This paper proves several new properties of the Meet in the Middle (MMe) bidirectional heuristic search algorithm when applied to graphs with unit edge costs. Primarily, it is shown that the length of the first path discovered by MMe never exceeds the optimal length by more than one and that if the length of the first path found is odd, then it must be optimal. These properties suggest that the search strategy should emphasize finding a complete path as soon as possible. Computational experiments demonstrate that fully exploiting these new properties can decrease the number of nodes expanded by anywhere from twofold to over tenfold.

In this paper we present a lossless technique to compress pattern databases (PDBs) in the Pancake Sorting problems. This compression technique together with the choice of zero-cost operators in the construction of additive PDBs reduces the memory requirement for PDBs in these problems to a great extent, thus making otherwise intractable problems able to be efficiently handled. Also, using this method, we can construct some problem-size independent PDBs. This precludes the necessity of constructing new PDBs for new problems with different numbers of pancakes. In addition to our compression technique, by maximizing over the heuristic value of additive PDBs and the modified version of the gap heuristic, we have obtained powerful heuristics for the burnt pancake problem.

The Pancake problem has become a classical combinatorial problem. Different attempts have been made to optimally solve it and/or to derive tighter bounds on the diameter of its state space for a different number of discs. Until very recently, the most successful technique for solving different instances optimally was based on Pattern Databases. Although different approaches have been tried, solutions with Pattern Databases on Pancakes with more than 19 discs have never been reported. In this work, a new technique is introduced which allows the definition of Additive Pattern Databases for solving Pancakes of an arbitrary length. As a result, this technique solves Pancake problems with twice as many discs as the largest ones solved nowadays with other techniques based on Pattern Databases saving up to two orders of magnitude of space.

We describe the gap heuristic for the pancake problem, which dramatically outperforms current abstraction-based heuristics for this problem. The gap heuristic belongs to a family of landmark heuristics that have recently been very successfully applied to planning problems.