Is it possible to trace the descent of a person only using his/her genome sequence?
In short, yes, it is possible. There are companies that sequence part of your genome and then can trace it back to your ancestors. All human family trees can be traced back to their African origin 200 000 years ago, but the companies that sequence your genes do not do that. For example, 23andMe sequences only 1 million of your base pairs (single nucleotide polymorphisms (SNPs)). They trace your most recent heritage, which could lead to Europe, Africa, or Asia. They can basically trace which part of your chromosomes (and thus your ancestry) came from your mom or your dad:
Unlike the sex chromosomes and the mitochondrial DNA, which are inherited as blocks, the 22 biparental chromosomes, known as autosomes, are scrambled during reproduction. Through a process known as recombination, each parent pulls his or her paired set of 22 autosomes into chunks, then reassembles a new single set using half the material from each pair. The two single sets of chromomes from each parent are combined into a new paired set when a sperm fertilizes an egg.
Back when I was doing my PhD, there was a group in the same department as me working on an interesting project exploring the extent to which surnames (generally paternally inherited, at least in the modern west) and Y chromosomes (always paternally inherited) shared their descent.
The answers are always complicated, especially for more common surnames which have multiple origins. There are also confounding factors, such as the rate of non-paternity (which can be surprisingly high, often around 1-2%). It is, however, striking just how much you can tell about a person's heritage, just from a relatively small amount of genetic information.