
A Dichotomy for the Generalized Model Counting Problem for Unions of Conjunctive Queries
We study the generalized model counting problem, defined as follows: giv...
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A Simple SublinearTime Algorithm for Counting Arbitrary Subgraphs via Edge Sampling
In the subgraph counting problem, we are given a input graph G(V, E) and...
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Model Counting for Conjunctive Queries Without SelfJoins
We study the problem of model counting for Boolean Conjunctive Queries (...
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Universal (and Existential) Nulls
Incomplete Information research is quite mature when it comes to so call...
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Answer Counting under Guarded TGDs
We study the complexity of answer counting for ontologymediated queries...
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Intensive use of computing resources for dominations in grids and other combinatorial problems
Our goal is to prove new results in graph theory and combinatorics thank...
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Counting Problems over Incomplete Databases
We study the complexity of various fundamental counting problems that ar...
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Counting Answers to Existential Questions
Conjunctive queries select and are expected to return certain tuples from a relational database. We study the potentially easier problem of counting all selected tuples, rather than enumerating them. In particular, we are interested in the problem's parameterized and data complexity, where the query is considered to be small or fixed, and the database is considered to be large. We identify two structural parameters for conjunctive queries that capture their inherent complexity: The dominating star size and the linked matching number. If the dominating star size of a conjunctive query is large, then we show that counting solution tuples to the query is at least as hard as counting dominating sets, which yields a finegrained complexity lower bound under the Strong Exponential Time Hypothesis as well as a #W[2]hardness result. Moreover, if the linked matching number of a conjunctive query is large, then we show that the structure of the query is so rich that arbitrary queries up to a certain size can be encoded into it; this essentially establishes #A[2]completeness. Using ideas stemming from Lovász, we lift complexity results from the class of conjunctive queries to arbitrary existential or universal formulas that might contain inequalities and negations on constraints over the free variables. As a consequence, we obtain a complexity classification that generalizes previous results of Chen, Durand, and Mengel (ToCS 2015; ICDT 2015; PODS 2016) for conjunctive queries and of Curticapean and Marx (FOCS 2014) for the subgraph counting problem. Our proof also relies on graph minors, and we show a strengthening of the ExcludedGridTheorem which might be of independent interest: If the linked matching number is large, then not only can we find a large grid somewhere in the graph, but we can find a large grid whose diagonal has disjoint paths leading into an assumed nodewelllinked set.
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