An EPTAS for Cardinality Constrained Multiple Knapsack via Iterative Randomized Rounding

We study the Uniform Cardinality Constrained Multiple Knapsack problem (CMK), a natural generalization of Multiple Knapsack with applications ranging from cloud computing to radio networks. The input is a set of items, each has a value and a weight, and a set of uniform capacity bins. The goal is to assign a subset of the items of maximum total value to the bins such that $(i)$ the capacity of any bin is not exceeded, and $(ii)$ the number of items assigned to each bin satisfies a given cardinality constraint. The best known approximation ratio for CMK is $1-\frac{\ln (2)}{2} -\epsilon \approx 0.653$, which follows from a result for a generalization of the problem. Our main contribution is an efficient polynomial time approximation scheme (EPTAS) for CMK. This essentially resolves the complexity status of the problem, since the existence of a fully polynomial time approximation scheme (FPTAS) is ruled out. Our technique is based on the following simple algorithm: in each iteration, solve a configuration linear program (LP) of the problem; then, sample configurations (i.e., feasible subsets of items for a single bin) according to a distribution specified by the LP solution. The algorithm terminates once each bin is assigned a configuration. We believe that our generic technique may lead to efficient approximations for other assignment problems

An AFPTAS for Bin Packing with Partition Matroid via a New Method for LP Rounding

We consider the Bin Packing problem with a partition matroid constraint. The input is a set of items of sizes in [0,1], and a partition matroid over the items. The goal is to pack the items in a minimum number of unit-size bins, such that each bin forms an independent set in the matroid. This variant of classic Bin Packing has natural applications in secure storage on the Cloud, as well as in equitable scheduling and clustering with fairness constraints. Our main result is an asymptotic fully polynomial-time approximation scheme (AFPTAS) for Bin Packing with a partition matroid constraint. This scheme generalizes the known AFPTAS for Bin Packing with Cardinality Constraints and improves the existing asymptotic polynomial-time approximation scheme (APTAS) for Group Bin Packing, which are both special cases of Bin Packing with partition matroid. We derive the scheme via a new method for rounding a (fractional) solution for a configuration-LP. Our method uses this solution to obtain prototypes, in which items are interpreted as placeholders for other items, and applies fractional grouping to modify a fractional solution (prototype) into one having desired integrality properties

Budgeted Matroid Maximization: a Parameterized Viewpoint

We study budgeted variants of well known maximization problems with multiple matroid constraints. Given an $\ell$-matchoid \cm on a ground set $E$, a profit function $p:E \rightarrow \mathbb{R}_{\geq 0}$, a cost function $c:E \rightarrow \mathbb{R}_{\geq 0}$, and a budget $B \in \mathbb{R}_{\geq 0}$, the goal is to find in the $\ell$-matchoid a feasible set $S$ of maximum profit $p(S)$ subject to the budget constraint, i.e., $c(S) \leq B$. The {\em budgeted $\ell$-matchoid} (BM) problem includes as special cases budgeted $\ell$-dimensional matching and budgeted $\ell$-matroid intersection. A strong motivation for studying BM from parameterized viewpoint comes from the APX-hardness of unbudgeted $\ell$-dimensional matching (i.e., $B = \infty$) already for $\ell = 3$. Nevertheless, while there are known FPT algorithms for the unbudgeted variants of the above problems, the {\em budgeted} variants are studied here for the first time through the lens of parameterized complexity. We show that BM parametrized by solution size is $W[1]$-hard, already with a degenerate single matroid constraint. Thus, an exact parameterized algorithm is unlikely to exist, motivating the study of {\em FPT-approximation schemes} (FPAS). Our main result is an FPAS for BM (implying an FPAS for $\ell$-dimensional matching and budgeted $\ell$-matroid intersection), relying on the notion of representative set $-$ a small cardinality subset of elements which preserves the optimum up to a small factor. We also give a lower bound on the minimum possible size of a representative set which can be computed in polynomial time

