The perfect phylogeny problem is of central importance to both evolutionary biology and population genetics. Missing values are a common occurrence in both sequence and genotype data, but they make the problem of finding a perfect phylogeny NPhard even for binary characters. We introduce new and efficient perfect phylogeny algorithms for broad classes of binary and multistate data with missing values. Specifically, we address binary missing data consistent with the rich data hypothesis (RDH) introduced by Halperin and Karp and give an efficient algorithm for enumerating phylogenies. This algorithm is useful for computing the probability of data with missing values under the coalescent model. In addition, we use the partition intersection (PI) graph and chordal graph theory to generalize the RDH to multi-state characters with missing values. For a bounded number of states, we provide a fixed parameter tractable algorithm for the perfect phylogeny problem with missing data. Utilizing the PI graph, we are able to show that under multiple biologically motivated models for character data, our generalized RDH holds with high probability, and we evaluate our results with extensive empirical analysis.

Recent advances in ultra-high-throughput sequencing technology are allowing researchers to generate immense amounts of raw data in the form of short reads from ultra high-throughput platforms. We demonstrate how Field Programmable Gate Arrays (FPGAs) may be used to address computing challenges associated with next-generation genome sequencing. A common prerequisite to utilizing data generated by next-generation sequencers is alignment to a reference genome. While dynamic programming (DP) alignment algorithms are generally avoided on conventional architectures due to their computational complexity, they can be tailored for efficient implementation on systolic architectures. We implemented application-specific DP algorithms for aligning data from ultra high throughput sequencers utilizing a reconfigurable computing cluster of BEE2 boards. In our design each FPGA is capable of rapidly aligning multiple sequences in parallel against a long reference genome using multiple systolic arrays. The reconfigurable cluster proves to be scalable and capable of processing real world datasets as large as the Human genome in time proportional to data acquisition. We examine the advantages and practicality of this approach by benchmarking using Illumina sequence data from a large high-throughput sequencing project. We addressed an open question of whether a DP algorithm efficiently implementable on an FPGA can offer a quantitative improvement over the heuristic methods currently employed. Our extensive validation showed that application specific algorithms and computing hardware can provide more accurate results than current heuristic methods and may be particularly useful in circumstances where error rates or evolutionary divergence is high. While directly addressing the important problem of assembling genomes, the methods presented are also relevant to many other "omics" research applications.

We demonstrate how Field Programmable Gate Arrays (FPGAs) may be used to address the computing challenges associated with assembling genome sequences from recent ultra-high-throughput sequencing technologies. Advances in sequencing technology allow researchers to generate immense amounts of raw data in the form of short reads with high error rates. A prerequisite to effectively utilizing this data for most applications is accurate alignment to a reference genome. While dynamic programming (DP) alignment algorithms are generally avoided on conventional architectures due to their computational complexity, they can be tailored for efficient implementation on systolic architectures. We describe and implement the first system capable of assembling large genomes using DP. We implemented application-specific DP algorithms for aligning data from ultra-high-throughput sequencers in a reconfigurable computing cluster. To obtain the necessary throughput while maintaining scoring integrity, we extended the compact encoding scheme of Lipton and Lopresti for our application. Each FPGA is capable of rapidly aligning multiple reads in parallel against a long reference genome. The reconfigurable cluster proves to be scalable and capable of processing real world datasets with a sustained performance of 11 tera cell updates per second. We examine the advantages and practicality of our system by benchmarking real genomic data from a large sequencing project. Our exhaustive validation confirms that application specific computing hardware can provide more accurate results than current heuristic methods and remain practical. While directly addressing the important problem of genomic assembly, particularly in circumstances where error rates or evolutionary divergence is high, the methods presented are also relevant to many other current applications for this type of data.