Summary: The pancake problem is a famous search problem where the objective is to sort a sequence of objects (pancakes) through a minimal number of prefix reversals (flips). The best approaches for the problem are based on heuristic search with abstraction (pattern database) heuristics. We present a new class of abstractions for the pancake problem called relative-order abstractions. Relative-order abstractions have three advantages over the object-location abstractions considered in previous work. First, they are size-independent, i.e., do not need to be tailored to a particular instance size of the pancake problem. Second, they are more compact in that they can represent a larger number of pancakes within abstractions of bounded size. Finally, they can exploit symmetries in the problem specification to allow multiple heuristic lookups, significantly improving search performance over a single lookup. Our experiments show that compared to object-location abstractions, our new techniques lead to an improvement of one order of magnitude in runtime and up to three orders of magnitude in the number of generated states.
For the entire collection see [Zbl 1207.68003].