Actually it is something which is far from being straightforward. First there is no real means to know the genome of a person. What machines like Illumina do i

Actually it is something which is far from being straightforward. First there is no real means to know the genome of a person. What machines like Illumina do is to provide short reads, tiny parts of the genome, without telling which part is connected to which. Next an "assembler" software is used to create a genome from the reads by comparing edges, but it drops a significant part of the reads to do so, because the method (BW/De Bruijn) can not deal with all reads or produces assembling that cannot be fully decoded (it describes loops between reads, etc). To improve the quality of the decoding, a "scaffolder" is used to "graft" some of the remaining parts on the assembly result. Now to claim that someone as some origin, you must have a referential, which tells what is a genome of a British geographical area, an Indian area, etc. To my knowledge the published works describe taking the genome of only a few hundred people in each "area" and they assume these genomes are representative of the people that lived there 1,000 or even 20,000 years ago! At last you have to compare the genome that you collected to this referential to make the claim that someone has ancestors from this or that area.