Given a set of distances between every pair of points of an integral point set P of n points; say D = {${d_i}$}

Q1.What is the least time complexity possible/known for recreating the Integral point set P given D through a Turing machine computable algorithm?

Q2.What is the shortest string which can describe P?

```
eg
-Using D to describe P may be a shorter method than P itself;
-Scaling D down to elements all relatively prime may still shorten the
description string.
-Using a certain set of computed values to describe P may further minimise
the expression ( provided they exist).
-Just P= IntegralPointSet(n) will be problematic as
It is not Turing computable. ( comments?)
It does not define exactly the point set we want out of possibly many
such integral point sets.
```

Which gets me to the third Question...

Q3.What is theshortest string required to uniquely identify a particular integral point set of cardinality namongst all other such integral point sets?