Developed and introduced by Satish Kumar Thittamaranahalli (T. K. Satish Kumar), the idea of the constraint composite graph is a big step towards unifying different approaches for exploiting "structure" in weighted constraint satisfaction problems.
The goal is then to find an assignment of values to all the variables from their respective domains so that the total cost is minimized.
Weighted constraint satisfaction problems find innumerable applications in artificial intelligence and computer science.
They are also variously referred to as markov random fields (in statistics and signal processing) and energy minimization problems (in physics).
Result 2 shows that the constraint composite graph can also be used to capture the numerical structure of the weighted constraints (since a minimum weighted vertex cover can be computed in polynomial time for bipartite graphs).