Online Bin Covering: Expectations vs. Guarantees

Bin covering is a dual version of classic bin packing. Thus, the goal is to cover as many bins as possible, where covering a bin means packing items of total size at least one in the bin. For online bin covering, competitive analysis fails to distinguish between most algorithms of interest; all "reasonable" algorithms have a competitive ratio of 1/2. Thus, in order to get a better understanding of the combinatorial difficulties in solving this problem, we turn to other performance measures, namely relative worst order, random order, and max/max analysis, as well as analyzing input with restricted or uniformly distributed item sizes. In this way, our study also supplements the ongoing systematic studies of the relative strengths of various performance measures. Two classic algorithms for online bin packing that have natural dual versions are Harmonic and Next-Fit. Even though the algorithms are quite different in nature, the dual versions are not separated by competitive analysis. We make the case that when guarantees are needed, even under restricted input sequences, dual Harmonic is preferable. In addition, we establish quite robust theoretical results showing that if items come from a uniform distribution or even if just the ordering of items is uniformly random, then dual Next-Fit is the right choice.Comment: IMADA-preprint-c

The Advice Complexity of a Class of Hard Online Problems

The advice complexity of an online problem is a measure of how much knowledge of the future an online algorithm needs in order to achieve a certain competitive ratio. Using advice complexity, we define the first online complexity class, AOC. The class includes independent set, vertex cover, dominating set, and several others as complete problems. AOC-complete problems are hard, since a single wrong answer by the online algorithm can have devastating consequences. For each of these problems, we show that $\log\left(1+(c-1)^{c-1}/c^{c}\right)n=\Theta (n/c)$ bits of advice are necessary and sufficient (up to an additive term of $O(\log n)$) to achieve a competitive ratio of $c$. The results are obtained by introducing a new string guessing problem related to those of Emek et al. (TCS 2011) and B\"ockenhauer et al. (TCS 2014). It turns out that this gives a powerful but easy-to-use method for providing both upper and lower bounds on the advice complexity of an entire class of online problems, the AOC-complete problems. Previous results of Halld\'orsson et al. (TCS 2002) on online independent set, in a related model, imply that the advice complexity of the problem is $\Theta (n/c)$. Our results improve on this by providing an exact formula for the higher-order term. For online disjoint path allocation, B\"ockenhauer et al. (ISAAC 2009) gave a lower bound of $\Omega (n/c)$ and an upper bound of $O((n\log c)/c)$ on the advice complexity. We improve on the upper bound by a factor of $\log c$. For the remaining problems, no bounds on their advice complexity were previously known.Comment: Full paper to appear in Theory of Computing Systems. A preliminary version appeared in STACS 201

Likelihood of death within one year among a national cohort of hospital inpatients in Scotland

No abstract available

Stable Isotope Enrichment (Δ¹⁵N) in the Predatory Flower Bug (<i>Orius majusculus</i>) Predicts Fitness-Related Differences between Diets

Mass rearing of insects, used both as biological control agents and for food and feed, is receiving increasing attention. Efforts are being made to improve diets that are currently in use, and to identify alternative diets, as is the case with the predatory flower bug (Orius majusculus) and other heteropteran predators, due to the high costs of their current diet, the eggs of the Mediterranean flour moth (E. kuehniella). The assessment of alternative diets may include measurements of the predator&rsquo;s fitness-related traits (development time, weight, etc.), and biochemical analyses such as lipid and protein content in the diet and the insects. However, assessing diet quality via the predator&rsquo;s fitness-related traits is laborious, and biochemical composition is often difficult to relate to the measured traits. Isotope analysis, previously used for diet reconstruction studies, can also serve as a tool for the assessment of diet quality. Here, the variation in discrimination factors or isotope enrichment (&Delta;15N and &Delta;13C) indicates the difference in isotopic ratio between the insect and its diet. In this study, we investigated the link between &Delta;15N and diet quality in the predatory bug Orius majusculus. Three groups of bugs were fed different diets: Ephestia kuehniella eggs, protein-rich Drosophila melanogaster and lipid-rich D. melanogaster. The isotopic enrichment and fitness-related measurements were assessed for each group. Results show a relation between &Delta;15N and fitness-related measurements, which conform to the idea that lower &Delta;15N indicates a higher diet quality