Novelty vs. Potential Heuristics: A Comparison of Hardness Measures for Satisficing Planning

Classical planning considers a given task and searches for a plan to solve it. Some tasks are harder to solve than others. We can measure the 'hardness' of a task with the novelty width and the correlation complexity. In this work, we compare these measures. Additionally, we introduce the river measure, a new measure that is based on potential heuristics and therefore similar to the correlation complexity but also comparable to the novelty width. We show that the river measure is upper bounded by the correlation complexity and by the novelty width +1. Furthermore, we show that we can convert a planning task with a polynomial blowup of the task size to ensure that a heuristic of dimension 2 exists that gives rise to backtrack-free search.