On Product Covering in Supply Chain Models: Natural Complete Problems for W[3] and W[4]

Chen, Jianer; Zhang, Fenghui

doi:10.1007/11496199_43

Cited by 6 publications

(4 citation statements)

References 12 publications

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“…Is this problem hard for A [2]? Conversely, these problems might be hard for some higher level of the W-hierarchy, which would be also quite an interesting result, as only few natural hard problems are known for these levels; see [14].…”

Section: Conclusion and Questions For Future Researchmentioning

confidence: 97%

A multi-parameter analysis of hard problems on deterministic finite automata

Fernau¹,

Heggernes²,

Villanger³

2015

Journal of Computer and System Sciences

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We initiate a multi-parameter analysis of two well-known NP-hard problems on deterministic finite automata (DFAs): the problem of finding a short synchronizing word, and that of finding a DFA on few states consistent with a given sample of the intended language and its complement. For both problems, we study natural parameterizations and classify them with the tools provided by Parameterized Complexity. Somewhat surprisingly, in both cases, rather simple FPT algorithms can be shown to be optimal, mostly assuming the (Strong) Exponential Time Hypothesis.

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Section: Conclusion and Questions For Future Researchmentioning

confidence: 97%

A multi-parameter analysis of hard problems on deterministic finite automata

Fernau¹,

Heggernes²,

Villanger³

2015

Journal of Computer and System Sciences

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“…But it is an open question if this extension problem belongs to W[3]. Notice that there are few natural parameterized problems higher up in the W-hierarchy; see Chen and Zhang (2006). However, the very idea of extension problems (not only applicable to formal language problems) seems to lead to such problems; we also refer to Bläsius et al (2019), Casel et al (2018.…”

Section: Extensions and Orderings Of Wordsmentioning

confidence: 99%

Synchronizing words and monoid factorization, yielding a new parameterized complexity class?

Fernau

Bruchertseifer²

2022

Math. Struct. Comp. Sci.

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The concept of a synchronizing word is a very important notion in the theory of finite automata. We consider the associated decision problem to decide if a given DFA possesses a synchronizing word of length at most k, where k is the standard parameter. We show that this problem DFA-SW is equivalent to the problem Monoid Factorization introduced by Cai, Chen, Downey, and Fellows. Apart from the known $\textsf{W}[2]$ -hardness results, we show that these problems belong to $\textsf{A}[2]$ , $\textsf{W}[\textsf{P}],$ and $\textsf{WNL}$ . This indicates that DFA-SW is not complete for any of these classes, and hence, we suggest a new parameterized complexity class $\textsf{W}[\textsf{Sync}]$ as a proper home for these (and more) problems. We present quite a number of problems that belong to $\textsf{W}[\textsf{Sync}]$ or are hard or complete for this new class.

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“…To the best of our knowledge, it is only the third known example of a natural problem with this property. The first one was given by Chen and Zhang in the context of supply chain management [12]; Bläsius, Friedrich, and Schirneck added the discovery of inclusion dependencies in relational data [7]. Beyond the W [3]-hardness we also derive a lower bound based on the exponential time hypothesis, and give an algorithm for the extension oracle running in time O(|H| |X|+1 • |V |), meeting the lower bound.…”

Section: Introductionmentioning

confidence: 98%

Efficiently Enumerating Hitting Sets of Hypergraphs Arising in Data Profiling

Bläsius

Friedrich

Lischeid

et al. 2019

2019 Proceedings of the Twenty-First Workshop on Algorithm Engineering and Experiments (ALENEX)

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We devise an enumeration method for inclusion-wise minimal hitting sets in hypergraphs. It has delay O(m k * +1 • n 2 ) and uses linear space. Hereby, n is the number of vertices, m the number of hyperedges, and k * the rank of the transversal hypergraph. In particular, on classes of hypergraphs for which the cardinality k * of the largest minimal hitting set is bounded, the delay is polynomial. The algorithm solves the extension problem for minimal hitting sets as a subroutine. We show that the extension problem is W [3]-complete when parameterised by the cardinality of the set which is to be extended. For the subroutine, we give an algorithm that is optimal under the exponential time hypothesis. Despite these lower bounds, we provide empirical evidence showing that the enumeration outperforms the theoretical worst-case guarantee on hypergraphs arising in the profiling of relational databases, namely, in the detection of unique column combinations.

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On Product Covering in Supply Chain Models: Natural Complete Problems for W[3] and W[4]

Cited by 6 publications

References 12 publications

A multi-parameter analysis of hard problems on deterministic finite automata

A multi-parameter analysis of hard problems on deterministic finite automata

Synchronizing words and monoid factorization, yielding a new parameterized complexity class?

Efficiently Enumerating Hitting Sets of Hypergraphs Arising in Data Profiling

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