of H if and only if there exists a halfspace h that fully contains S' , and no other set of S is fully contained in h. In this case, we say that h realizes S'. We say a set S is shattered, if all its subsets are realized. The VC-dimension of a hypergraph H is the size of the largest shattered set. We show that the VC-dimension for pairwise disjoint convex sets in the plane is bounded by 3, and this is tight. In contrast, we show the VC-dimension of convex sets in the plane (not necessarily disjoint) is unbounded. We provide a quadratic lower bound in the number of pairs of intersecting sets in a shattered family of convex sets in the plane. We also show that the VC-dimension is unbounded for pairwise disjoint convex sets in R^d , for d > 2. We focus on, possibly intersecting, segments in the plane and determine that the VC-dimension is always at most 5. And this is tight, as we construct a set of five segments that can be shattered. We give two exemplary applications. One for a geometric set cover problem and one for a range-query data structure problem, to motivate our findings.

A Tight Bound for Stochastic Submodular Cover

We show that the Adaptive Greedy algorithm of Golovin and Krause achieves an approximation bound of (ln(Q/η)+1) for Stochastic Submodular Cover: here Q is the “goal value” and η is the minimum gap between Q and any attainable utility value Q'<Q. Although this bound was claimed by Golovin and Krause in the original version of their paper, the proof was later shown to be incorrect by Nan & Saligrama. The subsequent corrected proof of Golovin and Krause gives a quadratic bound of (ln(Q/η)+1)2. A bound of 56(ln(Q/η)+1) is implied by work of Im et al. Other bounds for the problem depend on quantities other than Q and η. Our bound restores the original bound claimed by Golovin and Krause, generalizing the well-known (ln m+1) approximation bound on the greedy algorithm for the classical Set Cover problem, where m is the size of the ground set.

Firefighting Equipment Arrangement Optimization for an Offshore Platform Considering Travel Distances

The offshore plant, due to its characteristics, is subject to many restrictions on the material and design of the pipes. Because the design of the firefighting piping depends on the pre-set fire protection design, it is possible to reduce the cost of the piping design by optimizing the arrangement of the firefighting equipment. Existing studies have low accuracy in obtaining service areas under these conditions. In addition, the arrangement optimization problem is generally modeled as a set cover problem (SCP). However, except for the traditional greedy approximation, this problem is not well researched for general solutions. In this paper, first, a modified iterative-deepening search (MIDS), which accurately obtains a service area according to the travel distance in the grid space, is proposed before optimization. Additionally, this paper seeks to define a set cover problem by combining the subsets obtained by MIDS. Second, by using the traditional greedy algorithm, we obtained the initial arrangement of the firefighting equipment. Then, we proposed a method to obtain an approximate optimization solution using a modified greedy method including rearrangement. The validity of the proposed coverage area acquisition and arrangement optimization method is verified by comparing the performance with other algorithms. Finally, this study was applied to the drawings of an actual offshore platform.

Semi-supervised time series classification method for quantum computing

In this paper we develop methods to solve two problems related to time series (TS) analysis using quantum computing: reconstruction and classification. We formulate the task of reconstructing a given TS from a training set of data as an unconstrained binary optimization (QUBO) problem, which can be solved by both quantum annealers and gate-model quantum processors. We accomplish this by discretizing the TS and converting the reconstruction to a set cover problem, allowing us to perform a one-versus-all method of reconstruction. Using the solution to the reconstruction problem, we show how to extend this method to perform semi-supervised classification of TS data. We present results indicating our method is competitive with current semi- and unsupervised classification techniques, but using less data than classical techniques.

A formal approach to finding inconsistencies in a metamodel

Checking the consistency of a metamodel involves finding a valid metamodel instance that provably meets the set of constraints that are defined over the metamodel. These constraints are often specified in Object Constraint Language. Often, a metamodel is inconsistent due to conflicts among the constraints. Existing approaches and tools are typically incapable of pinpointing the conflicting constraints, and this makes it difficult for users to debug and fix their metamodels. In this paper, we present a formal approach for locating conflicting constraints in inconsistent metamodels. Our approach has four distinct features: (1) users can rank individual metamodel features using their own domain-specific knowledge, (2) we transform these ranked features to a weighted maximum satisfiability modulo theories problem and solve it to compute the set of maximum achievable features, (3) we pinpoint the conflicting constraints by solving the set cover problem using a novel algorithm, and (4) we have implemented our approach into a fully automated tool called MaxUSE. Our evaluation results, using our assembled set of benchmarks, demonstrate the scalability of our work and that it is capable of efficiently finding conflicting constraints.