Interchangeability algorithm

In computer science, an interchangeability algorithm is a technique used to more efficiently solve constraint satisfaction problems (CSP).

A CSP is a mathematical problem in which objects, represented by variables, are subject to constraints on the values of those variables; the goal in a CSP is to assign values to the variables that are consistent with the constraints.

If two variables A and B in a CSP may be swapped for each other (that is, A is replaced by B and B is replaced by A) without changing the nature of the problem or its solutions, then A and B are interchangeable variables.

Interchangeable variables represent a symmetry of the CSP and by exploiting that symmetry, the search space for solutions to a CSP problem may be reduced.

[1][2] The interchangeability algorithm reduces the search space of backtracking search algorithms, thereby improving the efficiency of NP-complete CSP problems.

[3] Finds neighborhood interchangeable values in a CSP.

Repeat for each variable: The algorithm can be used to explicitly find solutions to a constraint satisfaction problem.

The algorithm can also be run for k steps as a preprocessor to simplify the subsequent backtrack search.

Similarly, the complexity analysis of the k-interchangeability algorithm for a worst case

The colors yellow, green, brown, red, blue, pink represent vertex Y and are fully interchangeable by definition.

In Computer Science, the interchangeability algorithm has been extensively used in the fields of artificial intelligence, graph coloring problems, abstraction frame-works and solution adaptation.