计算BID概率数据库中类概率的复杂性
The Complexity of Computing Class Probabilities in BID Probabilistic Databases
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- National Technical University of Athens（雅典国立技术大学）
- Archimedes, Athena Research Center（阿尔基米德，雅典研究中心）
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中文总结 AI 辅助
本文研究BID概率数据库中计算类概率的复杂性，证明其#P-难，同时给出FPRAS和参数化算法，并探讨兼容性约束导致的更高复杂性。
中文摘要 AI 辅助
我们研究了块独立不相交（BID）概率数据库中计算类概率的问题。给定数据库中每个块实现每个可行元组类型的概率，目标是计算由给定元组多重性向量指定的世界类的概率，从而将具有相同实现元组类型袋（多重集）的世界分组在一起。对于这个问题，我们证明了即使在非常受限和结构化的输入下，它也是#P-难的。另一方面，我们表明它承认一个FPRAS，以及以元组类型数量和建模块与元组之间连接的关联图的树宽为参数的XP时间算法。最后，我们表明，在块实现之间增加某些兼容性约束会使问题分别以路径宽和树宽为参数成为#XLP-和#XALP-难的，从而在标准假设下排除了FPT算法。我们留下一个开放问题：在没有兼容性约束的情况下，这是否也成立。
英文摘要
We study the problem of computing class probabilities in block-independent disjoint (BID) probabilistic databases. Given the probability with which each block in the database realizes each feasible tuple type, the goal is to compute the probability of a class of worlds specified by a given tuple multiplicity vector, thus grouping together worlds with the same bag (multiset) of realized tuple types. For this problem, we prove $\#\mathsf{P}$-hardness even for very restricted and structured inputs. On the other hand, we show that it admits an FPRAS, as well as $\mathsf{XP}$-time algorithms parameterized by the number of tuple types and the treewidth of an incidence graph modeling the connections between blocks and tuples. Finally, we show that augmenting the problem with certain compatibility constraints between block realizations renders it $\#\mathsf{XLP}$- and $\#\mathsf{XALP}$-hard parameterized by pathwidth and treewidth respectively, ruling out $\mathsf{FPT}$ algorithms under standard assumptions. We leave as an open question whether this also holds in the absence of compatibility constraints.
