Shotgun sequencing, a method of assembling short, repetitive sequencing reads into a consensus sequence, was adopted by Celera Genomics during their genome sequencing work. This method, which requires large amounts of computational processing to assemble a consensus sequence, was originally thought to be too advanced for the technology of the time (2000-2003) by the International Human Genome Sequencing Consortium (IHGSC) - in part due to their government funding requiring methods that had demonstrated success previously. Celera Genomics did not have these same restrictions imposed on their work, and their private funding permitted them to use novel approaches - including shotgun sequencing.
Advances in computing power, improving speeds while reducing costs, have allowed shotgun sequencing to become the dominant method used (especially in second generation / Illumina sequencing).
The clone-by-clone approach, used by the IHGSC, had been used successfully before, and had a greater likelihood of working. This involved cloning short sections of the human genome into bacterial artificial chromosomes (BACs, a sort-of large plasmid), which were then amplified and ordered in a library. These were then sequenced, allowing them to be ordered based on their position in the library. This was less computationally intensive, as the order of the sequence reads in the overall human genome was already known, and only required ordering.
The clone-by-clone approach was much more labour-intensive, requiring the sections of the human genome to be inserted into the BACs, and then ordering them based on genetic markers and maps. Shotgun sequencing is cheaper to carry out, and can be easily compiled into a consensus sequence.