Consistency of Chordal RCC-8 Networks

Abstract

We consider chordal RCC-8 networks and show that we can check their consistency by enforcing partial path consistency with weak composition. We prove this by using the fact that RCC-8 networks with relations from the maximal tractable subsets H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">8</sub> , C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">8</sub> , and Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">8</sub> of RCC-8 have the patchwork property. The use of partial path consistency has important practical consequences that we demonstrate with the implementation of the new reasoner PyRCC∇, which is developed by extending the state of the art reasoner PyRCC8. Given an RCC-8 network with only tractable RCC-8 relations, we show that it can be solved very efficiently with PyRCC∇ by making its underlying constraint graph chordal and running path consistency on this sparse graph instead of the completion of the given network. In the same way, partial path consistency can be used as the consistency checking step in backtracking algorithms for networks with arbitrary RCC-8 relations resulting in very improved pruning for sparse networks while incurring a penalty for dense networks.