Relative-Order Abstractions for the Pancake Problem

  • Authors:

  • Malte Helmert;Gabriele Röger

  • Affiliations:

  • Albert-Ludwigs-Universität Freiburg, Germany, {helmert,roeger}@informatik.uni-freiburg.de;Albert-Ludwigs-Universität Freiburg, Germany, {helmert,roeger}@informatik.uni-freiburg.de

  • Venue:
  • Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
  • Year:
  • 2010

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Abstract

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.