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Domingo, Carlos; Mishra, Nina; Pitt, Leonard

doi:10.1023/a:1007627028578

Cited by 54 publications

(6 citation statements)

References 38 publications

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“…The connection to enumeration has also inspired the intriguing result that Dual is likely not coNP-hard as it can be solved in polynomial time when given access to O( log 2 N /log log N ) suitably guessed nondeterministic bits [3,25], where N denotes the total input size of the pair (H, G). There are classes of hypergraphs for which Dual is indeed in P, see for example [8,20,25,43], or at least in FPT with respect to certain structural parameters [27]. For a much more thorough overview of decision problems associated with enumeration, see the recent work by Creignou et al [15].…”

Section: Approximation and Discoverymentioning

confidence: 99%

The Complexity of Dependency Detection and Discovery in Relational Databases

Bläsius¹,

Friedrich²,

Schirneck³

2021

Preprint

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Multi-column dependencies in relational databases come associated with two different computational tasks. The detection problem is to decide whether a dependency of a certain type and size holds in a given database, the discovery problem asks to enumerate all valid dependencies of that type. We settle the complexity of both of these problems for unique column combinations (UCCs), functional dependencies (FDs), and inclusion dependencies (INDs).We show that the detection of UCCs and FDs is W[2]-complete when parameterized by the solution size. The discovery of inclusion-wise minimal UCCs is proven to be equivalent under parsimonious reductions to the transversal hypergraph problem of enumerating the minimal hitting sets of a hypergraph. The discovery of FDs is equivalent to the simultaneous enumeration of the hitting sets of multiple input hypergraphs.We further identify the detection of INDs as one of the first natural W[3]-complete problems. The discovery of maximal INDs is shown to be equivalent to enumerating the maximal satisfying assignments of antimonotone, 3-normalized Boolean formulas.

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Section: Approximation and Discoverymentioning

confidence: 99%

The Complexity of Dependency Detection and Discovery in Relational Databases

Bläsius¹,

Friedrich²,

Schirneck³

2021

Preprint

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“…It is straightforward to show that no algorithm can do this in time polynomial in the size of the input. Consider the example of the matching graph M n = {(1, 2), (3,4), . .…”

Section: Generation Problemmentioning

confidence: 99%

“…Fixed-parameter tractability results have been obtained for the transversal hypergraph recognition problem with a wide variety of parameters, including vertex degree parameters ( [46,3,47,48,47]), hyperedge size or number parameters ( [49,48,50]), and hyperedge intersection or union size parameters ( [51,48]). For a more complete survey, the interested reader may consult [2, §4, §7].…”

Section: Fixed-parameter Tractabilitymentioning

confidence: 99%

“…The problem of generating the collection of MHSes for a given set family is of interest in a wide variety of domains, and it has been explicitly studied (under a variety of names) in the contexts of combinatorics (Section 2.1, [1]), Boolean algebra (Section 2.2, [2,3,4]), fault diagnosis (Section 2.3, [5,6,7,8,9,10,11]), data mining (Section 2.5, [12,13,14,15]), and computational biology (Section 2.4, [16,17,18,19,20,21]), among others. While some interesting results have been obtained for the associated decision problem, the computational complexity of this problem is currently unknown.…”

Section: Introductionmentioning

confidence: 99%

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The Minimal Hitting Set Generation Problem: Algorithms and Computation

Gainer-Dewar¹,

Vera-Licona²

2017

SIAM J. Discrete Math.

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Finding inclusion-minimal hitting sets for a given collection of sets is a fundamental combinatorial problem with applications in domains as diverse as Boolean algebra, computational biology, and data mining. Much of the algorithmic literature focuses on the problem of recognizing the collection of minimal hitting sets; however, in many of the applications, it is more important to generate these hitting sets. We survey twenty algorithms from across a variety of domains, considering their history, classification, useful features, and computational performance on a variety of synthetic and real-world inputs. We also provide a suite of implementations of these algorithms with a ready-to-use, platform-agnostic interface based on Docker containers and the AlgoRun framework, so that interested computational scientists can easily perform similar tests with inputs from their own research areas on their own computers or through a convenient Web interface.

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“…This is an NPO PB problem [5], with the goal to maximise the number of vertices not in the vertex cover. As well as being a useful problem to state and study in terms of computational complexity, minimum vertex cover has wide applicability to real world problems [20][21][22][23][24]. The algorithm is shown to produce high-quality solutions efficiently for various classes of minimum vertex cover problem instances.…”

Section: Introductionmentioning

confidence: 99%

A quantum walk-assisted approximate algorithm for bounded NP optimisation problems

Marsh

Wang

2019

Quantum Inf Process

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This paper describes an application of the Quantum Approximate Optimisation Algorithm (QAOA) to efficiently find approximate solutions for computational problems contained in the polynomially bounded NP optimisation complexity class (NPO PB). We consider a generalisation of the QAOA state evolution to alternating quantum walks and solution-quality-dependent phase shifts, and use the quantum walks to integrate the problem constraints of NPO problems. We apply the recent concept of a hybrid quantum-classical variational scheme to attempt finding the highest expectation value, which contains a high-quality solution. The algorithm is applied to the problem of minimum vertex cover, showing promising results using only a fixed and low number of optimisation parameters.

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Untitled

Cited by 54 publications

References 38 publications

The Complexity of Dependency Detection and Discovery in Relational Databases

The Complexity of Dependency Detection and Discovery in Relational Databases

The Minimal Hitting Set Generation Problem: Algorithms and Computation

A quantum walk-assisted approximate algorithm for bounded NP optimisation problems

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