Blocks World Tamed Ten Thousand Blocks in under a Second

Blocks World (BW) has been a standard example of a planning domain for almost thirty years, and it is still commonly used to illustrate the capabilities both of formalisms and of planners. As a minimum, therefore, we should know certain basic things about the domain. It is clear that BW planning, in the sense of nding some plan or other, is trivial, and it was shown in 1991 that nding optimal (shortest) plans is NP hard. Various polynomial time algorithms for approximating optimal BW planning exist, and there have been attempts to implement these domain-speciic methods in more general planning frameworks. Here we report new complexity bounds for some of the approximation algorithms, and discuss experimental results obtained with randomly generated BW problems. The work reported here greatly extends that described in TR-ARP-7-94.