Symmetric Submodular Function Minimization Under Hereditary Family Constraints

We present an efficient algorithm to find non-empty minimizers of a symmetric submodular function over any family of sets closed under inclusion. This for example includes families defined by a cardinality constraint, a knapsack constraint, a matroid independence constraint, or any combination of such constraints. Our algorithm make $O(n^3)$ oracle calls to the submodular function where $n$ is the cardinality of the ground set. In contrast, the problem of minimizing a general submodular function under a cardinality constraint is known to be inapproximable within $o(\sqrt{n/\log n})$ (Svitkina and Fleischer [2008]). The algorithm is similar to an algorithm of Nagamochi and Ibaraki [1998] to find all nontrivial inclusionwise minimal minimizers of a symmetric submodular function over a set of cardinality $n$ using $O(n^3)$ oracle calls. Their procedure in turn is based on Queyranne's algorithm [1998] to minimize a symmetric submodularComment: 13 pages, Submitted to SODA 201

Robust randomized matchings

The following game is played on a weighted graph: Alice selects a matching $M$ and Bob selects a number $k$. Alice's payoff is the ratio of the weight of the $k$ heaviest edges of $M$ to the maximum weight of a matching of size at most $k$. If $M$ guarantees a payoff of at least $\alpha$ then it is called $\alpha$-robust. In 2002, Hassin and Rubinstein gave an algorithm that returns a $1/\sqrt{2}$-robust matching, which is best possible. We show that Alice can improve her payoff to $1/\ln(4)$ by playing a randomized strategy. This result extends to a very general class of independence systems that includes matroid intersection, b-matchings, and strong 2-exchange systems. It also implies an improved approximation factor for a stochastic optimization variant known as the maximum priority matching problem and translates to an asymptotic robustness guarantee for deterministic matchings, in which Bob can only select numbers larger than a given constant. Moreover, we give a new LP-based proof of Hassin and Rubinstein's bound

Distribution and genetic variability of Staphylinidae across a gradient of anthropogenically influenced insular landscapes

This paper describes the distribution and genetic variability of rove beetles (Coleoptera Staphylinidae) in anthropogenically influenced insular landscapes. The study was conducted in the Azores archipelago, characterized by high anthropogenic influence and landscape fragmentation. Collections were made in five islands, from eight habitats, along a gradient of anthropogenic influence. The species of Staphylinidae from the Azores collected for this study were widely distributed and showed low habitat fidelity. Rove beetle richness was associated with anthropogenic influence and habitat type, increasing from less to more anthropogenic impacted habitats. However, genetic diversity of profiled species (i.e. with three or more specimens per species/habitat) does not seem affected by anthropogenic influence in the different habitat types, isolation or landscape fragmentation. COI haplotypes were, as a rule, not exclusive to a given island or habitat. High level of genetic divergence and nucleotide saturation was found in closely related morphological designated species, demonstrating possible disparities between currently defined taxonomic units based on morphology and molecular phylogenies of Staphylinidae. This study found evidence of cryptic speciation in the Atheta fungi (Gravenhorst) species complex which had thus far remained undetected. Similar trends were found for Oligota parva Kraatz, Oxytelus sculptus Gravenhorst, Oligota pumilio Kiesenwetter. Previous studies with lower taxonomical resolution may have underestimated the biotic diversity reported in the Azores in comparison to other Macaronesian archipelagos.info:eu-repo/semantics/publishedVersio