Properties and algorithms of the (n, k)-star graphs

The (n, k)-star interconnection network was proposed in 1995 as an attractive alternative to the n-star topology in parallel computation. The (n, k )-star has significant advantages over the n-star which itself was proposed as an attractive alternative to the popular hypercube. The major advantage of the (n, k )-star network is its scalability, which makes it more flexible than the n-star as an interconnection network. In this thesis, we will focus on finding graph theoretical properties of the (n, k )-star as well as developing parallel algorithms that run on this network. The basic topological properties of the (n, k )-star are first studied. These are useful since they can be used to develop efficient algorithms on this network. We then study the (n, k )-star network from algorithmic point of view. Specifically, we will investigate both fundamental and application algorithms for basic communication, prefix computation, and sorting, etc. A literature review of the state-of-the-art in relation to the (n, k )-star network as well as some open problems in this area are also provided.

Properties and algorithms of the (n, k)-arrangement graphs

The (n, k)-arrangement interconnection topology was first introduced in 1992. The (n, k )-arrangement graph is a class of generalized star graphs. Compared with the well known n-star, the (n, k )-arrangement graph is more flexible in degree and diameter. However, there are few algorithms designed for the (n, k)-arrangement graph up to present. In this thesis, we will focus on finding graph theoretical properties of the (n, k)- arrangement graph and developing parallel algorithms that run on this network. The topological properties of the arrangement graph are first studied. They include the cyclic properties. We then study the problems of communication: broadcasting and routing. Embedding problems are also studied later on. These are very useful to develop efficient algorithms on this network. We then study the (n, k )-arrangement network from the algorithmic point of view. Specifically, we will investigate both fundamental and application algorithms such as prefix sums computation, sorting, merging and basic geometry computation: finding convex hull on the (n, k )-arrangement graph. A literature review of the state-of-the-art in relation to the (n, k)-arrangement network is also provided, as well as some open problems in this area.

Improving Short DNA Sequence Alignment with Parallel Computing

Variations in different types of genomes have been found to be responsible for a large degree of physical diversity such as appearance and susceptibility to disease. Identification of genomic variations is difficult and can be facilitated through computational analysis of DNA sequences. Newly available technologies are able to sequence billions of DNA base pairs relatively quickly. These sequences can be used to identify variations within their specific genome but must be mapped to a reference sequence first. In order to align these sequences to a reference sequence, we require mapping algorithms that make use of approximate string matching and string indexing methods. To date, few mapping algorithms have been tailored to handle the massive amounts of output generated by newly available sequencing technologies. In otrder to handle this large amount of data, we modified the popular mapping software BWA to run in parallel using OpenMPI. Parallel BWA matches the efficiency of multithreaded BWA functions while providing efficient parallelism for BWA functions that do not currently support multithreading. Parallel BWA shows significant wall time speedup in comparison to multithreaded BWA on high-performance computing clusters, and will thus facilitate the analysis of genome sequencing data.