Problem
Research questions and friction points this paper is trying to address.
BID probabilistic databases
class probabilities
tuple multiplicity vector
The Complexity of Computing Class Probabilities in BID Probabilistic Databases
🤖 AI Summary
研究了BID概率数据库中计算类概率的问题，证明了其复杂性，并提出了FPRAS和基于参数的算法来解决。
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
BID Probabilistic Databases
FPRAS
Tree Width
Compatibility Constraints
#P-hard
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