Microbial diversity is typically characterized by clustering ribosomal RNA (SSU-rRNA) sequences into operational taxonomic units (OTUs). Targeted sequencing of environmental SSU-rRNA markers via PCR may fail to detect OTUs due to biases in priming and amplification. Analysis of shotgun sequenced environmental DNA, known as metagenomics, avoids amplification bias but generates fragmentary, non-overlapping sequence reads that cannot be clustered by existing OTU-finding methods. To circumvent these limitations, we developed PhylOTU, a computational workflow that identifies OTUs from metagenomic SSU-rRNA sequence data through the use of phylogenetic principles and probabilistic sequence profiles. Using simulated metagenomic data, we quantified the accuracy with which PhylOTU clusters reads into OTUs. Comparisons of PCR and shotgun sequenced SSU-rRNA markers derived from the global open ocean revealed that while PCR libraries identify more OTUs per sequenced residue, metagenomic libraries recover a greater taxonomic diversity of OTUs. In addition, we discover novel species, genera and families in the metagenomic libraries, including OTUs from phyla missed by analysis of PCR sequences. Taken together, these results suggest that PhylOTU enables characterization of part of the biosphere currently hidden from PCR-based surveys of diversity?

Classical problems of sorting and searching assume an underlying linear ordering of the objects being compared. In this paper, we study these problems in the context of partially ordered sets, in which some pairs of objects are incomparable. This generalization is interesting from a combinatorial perspective, and it has immediate applications in ranking scenarios where there is no underlying linear ordering, e.g., conference submissions. It also has applications in reconstructing certain types of networks, including biological networks. Our results represent significant progress over previous results from two decades ago by Faigle and Turán. In particular, we present the first algorithm that sorts a width-w poset of size n with query complexity $O(n(w+\log n))$ and prove that this query complexity is asymptotically optimal. We also describe a variant of Mergesort with query complexity $O(wn\log\frac{n}{w})$ and total complexity $O(w^{2}n\log\frac{n}{w})$; an algorithm with the same query complexity was given by Faigle and Turán, but no efficient implementation of that algorithm is known. Both our sorting algorithms can be applied with negligible overhead to the more general problem of reconstructing transitive relations. We also consider two related problems: finding the minimal elements, and its generalization to finding the bottom k “levels,” called the k-selection problem. We give efficient deterministic and randomized algorithms for finding the minimal elements with query complexity and total complexity $O(wn)$. We provide matching lower bounds for the query complexity up to a factor of 2 and generalize the results to the k-selection problem. Finally, we present efficient algorithms for computing a linear extension of a poset and computing the heights of all elements.

Classical problems of sorting and searching assume an underlying linear ordering of the objects being compared. In this paper, we study these problems in the context of partially ordered sets, in which some pairs of objects are incomparable. This generalization is interesting from a combinatorial perspective, and it has immediate applications in ranking scenarios where there is no underlying linear ordering, e.g., conference submissions. It also has applications in reconstructing certain types of networks, including biological networks. Our results represent significant progress over previous results from two decades ago by Faigle and Turán. In particular, we present the first algorithm that sorts a width-w poset of size n with optimal query complexity O(n(w + log n)). We also describe a variant of Mergesort with query complexity and total complexity ; an algorithm with the same query complexity was given by Faigle and Turán, but no efficient implementation of that algorithm is known. Both our sorting algorithms can be applied with negligible overhead to the more general problem of reconstructing transitive relations. We also consider two related problems: finding the minimal elements, and its generalization to finding the bottom k “levels”, called the k-selection problem. We give efficient deterministic and randomized algorithms for finding the minimal elements with O(wn) query and total complexity. We provide matching lower bounds for the query complexity up to a factor of 2 and generalize the results to the k-selection problem. Finally, we present efficient algorithms for computing a linear extension of a poset and computing the heights of all elements.

We consider the problem of positioning data collecting base stations in a sensor network. We show that in general, the choice of positions has a marked influence on the data rate, or equivalently, the power efficiency, of the network. In our model, which is partly motivated by an experimental environmental monitoring system, the optimum data rate for a fixed layout of base stations can be found by a maximum flow algorithm. Finding the optimum layout of base stations, however, turns out to be an NP-complete problem, even in the special case of homogeneous networks. Our analysis of the optimum layout for the special case of the regular grid shows that all layouts that meet certain constraints are equally good. We also consider two classes of random graphs, chosen to model networks that might be realistically encountered, and empirically evaluate the performance of several base station positioning algorithms on instances of these classes. In comparison to manually choosing positions along the periphery of the network or randomly choosing them within the network, the algorithms tested find positions, which significantly improve the data rate and power efficiency of the network.