An empirical investigation into the exceptionally hard problems

Recently \exceptionally hard" problems have been found in the easy region of problem spaces which can be orders of magnitude harder to solve than even the hardest problems in the phase transistion. However there is some uncertainty over whether this phenomena of exceptionally hard problems occurs for all algorithms, occurs only for complete algorithms or is purely algorithm dependent. The purpose of this paper is to assess the performance of a range of algorithms on problems in the easy region in order to address this issue. We present results of an empirical investigation which show that both soluble and insoluble exceptionally hard problems can occur for even very sophisticated complete search algorithms, although the likelihood of such problems occuring varies signi cantly depending on the algorithm being used to solve them. genet, an incomplete, iterative repair-based search did not encounter any soluble, exceptionally hard problems in the easy region.