Rerootable Hypertree Decompositions

2026-08-18

AI Summary

本文讨论了超树分解中的重根性问题，通过定义一种放宽的规范形式来解决该问题，从而获得可重根且易于处理的分解类。

Abstract

Hypertree decompositions are a cornerstone in the theory of answering conjunctive queries efficiently. However, they are not yet widely adopted in practice. Problems related to, e.g., the uniqueness of decompositions and succinct representations of all decompositions have so far mostly been neglected by the theory literature. In this paper, we present the first in-depth discussion of rerootability in hypertree decompositions---a property which we argue is essential for such problems. Rerootability leads us to projection-freeness, and we have to discuss normal form to recover tractability. Normal form, however, again obstructs rerootability, and for this reason, we define a relaxed notion of normal form which leads to a truly rerootable and tractable class. Experimental evidence suggests that the price we pay in terms of width increase for transitioning to this class of decompositions is moderate in practice.

Problem

• hypertree decompositions
• uniqueness of decompositions
• succinct representations

Innovation

• rerootability
• hypertree decompositions
• projection-freeness
• normal form