An Experimental Investigation on the Pancake Problem

In this paper, we present an experimental investigation on the pancake problem. Also called sorting by prefix reversals (SBPR), this problem is linked to the genome rearrangement problem also called sorting by reversals (SBR). The pancake problem is a NP-hard problem. Until now, the best theoretical R-approximation was 2 with an algorithm, which gives a 1.22 experimental R-approximation on stacks with a size inferior to 70. In the current work, we used a Monte-Carlo Search (MCS) approach with nested levels and specific domain-dependent simulations. First, in order to sort large stacks of pancakes, we show that MCS is a relevant alternative to Iterative Deepening Depth First Search (IDDFS). Secondly, at a given level and with a given number of polynomial-time domain-dependent simulations, MCS is a polynomial-time algorithm as well. We observed that MCS at level 3 gives a 1.04 experimental R-approximation, which is a breakthrough. At level 1, MCS solves stacks of size 512 with an experimental R-approximation value of 1.20.