Robust Assignments via Ear Decompositions and Randomized Rounding

Many real-life planning problems require making a priori decisions before all parameters of the problem have been revealed. An important special case of such problem arises in scheduling problems, where a set of tasks needs to be assigned to the available set of machines or personnel (resources), in a way that all tasks have assigned resources, and no two tasks share the same resource. In its nominal form, the resulting computational problem becomes the \emph{assignment problem} on general bipartite graphs. This paper deals with a robust variant of the assignment problem modeling situations where certain edges in the corresponding graph are \emph{vulnerable} and may become unavailable after a solution has been chosen. The goal is to choose a minimum-cost collection of edges such that if any vulnerable edge becomes unavailable, the remaining part of the solution contains an assignment of all tasks. We present approximation results and hardness proofs for this type of problems, and establish several connections to well-known concepts from matching theory, robust optimization and LP-based techniques.Comment: Full version of ICALP 2016 pape

The chloroplast 32 kDa protein is synthesized on thylakoid-bound ribosomes in Chlamydomonas reinhardtii

AbstractA cloned cpDNA fragment containing a portion of the gene for the 32–36 kDa thylakoid protein of Chlamydomonas (polypeptide D-1) was isolated. Hybridization probing of RNA from soluble and membrane fractions of Chlamydomonas showed that the mRNA for D-1 is bound to thylakoid membranes. Run-off translation of thylakoid-bound polysomes (rough thylakoids) with [35S]-methionine yields polypeptide D-1 as the major product. Peptide mapping with S. aureus V-8 protease of D-1 synthesized (1) in vivo, (2) in vitro by rough thylakoids and (3) in the reticulocyte lysate directed by non-polyadenylated RNA showed that D-1 is synthesized as a precursor in the reticulocyte lysate but as the mature polypeptide by rough thylakoids