The sequencing of fragments using automated DNA sequencers in HGP, worked on the principle of the method that was developed by:

Frederick Sanger

The correct answer is Option (4) → Frederick Sanger 

The fragments were sequenced using automated DNA sequencers that worked on the principle of a method developed by Frederick Sanger. (Remember, Sanger is also credited for developing method for determination of amino acid sequences in proteins). These sequences were then arranged based on some overlapping regions present in them. This required generation of overlapping fragments for sequencing. Alignment of these sequences was humanly not possible. Therefore, specialised computer based programs were developed.