We analysed whole genome sequences of 560 breast cancers to advance understanding of the driver mutations conferring clonal advantage and the mutational processes generating somatic mutations. 93 protein-coding cancer genes carried likely driver mutations. Some non-coding regions exhibited high mutation frequencies but most have distinctive structural features probably causing elevated mutation rates and do not harbour driver mutations. Mutational signature analysis was extended to genome rearrangements and revealed 12 base substitution and six rearrangement signatures. Three rearrangement signatures, characterised by tandem duplications or deletions, appear associated with defective homologous recombination based DNA repair: one with deficient BRCA1 function; another with deficient BRCA1 or BRCA2 function; the cause of the third is unknown. This analysis of all classes of somatic mutation across exons, introns and intergenic regions highlights the repertoire of cancer genes and mutational processes operative, and progresses towards a comprehensive account of the somatic genetic basis of breast cancer.

Aimed at an audience of researchers and graduate students in computational geometry and algorithm design, this book uses the Geometric Spanner Network Problem to showcase a number of useful algorithmic techniques, data structure strategies, and geometric analysis techniques with many applications, practical and theoretical. The authors present rigorous descriptions of the main algorithms and their analyses for different variations of the Geometric Spanner Network Problem. Though the basic ideas behind most of these algorithms are intuitive, very few are easy to describe and analyze. For most of the algorithms, nontrivial data structures need to be designed, and nontrivial techniques need to be developed in order for analysis to take place. Still, there are several basic principles and results that are used throughout the book. One of the most important is the powerful well-separated pair decomposition. This decomposition is used as a starting point for several of the spanner constructions.

No abstract

We consider algorithms for preprocessing labelled lists and trees so that, for any two nodes u and v we can answer queries of the form: What is the mode or median label in the sequence of labels on the path from u to v.

No abstract

Abstract. We consider the problem of finding an obstacle-avoiding path between two points s and t in the plane, amidst a set of disjoint polygonal obstacles with a total of n vertices. The length of this path should be within a small constant factor c of the length of the shortest possible obstacle-avoiding s-t path measured in the Lv-metric. Such an approximate shortest path is called a c-short path, or a short path with stretch ]actor c. The goal is to preprocess the obstacle-scattered plane by creating an efficient data structure that enables fast reporting of a c-short path (or its length). In this paper, we give a family of algorithms for the above problem that achieve an interesting trade-off between the stretch factor, the query time and the preprocessing bounds. Our main results are algorithms that achieve logarithmic length query time, after subquadratic time and space preprocessing.

No abstract

ABSTRACT. Given a weighted graph G = (V, E) and a real number t ≥ 1, a t-spanner of G is a spanning subgraph G with the property that for every edge xy in G, there exists a path between x and y in G whose weight is no more than t times the weight of the edge xy. We review results and present open problems on different variants of the problem of constructing plane geometric t-spanners.