Refining complexity analyses in planning by exploiting the exponential time hypothesis

The use of computational complexity in planning, and in AI in general, has always been a disputed topic. A major problem with ordinary worst-case analyses is that they do not provide any quantitative information: they do not tell us much about the running time of concrete algorithms, nor do they tell us much about the running time of optimal algorithms. We address problems like this by presenting results based on the exponential time hypothesis (ETH), which is a widely accepted hypothesis concerning the time complexity of 3-SAT. By using this approach, we provide, for instance, almost matching upper and lower bounds onthe time complexity of propositional planning.Funding Agencies|National Graduate School in Computer Science (CUGS), Sweden; Swedish Research Council (VR) [621-2014-4086]</p

Algorithms and Limits for Compact Plan Representations

Compact representations of objects is a common concept in computer science. Automated planning can be viewed as a case of this concept: a planning instance is a compact implicit representation of a graph and the problem is to find a path (a plan) in this graph. While the graphs themselves are represented compactly as planning instances, the paths are usually represented explicitly as sequences of actions. Some cases are known where the plans always have compact representations, for example, using macros. We show that these results do not extend to the general case, by proving a number of bounds for compact representations of plans under various criteria, like efficient sequential or random access of actions. In addition to this, we show that our results have consequences for what can be gained from reformulating planning into some other problem. As a contrast to this we also prove a number of positive results, demonstrating restricted cases where plans do have useful compact representations, as well as proving that macro plans have favourable access properties. Our results are finally discussed in relation to other relevant contexts. 1

Algorithms and Limits for Compact Plan Representations

Compact representations of objects is a common concept in computer science. Automated planning can be viewed as a case of this concept: a planning instance is a compact implicit representation of a graph and the problem is to find a path (a plan) in this graph. While the graphs themselves are represented compactly as planning instances, the paths are usually represented explicitly as sequences of actions. Some cases are known where the plans always have compact representations, for example, using macros. We show that these results do not extend to the general case, by proving a number of bounds for compact representations of plans under various criteria, like efficient sequential or random access of actions. In addition to this, we show that our results have consequences for what can be gained from reformulating planning into some other problem. As a contrast to this we also prove a number of positive results, demonstrating restricted cases where plans do have useful compact representations, as well as proving that macro plans have favourable access properties. Our results are finally discussed in relation to other relevant contexts