Each assembly can be represented as a set of individual assembly points (links), and that is the view that CAMSA takes on the input scaffold assemblies. This approach is very flexible and allows for a very broad range of scaffold assemblies obtained from both in silico and in vitro techniques.

We say that a scaffold has two extremities: head and tail, which can be viewed as 3' and 5' extremities of this scaffold. Thus the forward oriented scaffold A will be described as +A and negatively oriented scaffold will be denoted as -A. When no orientation of scaffold A is given, it will be denoted simply as A.

In our terminology, an assembly point is an evidence, that two scaffolds need to be placed together. We classify into 3 categories:

1. oriented: p=(+A, +B) two scaffolds are reported as adjacent, and orientation of both scaffolds is specified. In this case, the head of scaffold A is adjacent to the tail of scaffold B.
2. semi-oriented: p=(+A, B) two scaffolds are reported adjacent, but the orientation of only a single scaffold is known. In other words, we know by which extremity scaffold A (head) has to be adjacent to the scaffold B, but we don't know which extremity of scaffold B (head or tail) will be involved with A.
3. non-oriented: p=(A, B) two scaffolds are reported adjacent, but the orientations of both scaffolds are not known.

Such view inspires us to include the notion of assembly point realization. For a given assembly point p a realization is an oriented assembly point, that can be inferred from p by setting orientation to unoriented scaffolds participating in it.

Example: given a semi-oriented assembly point p=(+A, B), there exist two realizations of it:

• (+A, +B)
• (+A, -B)

With this in mind, we note, that each oriented assembly point has exactly a single orientation: itself. Every semi-oriented assembly point has exactly 2 orientations (by two possible orientations of the unoriented scaffolds), and every non-oriented assembly point has 4 orientation.