Backdoors to planning

摘要

Backdoors measure the distance to tractable fragments and have become an important tool to find fixed-parameter tractable (fpt) algorithms for hard problems in AI and beyond. Despite their success, backdoors have not been used for planning, a central problem in AI that has a high computational complexity. In this work, we introduce two notions of backdoors building upon the causal graph. We analyze the complexity of finding a small backdoor (detection) and using the backdoor to solve the problem (evaluation) in the light of planning with (un)bounded plan length/domain of the variables. For each setting we present either an fpt-result or rule out the existence thereof by showing parameterized intractability. For several interesting cases we achieve the most desirable outcome: detection and evaluation are fpt. In addition, we explore the power of polynomial preprocessing for all fpt-results, i.e., we investigate whether polynomial kernels exist. We show that for the detection problems, polynomial kernels exist whereas we rule out the existence of polynomial kernels for the evaluation problems.