The Complexity of Scheduling for p-norms of Flow and Stretch

We consider computing optimal k-norm preemptive schedules of jobs that arrive over time. In particular, we show that computing the optimal k-norm of flow schedule, is strongly NP-hard for k in (0, 1) and integers k in (1, infinity). Further we show that computing the optimal k-norm of stretch schedule, is strongly NP-hard for k in (0, 1) and integers k in (1, infinity).Comment: Conference version accepted to IPCO 201

rrnDB: documenting the number of rRNA and tRNA genes in bacteria and archaea

A dramatic exception to the general pattern of single-copy genes in bacterial and archaeal genomes is the presence of 1–15 copies of each ribosomal RNA encoding gene. The original version of the Ribosomal RNA Database (rrnDB) cataloged estimates of the number of 16S rRNA-encoding genes; the database now includes the number of genes encoding each of the rRNAs (5S, 16S and 23S), an internally transcribed spacer region, and the number of tRNA genes. The rrnDB has been used largely by microbiologists to predict the relative rate at which microbial populations respond to favorable growth conditions, and to interpret 16S rRNA-based surveys of microbial communities. To expand the functionality of the rrnDB (http://ribosome.mmg.msu.edu/rrndb/index.php), the search engine has been redesigned to allow database searches based on 16S rRNA gene copy number, specific organisms or taxonomic subsets of organisms. The revamped database also computes average gene copy numbers for any collection of entries selected. Curation tools now permit rapid updates, resulting in an expansion of the database to include data for 785 bacterial and 69 archaeal strains. The rrnDB continues to serve as the authoritative, curated source that documents the phylogenetic distribution of rRNA and tRNA genes in microbial genomes

Online Non-clairvoyant Scheduling to Simultaneously Minimize All Convex Functions

We consider scheduling jobs online to minimize the objective i∈[n] wig(Ci − ri), where wi is the weight of job i, ri is its release time, Ci is its completion time and g is any non-decreasing convex function. Previously, it was known that the clairvoyant algorithm Highest-Density-First (HDF) is (2 + ɛ)-speed O(1)-competitive for this objective on a single machine for any fixed 0 < ɛ < 1 [21]. We show the first non-trivial results for this problem when g is not concave and the algorithm must be non-clairvoyant. More specifically, our results include: • A (2 + ɛ)-speed O(1)-competitive non-clairovyant algorithm on a single machine for all non-decreasing convex g, matching the performance of HDF for any fixed 0 < ɛ < 1. • A (3 + ɛ)-speed O(1)-competitive non-clairovyant algorithm on multiple identical machines for all non-decreasing convex g for any fixed 0 < ɛ < 1. Our positive result on multiple machines is the first non-trivial one even when the algorithm is clairvoyant. Interestingly, all performance guarantees above hold for all non-decreasing convex functions g simultaneously. We supplement our positive results by showing any algorithm that is oblivious to g is not O(1)-competitive with speed less than 2 on a single machine. Further, any non-clairvoyent algorithm that knows the function g cannot be O(1)-competitive with speed less than √ 2 on a single on m identical machines. machine or speed less than 2 − 1 m