Approximation algorithms for stochastic and risk-averse optimization

We present improved approximation algorithms in stochastic optimization. We prove that the multi-stage stochastic versions of covering integer programs (such as set cover and vertex cover) admit essentially the same approximation algorithms as their standard (non-stochastic) counterparts; this improves upon work of Swamy \& Shmoys which shows an approximability that depends multiplicatively on the number of stages. We also present approximation algorithms for facility location and some of its variants in the $2$-stage recourse model, improving on previous approximation guarantees. We give a $2.2975$-approximation algorithm in the standard polynomial-scenario model and an algorithm with an expected per-scenario $2.4957$-approximation guarantee, which is applicable to the more general black-box distribution model.Comment: Extension of a SODA'07 paper. To appear in SIAM J. Discrete Mat

Additional file 14 of Small RNA-seq analysis of single porcine blastocysts revealed that maternal estradiol-17beta exposure does not affect miRNA isoform (isomiR) expression

Table S8. IsomiR analysis. (XLSX 202 kb

Additional file 3 of Small RNA-seq analysis of single porcine blastocysts revealed that maternal estradiol-17beta exposure does not affect miRNA isoform (isomiR) expression

Table S1. Filtering details for potential miRNAs. (XLSX 73 kb

Additional file 5 of Small RNA-seq analysis of single porcine blastocysts revealed that maternal estradiol-17beta exposure does not affect miRNA isoform (isomiR) expression

Figure S3. Library sizes of mapped reads per RNA type. (PNG 617 kb

Additional file 10 of Small RNA-seq analysis of single porcine blastocysts revealed that maternal estradiol-17beta exposure does not affect miRNA isoform (isomiR) expression

Table S4. EdgeR result of all comparisons on isomiR level. (XLSX 32902 kb

Additional file 15 of Small RNA-seq analysis of single porcine blastocysts revealed that maternal estradiol-17beta exposure does not affect miRNA isoform (isomiR) expression

Table S9. IsomiR count table. (XLSX 594 kb

Additional file 9 of Small RNA-seq analysis of single porcine blastocysts revealed that maternal estradiol-17beta exposure does not affect miRNA isoform (isomiR) expression

Figure S6. Distance heatmap of all samples. (PNG 1065 kb

Additional file 7 of Small RNA-seq analysis of single porcine blastocysts revealed that maternal estradiol-17beta exposure does not affect miRNA isoform (isomiR) expression

Figure S4. Known and novel miRNAs and species annotation - unique sequences and read counts. In the outer ring the mapped unique sequences are shown related to mapped species. The inner cycle represents the corresponding read counts per species. (PNG 468 kb

Additional file 6 of Small RNA-seq analysis of single porcine blastocysts revealed that maternal estradiol-17beta exposure does not affect miRNA isoform (isomiR) expression

Table S3. Blast result with only hits related to miRNA features. (XLSX 246 kb

Additional file 12 of Small RNA-seq analysis of single porcine blastocysts revealed that maternal estradiol-17beta exposure does not affect miRNA isoform (isomiR) expression

Table S6. MiRmine result of potential embryo- and endometrium-specific miRNAs. (XLSX 67 kb