Efficient Algorithms for the Closest Pair Problem and Applications

The closest pair problem (CPP) is one of the well studied and fundamental problems in computing. Given a set of points in a metric space, the problem is to identify the pair of closest points. Another closely related problem is the fixed radius nearest neighbors problem (FRNNP). Given a set of points and a radius $R$, the problem is, for every input point $p$, to identify all the other input points that are within a distance of $R$ from $p$. A naive deterministic algorithm can solve these problems in quadratic time. CPP as well as FRNNP play a vital role in computational biology, computational finance, share market analysis, weather prediction, entomology, electro cardiograph, N-body simulations, molecular simulations, etc. As a result, any improvements made in solving CPP and FRNNP will have immediate implications for the solution of numerous problems in these domains. We live in an era of big data and processing these data take large amounts of time. Speeding up data processing algorithms is thus much more essential now than ever before. In this paper we present algorithms for CPP and FRNNP that improve (in theory and/or practice) the best-known algorithms reported in the literature for CPP and FRNNP. These algorithms also improve the best-known algorithms for related applications including time series motif mining and the two locus problem in Genome Wide Association Studies (GWAS)

Efficient network-guided multi-locus association mapping with graph cuts

As an increasing number of genome-wide association studies reveal the limitations of attempting to explain phenotypic heritability by single genetic loci, there is growing interest for associating complex phenotypes with sets of genetic loci. While several methods for multi-locus mapping have been proposed, it is often unclear how to relate the detected loci to the growing knowledge about gene pathways and networks. The few methods that take biological pathways or networks into account are either restricted to investigating a limited number of predetermined sets of loci, or do not scale to genome-wide settings. We present SConES, a new efficient method to discover sets of genetic loci that are maximally associated with a phenotype, while being connected in an underlying network. Our approach is based on a minimum cut reformulation of the problem of selecting features under sparsity and connectivity constraints that can be solved exactly and rapidly. SConES outperforms state-of-the-art competitors in terms of runtime, scales to hundreds of thousands of genetic loci, and exhibits higher power in detecting causal SNPs in simulation studies than existing methods. On flowering time phenotypes and genotypes from Arabidopsis thaliana, SConES detects loci that enable accurate phenotype prediction and that are supported by the literature. Matlab code for SConES is available at http://webdav.tuebingen.mpg.de/u/karsten/Forschung/scones/Comment: 20 pages, 6 figures, accepted at ISMB (International Conference on Intelligent Systems for Molecular Biology) 201

Screened poisson hyperfields for shape coding

We present a novel perspective on shape characterization using the screened Poisson equation. We discuss that the effect of the screening parameter is a change of measure of the underlying metric space. Screening also indicates a conditioned random walker biased by the choice of measure. A continuum of shape fields is created by varying the screening parameter or, equivalently, the bias of the random walker. In addition to creating a regional encoding of the diffusion with a different bias, we further break down the influence of boundary interactions by considering a number of independent random walks, each emanating from a certain boundary point, whose superposition yields the screened Poisson field. Probing the screened Poisson equation from these two complementary perspectives leads to a high-dimensional hyperfield: a rich characterization of the shape that encodes global, local, interior, and boundary interactions. To extract particular shape information as needed in a compact way from the hyperfield, we apply various decompositions either to unveil parts of a shape or parts of a boundary or to create consistent mappings. The latter technique involves lower-dimensional embeddings, which we call screened Poisson encoding maps (SPEM). The expressive power of the SPEM is demonstrated via illustrative experiments as well as a quantitative shape retrieval experiment over a public benchmark database on which the SPEM method shows a high-ranking performance among the existing state-of-the-art shape retrieval methods

Computational Contributions Towards Scalable and Efficient Genome-wide Association Methodology

Genome-wide association studies are experiments designed to find the genetic bases of physical traits: for example, markers correlated with disease status by comparing the DNA of healthy individuals to the DNA of affecteds. Over the past two decades, an exponential increase in the resolution of DNA-testing technology coupled with a substantial drop in their cost have allowed us to amass huge and potentially invaluable datasets to conduct such comparative studies. For many common diseases, datasets as large as a hundred thousand individuals exist, each tested at million(s) of markers (called SNPs) across the genome. Despite this treasure trove, so far only a small fraction of the genetic markers underlying most common diseases have been identified. Simply stated - our ability to predict phenotype (disease status) from a person's genetic constitution is still very limited today, even for traits that we know to be heritable from one's parents (e.g. height, diabetes, cardiac health). As a result, genetics today often lags far behind conventional indicators like family history of disease in terms of its predictive power. To borrow a popular metaphor from astronomy, this veritable "dark matter" of perceivable but un-locatable genetic signal has come to be known as missing heritability. This thesis will present my research contributions in two hotly pursued scientific hypotheses that aim to close this gap: (1) gene-gene interactions, and (2) ultra-rare genetic variants - both of which are not yet widely tested. First, I will discuss the challenges that have made interaction testing difficult, and present a novel approximate statistic to measure interaction. This statistic can be exploited in a Monte-Carlo like randomization scheme, making an exhaustive search through trillions of potential interactions tractable using ordinary desktop computers. A software implementation of our algorithm found a reproducible interaction between SNPs in two calcium channel genes in Bipolar Disorder. Next, I will discuss the functional enrichment pipeline we subsequently developed to identify sets of interacting genes underlying this disease. Lastly, I will talk about the application of coding theory to cost-efficient measurement of ultra-rare genetic variation (sometimes, as rare as just one individual carrying the mutation in the entire population)

Bit-parallel and SIMD alignment algorithms for biological sequence analysis

High-throughput next-generation sequencing techniques have hugely decreased the cost and increased the speed of sequencing, resulting in an explosion of sequencing data. This motivates the development of high-efficiency sequence alignment algorithms. In this thesis, I present multiple bit-parallel and Single Instruction Multiple Data (SIMD) algorithms that greatly accelerate the processing of biological sequences. The first chapter describes the BitPAl bit-parallel algorithms for global alignment with general integer scoring, which assigns integer weights for match, mismatch, and insertion/deletion. The bit-parallel approach represents individual cells in an alignment scoring matrix as bits in computer words and emulates the calculation of scores by a series of logic operations. Bit-parallelism has previously been applied to other pattern matching problems, producing fast algorithms. In timed tests, we show that BitPAl runs 7 - 25 times faster than a standard iterative algorithm. The second part involves two approaches to alignment with substitution scoring, which assigns a potentially different substitution weight to every pair of alphabet characters, better representing the relative rates of different mutations. The first approach extends the existing BitPAl method. The second approach is a new SIMD algorithm that uses partial sums of adjacent score differences. I present a simple partial sum method as well as one that uses parallel scan for additional acceleration. Results demonstrate that these algorithms are significantly faster than existing SIMD dynamic programming algorithms. Finally, I describe two extensions to the partial sums algorithm. The first adds support for affine gap penalty scoring. Affine gap scoring represents the biological likelihood that it is more likely for gaps to be continuous than to be distributed throughout a region by introducing a gap opening penalty and a gap extension penalty. The second extension is an algorithm that uses the partial sums method to calculate the tandem alignment of a pattern against a text sequence using a single pattern copy. Next generation sequencing data provides a wealth of information to researchers. Extracting that information in a timely manner increases the utility and practicality of sequence analysis algorithms. This thesis presents a family of algorithms which provide alignment scores in less time than previous algorithms