Minimization of Tree Patterns

Author:

CzerwiŃski Wojciech1,Martens Wim2,Niewerth Matthias2,Parys Paweł1

Affiliation:

1. University of Warsaw, Warsaw, Poland

2. University of Bayreuth, Bayreuth, Germany

Abstract

Many of today’s graph query languages are based on graph pattern matching. We investigate optimization of tree-shaped patterns that have transitive closure operators. Such patterns not only appear in the context of graph databases but also were originally studied for querying tree-structured data, where they can perform child, descendant, node label, and wildcard tests. The minimization problem aims at reducing the number of nodes in patterns and goes back to the early 2000s. We provide an example showing that, in contrast to earlier claims, tree patterns cannot be minimized by deleting nodes only. The example resolves the M = ? NR problem, which asks if a tree pattern is minimal if and only if it is nonredundant. The example can be adapted to prove that minimization is Σ P 2 -complete, which resolves another question that was open since the early research on the problem. The latter result shows that, unless NP = Π P 2 , more general approaches for minimizing tree patterns are also bound to fail in general.

Funder

Poland's National Science Centre

Deutsche Forschungsgemeinschaft

Publisher

Association for Computing Machinery (ACM)

Subject

Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software

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