On the NP-Hardness of Blocks World

Blocks world (cube world) has been one of the most popular model domains in artificial intelligence search and planning. The operation and effectiveness of alternative heuristic strategies, both basic and complex, can be observed easily in this domain. We show that finding an optimal solution is NP-hard in an important variant of the domain, and po cr ular extensions. This enlarges the range of mo el domains whose complexity has been explored mathematically, and it demonstrates that the complexity of search in blocks world is on the same level as for sliding block problems, the traveling salesperson problem, binpacking problems, and the like. These results also support the practice of using blocks world as a tutorial search domain in courses on artificial intelligence, to reveal both the value and limitations of heuristic search when seeking optimal solutions.