Symmetry breaking in Graceful Graphs

TLDR: Symmetry occurs frequently in Constraint Satisfaction Problems (CSPs) and can cause wasted search, because the search for solutions may repeatedly visit partial assignments symmetric to ones already considered.

Abstract: Symmetry occurs frequently in Constraint Satisfaction Problems (CSPs). For instance, in 3-colouring the nodes of a graph, a CSP model that assigns a specific colour to each node has sets of equivalent solutions in which the three colours are permuted. Symmetry in CSPs can cause wasted search, because the search for solutions may repeatedly visit partial assignments symmetric to ones already considered. If a partial assignment does not lead to a solution, neither will any symmetrically equivalent assignment. When searching for all solutions, for every solution found, all the symmetrically equivalent solutions will also be found.