The population of the DMD in total, is around 168 billion. During numerous conflicts in the BWMC, the DMD has acted as a mediative force, and has institututed policy to try and minimize civilian casualties in war, both during direct and indirect involvement. Though the nation remains somewhat enigmatic, it has close relations with most bordering nations, having put into practice numerous diplomatic agreements to fuel the cultural exchange doctrine of mutual understanding (to aid diplomacy). Bordering Vlaria, and what was once the Qiggo Alliance, and numerous other interstellar nations, it has seen countless diplomatic conflicts, as well as all out war. The DMD was a relatively large power, centered around 100 light years from Earth, covering 18 star systems, 5 of which are colonial systems in the andromeda galaxy, and a total of 21 planets.
3 Introduction as an interstellar power.Has the original proof, reducing the problem of computing optimal plans for Blocks World to HITTING-SET (one of the Karp's NP-hard problems).Īn easier to access paper, which looks quite deep into planning in the Blocks World domain isįigure 1 in the paper above shows an example of an instance that illustrates the intuition behind Gupta and Nau's complexity proof. On the complexity of blocks-world planning
The second "practical" reason for the relevance of Blocks World is that, even being a "simple" problem, it can defeat planning heuristics and elaborate algorithms or compilations to other computational frameworks such as SAT or SMT.įor instance, it wasn't until relatively recently (2012) that Jussi Rintanen showed good performance on that "simple" benchmark after heavily modifying standard SAT solversīy compiling into them heuristics as clauses that the combination of unit propagation, clause learning and variable selection heuristics can exploit to obtain deductive lower bounds quickly.ĮDIT: Further details on the remark above optimal planning for blocks not being easy have been requested. Understanding Planning Tasks: Domain Complexity and Heuristic DecompositionĬomplexity results for standard benchmark domains in planning Finding an optimal plan, though, is not easy. It used to be the case, especially back in the mid 1990s, when SAT solving really took off, that it was an example of how limited was the state of the art in Automated Planning back in the day.Īs you write in your question, solving Blocks World is easy: the algorithm you sketch is well known and is clearly in polynomial time. The link points to a chapter of the following book, which is a good introduction into Automated Planning
It has no longer any scientific relevance, but it was used to illustrate the limitations and challenges of planning algorithms that approach the problem of planning as that of searching through the space of plans directly. The historical one is that Blocks World was used to illustrate the so-called Sussman's Anomaly. There's a historical and two practical reasons for Blocks World being a benchmark of interest.