Efficiently enumerating minimal triangulations

Carmeli, Nofar; Kenig, Batya; Kimelfeld, Benny; Kröll, Markus

doi:10.1016/j.dam.2020.05.034

Cited by 8 publications

(28 citation statements)

References 26 publications

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“…This identity implies that J (T ) ≥ 0, because I (• • • ) ≥ 0. But the expressions I (• • • ) in (9) do not correspond to MVDs, because they do not include all variables Ω. The Shannon inequality (10) rectifies this, by showing that J (T ) lies between the max and the sum of m − 1 MVDs.…”

Section: From Mvds To Acyclic Schemasmentioning

confidence: 99%

Mining Approximate Acyclic Schemes from Relations

Kenig

Mundra

Prasaad

et al. 2020

Proceedings of the 2020 ACM SIGMOD International Conference on Management of Data

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Acyclic schemes have numerous applications in databases and in machine learning, such as improved design, more efficient storage, and increased performance for queries and machine learning algorithms. Multivalued dependencies (MVDs) are the building blocks of acyclic schemes. The discovery from data of both MVDs and acyclic schemes is more challenging than other forms of data dependencies, such as Functional Dependencies, because these dependencies do not hold on subsets of data, and because they are very sensitive to noise in the data; for example a single wrong or missing tuple may invalidate the schema. In this paper we present Maimon, a system for discovering approximate acyclic schemes and MVDs from data. We give a principled definition of approximation, by using notions from information theory, then describe the two components of Maimon: mining for approximate MVDs, then reconstructing acyclic schemes from approximate MVDs. We conduct an experimental evaluation of Maimon on 20 real-world datasets, and show that it can scale up to 1M rows, and up to 30 columns.

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Section: From Mvds To Acyclic Schemasmentioning

confidence: 99%

Mining Approximate Acyclic Schemes from Relations

Kenig

Mundra

Prasaad

et al. 2020

Proceedings of the 2020 ACM SIGMOD International Conference on Management of Data

Self Cite

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“…However, from an application point of view, computing only one tree decomposition might not be satisfactory. For that reason, Carmeli et al [7,8] considered the problem of listing all the minimal chordal completions of a graph, hence obtaining all the minimal tree decompositions of a graph. In the same line of research, Ravid et al [21] considered the same problem by adding a requirement on the order in which solutions are produced.…”

Section: Introductionmentioning

confidence: 99%

“…For the enumeration of minimal triangulations of a graph, Carmeli et al in [7,8] presented a highly non-trivial algorithm. Their algorithm runs in incremental polynomial time; its total complexity is quadratic in the number of solutions, and requires exponential space.…”

Section: Introductionmentioning

confidence: 99%

“…The algorithm is based on a result by Parra & Scheffler [20], according to which there is a bijection between the minimal triangulations of a graph and the maximal independent sets of a special graph of minimal separators of the input graph. In [8], they proved under Exponential Time Hypothesis that their approach cannot be improved to achieve polynomial delay. This intractability result also holds for the exponential space.…”

Section: Introductionmentioning

confidence: 99%

“…This intractability result also holds for the exponential space. In [7,8] and at a Dagstuhl seminar [4], it was left as an open problem whether a polynomial delay algorithm for this problem could be obtained. We answer this question by the affirmative.…”

Section: Introductionmentioning

confidence: 99%

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Polynomial delay algorithm for minimal chordal completions

Brosse,

Limouzy,

Mary

2021

Preprint

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Motivated by the problem of enumerating all tree decompositions of a graph, we consider in this article the problem of listing all the minimal chordal completions of a graph. In [8] (Pods 2017) Carmeli et al. proved that all minimal chordal completions or equivalently all proper tree decompositions of a graph can be listed in incremental polynomial time using exponential space. The total running time of their algorithm is quadratic in the number of solutions and the existence of an algorithm whose complexity depends only linearly on the number of solutions remained open. We close this question by providing a polynomial delay algorithm to solve this problem which, moreover, uses polynomial space.Our algorithm relies on Proximity Search, a framework recently introduced by Conte et al.[12] (Stoc 2019) which has been shown powerful to obtain polynomial delay algorithms, but generally requires exponential space. In order to obtain a polynomial space algorithm for our problem, we introduce a new general method called canonical path reconstruction to design polynomial delay and polynomial space algorithms based on proximity search.

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