Paper Info
Title
A Dichotomy for the Generalized Model Counting Problem for Unions of Conjunctive Queries
Abstract
ABSTRACTWe study the \em generalized model counting problem, defined as follows: given a database, and a set of deterministic tuples, count the number of subsets of the database that include all deterministic tuples and satisfy the query. This problem is computationally equivalent to the evaluation of the query over a tuple-independent probabilistic database where all tuples have probabilities in $\set0,\frac1 2, 1 $. Previous work has established a dichotomy for Unions of Conjunctive Queries (UCQ) when the probabilities are arbitrary rational numbers, showing that, for each query, its complexity is either in polynomial time or \#P-hard. The query is called \em safe in the first case, and \em unsafe in the second case. Here, we strengthen the hardness proof, by proving that an unsafe UCQ query remains \#P-hard even if the probabilities are restricted to $\set0,\frac1 2, 1 $. This requires a complete redesign of the hardness proof, using new techniques. A related problem is the \em model counting problem, which asks for the probability of the query when the input probabilities are restricted to $\set0,\frac1 2 $. While our result does not extend to model counting for all unsafe UCQs, we prove that model counting is \#P-hard for a class of unsafe queries called Type-I forbidden queries.
Year
DOI
Venue
2021
10.1145/3452021.3458313
International Conference on Management of Data
Keywords
DocType
Citations 
Model counting, Tuple-Independent Databases, #P-hardness
Conference
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Batya Kenig101.01
Dan Suciu296251349.54