MOTIVATION: Alternative splicing (AS) of introns from pre-mRNA produces diverse sets of transcripts across cell types and tissues, but is also dysregulated in many diseases. Alignment-free computational methods have greatly accelerated the quantification of mRNA transcripts from short RNA-seq reads, but they inherently rely on a catalog of known transcripts and might miss novel, disease-specific splicing events. By contrast, alignment of reads to the genome can effectively identify novel exonic segments and introns. Event-based methods then count how many reads align to predefined features. However, an alignment is more expensive to compute and constitutes a bottleneck in many AS analysis methods. RESULTS: Here, we propose fortuna, a method that guesses novel combinations of annotated splice sites to create transcript fragments. It then pseudoaligns reads to fragments using kallisto and efficiently derives counts of the most elementary splicing units from kallisto's equivalence classes. These counts can be directly used for AS analysis or summarized to larger units as used by other widely applied methods. In experiments on synthetic and real data, fortuna was around 7× faster than traditional align and count approaches, and was able to analyze almost 300 million reads in just 15 min when using four threads. It mapped reads containing mismatches more accurately across novel junctions and found more reads supporting aberrant splicing events in patients with autism spectrum disorder than existing methods. We further used fortuna to identify novel, tissue-specific splicing events in Drosophila. AVAILABILITY AND IMPLEMENTATION: fortuna source code is available at https://github.com/canzarlab/fortuna.

We present a 4-approximation algorithm for the problem of placing the fewest guards on a 1.5D terrain so that every point of the terrain is seen by at least one guard. This improves on the previous best approximation factor of 5 (see King in Proceedings of the 13th Latin American Symposium on Theoretical Informatics, pp. 629–640, 2006 ). Unlike most of the previous techniques, our method is based on rounding the linear programming relaxation of the corresponding covering problem. Besides the simplicity of the analysis, which mainly relies on decomposing the constraint matrix of the LP into totally balanced matrices, our algorithm, unlike previous work, generalizes to the weighted and partial versions of the basic problem.

We present a 4-approximation algorithm for the problem of placing the fewest guards on a 1.5D terrain so that every point of the terrain is seen by at least one guard. This improves on the currently best approximation factor of 5 (J. King, 2006). Unlike most of the previous techniques, our method is based on rounding the linear programming relaxation of the corresponding covering problem. Besides the simplicity of the analysis, which mainly relies on decomposing the constraint matrix of the LP into totally balanced matrices, our algorithm, unlike previous work, generalizes to the weighted and partial versions of the basic problem.

When you drive to somewhere 'far away', you will leave your current location via one of only a few 'important' traffic junctions.Starting from this informal observation, we develop an algorithmic approach-transit node routingthat allows us to reduce quickest-path queries in road networks to a small number of table lookups.We present two implementations of this idea, one based on a simple grid data structure and one based on highway hierarchies.For the road map of the United States, our best query times improve over the best previously published figures by two orders of magnitude.Our results exhibit various trade-offs between average query time (5 µs to 63 µs), preprocessing time (59 min to 1200 min), and storage overhead (21 bytes/node to 244 bytes/node).

Consider the following illumination problem: given a stage represented by a line segment L and a set of lightsources represented by a set of points S in the plane, assign powers to the lightsources such that every point on the stage receives a sufficient amount -- let's say one unit -- of light while minimizing the overall power consumption. By assuming that the amount of light arriving from a fixed lightsource decreases rapidly with the distance from the lightsource, this becomes an interesting optimization problem.We propose to reconsider the classical illumination problems as known from computational geometry literature (e.g. [12]) under this light attenuation model. This paper examines the simple problem introduced above and presents different solutions, based on convex optimization, discretization and linear programming, as well as a purely combinatorial approximation algorithm. Some experimental results are also provided.