Changes

Decomposition of variants involves the breaking down of a variant record into multiple records. It may be done vertically - as in multiallelics becoming biallelics or it can be done horizontally - a cluster of indels and SNPs represented as a complex variant being splitted up into several records. Horizontal decompositions in general do not have a unique solution.  Similarly, reconstruction combines several variant records into a single record.

Decomposition of variants involves the breaking down of a variant record into multiple records. It may be done vertically - as in multiallelics becoming biallelics or it can be done horizontally - a cluster of indels and SNPs represented as a complex variant being splitted up into several records. Horizontal decompositions in general do not have a unique solution.  Similarly, reconstruction combines several variant records into a single record and can be done vertically and horizontally too. Vertical decomposition of a multiallelic variant to a set of biallelic records is a many to one function.  Construction of a set of biallelic variants into a multiallelic record is not unique as you need to considered all possible permutations of the haplotypes containing your alleles. 

It is important to distinguish the difference between normalization and decomposition/reconstruction.  The notion of normalization implies that a variant can be reduced to a standardized form.  If you were to include decomposition and reconstruction in your notion of normalization, you are  bound to find inconsistencies simply due to the inherent issues of identifiability.

It is important to distinguish the difference between normalization and decomposition/reconstruction.  The notion of normalization implies that a variant can be reduced to a standardized form.  If you were to include decomposition and reconstruction in your notion of normalization, you are  bound to find inconsistencies simply due to the inherent issues of identifiability. Thus before you convince yourself that a representation is incorrect, consider the following factors: