Improved Algorithm for Degree Bounded Survivable Network Design Problem

We consider the Degree-Bounded Survivable Network Design Problem: the objective is to find a minimum cost subgraph satisfying the given connectivity requirements as well as the degree bounds on the vertices. If we denote the upper bound on the degree of a vertex v by b(v), then we present an algorithm that finds a solution whose cost is at most twice the cost of the optimal solution while the degree of a degree constrained vertex v is at most 2b(v) + 2. This improves upon the results of Lau and Singh and that of Lau, Naor, Salavatipour and Singh

Shared features and reciprocal complementation of the Chlamydomonas and Arabidopsis microbiota

Microscopic algae release organic compounds to the region immediately surrounding their cells, known as the phycosphere, constituting a niche for colonization by heterotrophic bacteria. These bacteria take up algal photoassimilates and provide beneficial functions to their host, in a process that resembles the establishment of microbial communities associated with the roots and rhizospheres of land plants. Here, we characterize the microbiota of the model alga Chlamydomonas reinhardtii and reveal extensive taxonomic and functional overlap with the root microbiota of land plants. Using synthetic communities derived from C. reinhardtii and Arabidopsis thaliana, we show that phycosphere and root bacteria assemble into taxonomically similar communities on either host. We show that provision of diffusible metabolites is not sufficient for phycosphere community establishment, which additionally requires physical proximity to the host. Our data suggest the existence of shared ecological principles driving the assembly of the A. thaliana root and C. reinhardtii phycosphere microbiota, despite the vast evolutionary distance between these two photosynthetic organisms