Coverage and adoption of altmetrics sources in the bibliometric community

Altmetrics, indices based on social media platforms and tools, have recently emerged as alternative means of measuring scholarly impact. Such indices assume that scholars in fact populate online social environments, and interact with scholarly products there. We tested this assumption by examining the use and coverage of social media environments amongst a sample of bibliometricians. As expected, coverage varied: 82% of articles published by sampled bibliometricians were included in Mendeley libraries, while only 28% were included in CiteULike. Mendeley bookmarking was moderately correlated (.45) with Scopus citation. Over half of respondents asserted that social media tools were affecting their professional lives, although uptake of online tools varied widely. 68% of those surveyed had LinkedIn accounts, while Academia.edu, Mendeley, and ResearchGate each claimed a fifth of respondents. Nearly half of those responding had Twitter accounts, which they used both personally and professionally. Surveyed bibliometricians had mixed opinions on altmetrics’ potential 72% valued download counts, while a third saw potential in tracking articles’ influence in blogs, Wikipedia, reference managers, and social media. Altogether, these findings suggest that some online tools are seeing substantial use by bibliometricians, and that they present a potentially valuable source of impact data

Research Blogs and the Discussion of Scholarly Information

The research blog has become a popular mechanism for the quick discussion of scholarly information. However, unlike peer-reviewed journals, the characteristics of this form of scientific discourse are not well understood, for example in terms of the spread of blogger levels of education, gender and institutional affiliations. In this paper we fill this gap by analyzing a sample of blog posts discussing science via an aggregator called ResearchBlogging.org (RB). ResearchBlogging.org aggregates posts based on peer-reviewed research and allows bloggers to cite their sources in a scholarly manner. We studied the bloggers, blog posts and referenced journals of bloggers who posted at least 20 items. We found that RB bloggers show a preference for papers from high-impact journals and blog mostly about research in the life and behavioral sciences. The most frequently referenced journal sources in the sample were: Science, Nature, PNAS and PLoS One. Most of the bloggers in our sample had active Twitter accounts connected with their blogs, and at least 90% of these accounts connect to at least one other RB-related Twitter account. The average RB blogger in our sample is male, either a graduate student or has been awarded a PhD and blogs under his own name

Viral ecogenomics across the Porifera

BackgroundViruses directly affect the most important biological processes in the ocean via their regulation of prokaryotic and eukaryotic populations. Marine sponges form stable symbiotic partnerships with a wide diversity of microorganisms and this high symbiont complexity makes them an ideal model for studying viral ecology. Here, we used morphological and molecular approaches to illuminate the diversity and function of viruses inhabiting nine sponge species from the Great Barrier Reef and seven from the Red Sea.ResultsViromic sequencing revealed host-specific and site-specific patterns in the viral assemblages, with all sponge species dominated by the bacteriophage order Caudovirales but also containing variable representation from the nucleocytoplasmic large DNA virus families Mimiviridae, Marseilleviridae, Phycodnaviridae, Ascoviridae, Iridoviridae, Asfarviridae and Poxviridae. Whilst core viral functions related to replication, infection and structure were largely consistent across the sponge viromes, functional profiles varied significantly between species and sites largely due to differential representation of putative auxiliary metabolic genes (AMGs) and accessory genes, including those associated with herbicide resistance, heavy metal resistance and nylon degradation. Furthermore, putative AMGs varied with the composition and abundance of the sponge-associated microbiome. For instance, genes associated with antimicrobial activity were enriched in low microbial abundance sponges, genes associated with nitrogen metabolism were enriched in high microbial abundance sponges and genes related to cellulose biosynthesis were enriched in species that host photosynthetic symbionts.ConclusionsOur results highlight the diverse functional roles that viruses can play in marine sponges and are consistent with our current understanding of sponge ecology. Differential representation of putative viral AMGs and accessory genes across sponge species illustrate the diverse suite of beneficial roles viruses can play in the functional ecology of these complex reef holobionts

The noise-lovers: cultures of speech and sound in second-century Rome

This chapter provides an examination of an ideal of the ‘deliberate speaker’, who aims to reflect time, thought, and study in his speech. In the Roman Empire, words became a vital tool for creating and defending in-groups, and orators and authors in both Latin and Greek alleged, by contrast, that their enemies produced babbling noise rather than articulate speech. In this chapter, the ideal of the deliberate speaker is explored through the works of two very different contemporaries: the African-born Roman orator Fronto and the Syrian Christian apologist Tatian. Despite moving in very different circles, Fronto and Tatian both express their identity and authority through an expertise in words, in strikingly similar ways. The chapter ends with a call for scholars of the Roman Empire to create categories of analysis that move across different cultural and linguistic groups. If we do not, we risk merely replicating the parochialism and insularity of our sources.Accepted manuscrip