可重根超树分解
Rerootable Hypertree Decompositions
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中文总结 AI 辅助
本文针对超树分解未广泛应用的问题，首次深入探讨其可重根性，定义宽松范式得到可重根且易处理的分解，实验显示宽度增加代价适度。
中文摘要 AI 辅助
超树分解是高效回答合取查询理论中的核心基础，但尚未在实践中广泛应用。理论文献迄今大多忽视了与分解唯一性、所有分解的简洁表示相关的问题。本文首次深入探讨超树分解中的可重根性——我们认为该性质对解决上述问题至关重要。可重根性会引出无投影特性，需讨论范式以恢复易处理性；但范式又会阻碍可重根性，因此我们定义了一种宽松的范式概念，由此得到一类真正可重根且易处理的分解。实验证据表明，转向该类分解时宽度增加的代价在实际中是适度的。
英文摘要
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.
