The phrase "a dense unit" is correct and usable in written English.
It can be used in contexts where you are describing a compact or tightly packed entity, often in scientific or technical discussions.
Example: "The material is composed of a dense unit that maximizes its strength and durability."
Alternatives: "a compact unit" or "a solid unit".
Each signature sum is derived from a dense unit of fixed size = τ+1.
Instead of the actual points, a dense unit (mathcal {U}) will now contain the mapped keys i.e. {K 1,K 2,…,K τ+1}.
Therefore, the smallest possible projection of a cluster from the higher dimensional subspace is of cardinality τ+1 and let us call it a dense unit, (mathcal {U}).
The signature (mathcal H) of a dense unit (mathcal {U}) is given by the sum of the labels of the points in it.
Since L is the sum of the labels of δ points in a dense unit (mathcal {U}), L can be made very large if we choose very large integers as the individual labels.
After repeating this process in all single dimensions, each entry of this hash table will contain a dense unit in the maximal subspace as we can store the colliding dimensions against each signature (mathcal H_{i} in hTable).
The size of hTable i can be adjusted to handle large databases of points by choosing an appropriate split factor sp. Instead of generating all dense units in all dimensions sp times, if we sort the keys of density-connected points, we can stop the computation of dense units when no more signature sums less than the upperlimit of hTable i are possible.
Thus, the final collisions after hashing all dense units in all dimensions generate dense units in the relevant maximal subspaces.
The rationale behind this is to avoid comparing the individual points among all dense units in order to decide whether they contain exactly same points or not.
This sequence in the Arabian platform forms an intraformational seal or dense unit (Van Buchem et al. 2002).
We assume a fixed size of τ+1 for the dense unit (mathcal {U}) which is the smallest possible cluster of dense points.
