I am trying to understand the use of symmetry in pattern databases (Heuristics, single agent search). This is too specialized of a topic to find common videos or explanations in general. I read the paper Pattern Databases by Joseph C. Culberson and Jonathan Schaeffer (University of Alberta) in Computational Intelligence, Volume 14, Number 3, 1998.In the paper, they explain the different kinds of symmetries we can use on the 15-Sliding Tile Puzzle such as Horizontal, Vertical and Mirror. But what I do not understand is how exactly are we going to use those symmetrical configurations of a puzzle to find a good lower bound on the estimated cost of a state from the goal. I would really appreciate if anybody can explain the process of using symmetry in pattern databases or can point toward a good explanation.
Symmetry in Pattern Databases
search algorithms;artificial intelligence;heuristics;search problem