On Injective Embeddings of Tree Patterns
Jakub Michaliszyn, Anca Muscholl, S{\l}awek Staworko, Piotr Wieczorek, and Zhilin Wu

TL;DR
This paper analyzes different types of injective embeddings of tree patterns, exploring their hierarchical relationships and computational complexities, including how restrictions on patterns affect model checking difficulty.
Contribution
It provides a comprehensive complexity analysis of various injective tree pattern embeddings and examines how pattern restrictions influence computational hardness.
Findings
Hierarchy of embedding types with varying complexities
Model checking is P or NP-complete depending on the embedding type
Restrictions on pattern structure can reduce complexity
Abstract
We study three different kinds of embeddings of tree patterns: weakly-injective, ancestor-preserving, and lca-preserving. While each of them is often referred to as injective embedding, they form a proper hierarchy and their computational properties vary (from P to NP-complete). We present a thorough study of the complexity of the model checking problem i.e., is there an embedding of a given tree pattern in a given tree, and we investigate the impact of various restrictions imposed on the tree pattern: bound on the degree of a node, bound on the height, and type of allowed labels and edges.
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Taxonomy
TopicsData Management and Algorithms · Advanced Database Systems and Queries · Advanced Graph Theory Research
