Enumeration on Trees under Relabelings

TL;DR

This paper extends enumeration algorithms for MSO queries on trees to efficiently handle relabelings, enabling fast updates and enumeration of answers in practical query languages.

Contribution

It introduces a method to support relabelings in enumeration algorithms for MSO queries on trees, maintaining linear preprocessing and delay.

Findings

Enumeration with linear preprocessing and delay for MSO queries on trees.

Efficient support for node relabelings in logarithmic time.

Application to practical query languages like aggregate and group-by.

Abstract

We study how to evaluate MSO queries with free variables on trees, within the framework of enumeration algorithms. Previous work has shown how to enumerate answers with linear-time preprocessing and delay linear in the size of each output, i.e., constant-delay for free first-order variables. We extend this result to support relabelings, a restricted kind of update operations on trees which allows us to change the node labels. Our main result shows that we can enumerate the answers of MSO queries on trees with linear-time preprocessing and delay linear in each answer, while supporting node relabelings in logarithmic time. To prove this, we reuse the circuit-based enumeration structure from our earlier work, and develop techniques to maintain its index under node relabelings. We also show how enumeration under relabelings can be applied to evaluate practical query languages, such as aggregate, group-by, and parameterized queries.