A Complexity Dichotomy in Spatial Reasoning via Ramsey Theory
Abstract
Constraint satisfaction problems (CSPs) for first-order reducts of finitely bounded homogeneous structures form a large class of computational problems that might exhibit a complexity dichotomy, P versus NP-complete. A powerful method to obtain polynomial-time tractability results for such CSPs is a certain reduction to polynomial-time tractable finite-domain CSPs defined over k-types, for a sufficiently large k. We give sufficient conditions when this method can be applied and illustrate how to use the general results to prove a new complexity dichotomy for first-order expansions of the basic relations of the well-studied spatial reasoning formalism RCC5. We also classify which of these CSPs can be expressed in Datalog. Our method relies on Ramsey theory; we prove that RCC5 has a Ramsey order expansion.
Cite
@article{arxiv.2008.10261,
title = {A Complexity Dichotomy in Spatial Reasoning via Ramsey Theory},
author = {Manuel Bodirsky and Bertalan Bodor},
journal= {arXiv preprint arXiv:2008.10261},
year = {2024}
}
Comments
The present version mentions the officially published journal article in ACM Transactions on Computation Theory. Moreover, a reference has been corrected