Massively parallel DNA sequencing technologies are revolutionizing genomics research. Billions of short reads generated at low costs can be assembled for reconstructing the whole genomes. Unfortunately, the large memory footprint of the existing de novo assembly algorithms makes it challenging to get the assembly done for higher eukaryotes like mammals. In this work, we investigate the memory issue of constructing de Bruijn graph, a core task in leading assembly algorithms, which often consumes several hundreds of gigabytes memory for large genomes. We propose a disk-based partition method, called Minimum Substring Partitioning (MSP), to complete the task using less than 10 gigabytes memory, without runtime slowdown. MSP breaks the short reads into multiple small disjoint partitions so that each partition can be loaded into memory, processed individually and later merged with others to form a de Bruijn graph. By leveraging the overlaps among the k-mers (substring of length k), MSP achieves astonishing compression ratio: The total size of partitions is reduced from Θ(kn) to Θ(n), wherenis the size of the short read database, andkis the length of ak-mer. Experimental results show that our method can build de Bruijn graphs using a commodity computer for any large-volume sequence dataset.

We study the complexity of geometric minimum spanning trees under a stochastic model of input: Suppose we are given a master set of points s1,s_2,...,sn in d-dimensional Euclidean space, where each point si is active with some independent and arbitrary but known probability pi. We want to compute the expected length of the minimum spanning tree (MST) of the active points. This particular form of stochastic problems is motivated by the uncertainty inherent in many sources of geometric data but has not been investigated before in computational geometry to the best of our knowledge. Our main results include the following.