Note that TDI is a weaker sufficient condition for integrality than total unimodularity.
2.
There are other general methods including the integer decomposition property and total dual integrality.
3.
The integrality gap is always at least 1.
4.
Typically, the integrality gap translates into the approximation ratio of an approximation algorithm.
5.
Finally, constraints 6 are the integrality constraints.
6.
Similarly, " integrality " is transitive.
7.
So the Atiyah Singer index theorem implies some deep integrality properties, as it implies that the topological index is integral.
8.
The basic idea behind LP decoding is to first represent the relax the integrality constraints on the variables into linear inequalities.
9.
In general, fractional graph coloring provides a shorter schedule than non-fractional graph coloring; there is an integrality gap.
10.
For example, a linear programming relaxation of an integer programming problem removes the integrality constraint and so allows non-integer rational solutions.
