The recent boom in microfluidics and combinatorial indexing strategies, combined with low sequencing costs, has empowered single-cell sequencing technology. Thousands—or even millions—of cells analyzed in a single experiment amount to a data revolution in single-cell biology and pose unique data science problems. Here, we outline eleven challenges that will be central to bringing this emerging field of single-cell data science forward. For each challenge, we highlight motivating research questions, review prior work, and formulate open problems. This compendium is for established researchers, newcomers, and students alike, highlighting interesting and rewarding problems for the coming years.

The classical Steiner tree problem in weighted graphs seeks a minimum weight connected subgraph containing a given subset of the vertices (terminals). We present a new polynomial-time heuristic that achieves a best-known approximation ratio of $1 + \frac{\ln 3}{2} \approx 1.55$ for general graphs and best-known approximation ratios of $\approx 1.28$ for both quasi-bipartite graphs (i.e., where no two nonterminals are adjacent) and complete graphs with edge weights 1 and 2. Our method is considerably simpler and easier to implement than previous approaches. We also prove the first known nontrivial performance bound ($1.5 \cdot$ OPT) for the iterated 1-Steiner heuristic of Kahng and Robins in quasi-bipartite graphs.

Massively parallel whole transcriptome sequencing, commonly referred as RNA-Seq, is quickly becoming the technology of choice for gene expression profiling. However, due to the short read length delivered by current sequencing technologies, estimation of expression levels for alternative splicing gene isoforms remains challenging.

Computational omics methods packaged as software have become essential to modern biological research. The increasing dependence of scientists on these powerful software tools creates a need for systematic assessment of these methods, known as benchmarking. Adopting a standardized benchmarking practice could help researchers who use omics data to better leverage recent technological innovations. Our review summarizes benchmarking practices from 25 recent studies and discusses the challenges, advantages, and limitations of benchmarking across various domains of biology. We also propose principles that can make computational biology benchmarking studies more sustainable and reproducible, ultimately increasing the transparency of biomedical data and results.