On the Complexity of Computing the Planning Width

Jiajia Song, Nir Lipovetzky, Sebastian Sardina, Seeun William Umboh

Track: Long Paper (9 pages including references)

Previous Publication: No, the submission has not been published or accepted at another conference.

Keywords: planning, complexity, width, optimisation

Abstract:

The width of a classical planning instance, among other metrics, indicates the computational difficulty of the instance. However, no result exists on the complexity of computing the width itself. In this
paper, we address this by utilising an optimisation complexity framework. We focus on planning instance with polynomially bounded solutions, and prove that computing their
width is $OptP[O(\log \log L)]$-hard, where L is the size of the
instance. In turn, for the upperbound, we show that computing width is in $OptP[O(\log L)]^{OptP[O(\log L)]}$. Problem
set $OptP[O(z(L))]$ is the optimisation complexity class with
their optimal value’ length in binary bounded by $O(z(L))$.
These results contribute to the understanding of width as a
proxy measure for the computational difficulty of planning,
and suggest that exploiting other structural restrictions beyond bounding solution length, can provide further insights
on the complexity of width computation.

Submission Number: 9