High-throughput RNA sequencing enables quantification of transcripts (both known and novel), exon/exon junctions and fusions of exons from different genes. Discovery of gene fusions-particularly those expressed with low abundance- is a challenge with short- and medium-length sequencing reads. To address this challenge, we implemented an RNA-Seq mapping pipeline within the LifeScope software. We introduced new features including filter and junction mapping, annotation-aided pairing rescue and accurate mapping quality values. We combined this pipeline with a Suffix Array Spliced Read (SASR) aligner to detect chimeric transcripts. Performing paired-end RNA-Seq of the breast cancer cell line MCF-7 using the SOLiD system, we called 40 gene fusions among over 120,000 splicing junctions. We validated 36 of these 40 fusions with TaqMan assays, of which 25 were expressed in MCF-7 but not the Human Brain Reference. An intra-chromosomal gene fusion involving the estrogen receptor alpha gene ESR1, and another involving the RPS6KB1 (Ribosomal protein S6 kinase beta-1) were recurrently expressed in a number of breast tumor cell lines and a clinical tumor sample.

Abstract Unit disk graphs are intersection graphs of circles of unit radius in the plane. We present simple and provably good heuristics for a number of classical NP‐hard optimization problems on unit disk graphs. The problems considered include maximum independent set, minimum vertex cover, minimum coloring, and minimum dominating set. We also present an on‐line coloring heuristic which achieves a competitive ratio of 6 for unit disk graphs. Our heuristics do not need a geometric representation of unit disk graphs. Geometric representations are used only in establishing the performance guarantees of the heuristics. Several of our approximation algorithms can be extended to intersection graphs of circles of arbitrary radii in the plane, intersection graphs of regular polygons, and intersection graphs of higher dimensional regular objects.

Two linear time (and hence asymptotically optimal) algorithms for computing the Euclidean distance transform of a two-dimensional binary image are presented. The algorithms are based on the construction and regular sampling of the Voronoi diagram whose sites consist of the unit (feature) pixels in the image. The first algorithm, which is of primarily theoretical interest, constructs the complete Voronoi diagram. The second, more practical, algorithm constructs the Voronoi diagram where it intersects the horizontal lines passing through the image pixel centers. Extensions to higher dimensional images and to other distance functions are also discussed.>