aligning sequence fragments is a relatively simple problem and was one of the key ideas behind shotgun sequencing, which was the precursor to modern-day genome sequencing. the cost of sequencing has also been dropping incredibly. the human genome, for scale, is 3,000,000,000 basepairs, or 3,000,000 kilobases. it would not be unreasonable to expect to have one's own entire sequence sequenced for under $100 in the next five to ten years.
on a related note: within three months, i will have completed my master of science in bioinformatics from boston university. bioinformatics, for those of you who are unfamiliar with the term, is a field dedicated to using computers and math to manage biological data and try to withdraw insight in a way that intelligently guides experimentation. it's awesome. if you're interested in trying to bring dinosaurs back to life, studying bioinformatics is a good start.