  Propagation of linear constraints has become a crucial sub-routine in modern
Mixed-Integer Programming (MIP) solvers. In practice, iterative algorithms with
tolerance-based stopping criteria are used to avoid problems with slow or
infinite convergence. However, these heuristic stopping criteria can pose
difficulties for fairly comparing the efficiency of different implementations
of iterative propagation algorithms in a real-world setting. Most
significantly, the presence of unbounded variable domains in the problem
formulation makes it difficult to quantify the relative size of reductions
performed on them. In this work, we develop a method to measure --
independently of the algorithmic design -- the progress that a given iterative
propagation procedure has made at a given point in time during its execution.
Our measure makes it possible to study and better compare the behavior of
bounds propagation algorithms for linear constraints. We apply the new measure
to answer two questions of practical relevance: (i) We investigate to what
extent heuristic stopping criteria can lead to premature termination on
real-world MIP instances. (ii) We compare a GPU-parallel propagation algorithm
against a sequential state-of-the-art implementation and show that the parallel
version is even more competitive in a real-world setting than originally
reported.
