Greedy Strategies and Larger Islands of Tractability for Conjunctive Queries and Constraint Satisfaction Problems

TL;DR

This paper introduces a new approach using greedy, non-monotonic strategies to identify larger tractable classes of conjunctive queries and constraint satisfaction problems, expanding the scope of known tractable instances.

Contribution

It develops a framework for exploiting non-monotonic strategies in hypergraph decompositions, enabling the discovery of broader tractable classes beyond existing methods.

Findings

Deciding the existence of greedy winning strategies is computationally tractable.

Greedy strategies induce valid decomposition trees that can be efficiently computed.

New islands of tractability encompass all previously known classes of tractable instances.

Abstract

Structural decomposition methods have been developed for identifying tractable classes of instances of fundamental problems in databases, such as conjunctive queries and query containment, of the constraint satisfaction problem in artificial intelligence, or more generally of the homomorphism problem over relational structures. Most structural decomposition methods can be characterized through hypergraph games that are variations of the Robber and Cops graph game that characterizes the notion of treewidth. In particular, decomposition trees somehow correspond to monotone winning strategies, where the escape space of the robber on the hypergraph is shrunk monotonically by the cops. In fact, unlike the treewidth case, there are hypergraphs where monotonic strategies do not exist, while the robber can be captured by means of more complex non-monotonic strategies. However, these powerful strategies do not correspond in general to valid decompositions. The paper provides a general way to exploit the power of non-monotonic strategies, by allowing a "disciplined" form of non-monotonicity, characteristic of cops playing in a greedy way. It is shown that deciding the existence of a (non-monotone) greedy winning strategy (and compute one, if any) is tractable. Moreover, despite their non-monotonicity, such strategies always induce valid decomposition trees, which can be computed efficiently based on them. As a consequence, greedy strategies allow us to define new islands of tractability for the considered problems properly including all previously known classes of tractable instances.