Hypertree Decompositions

Gottlob, Georg; Greco, Gianluigi; Leone, Nicola; Scarcello, Francesco

doi:10.1145/2902251.2902309

Cited by 54 publications

(7 citation statements)

References 144 publications

(162 reference statements)

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“…It is straightforward to see that this notion of a ghd of an incidence graph I coincides the classical notion (cf., [14,13]) of a complete generalised hypertree decomposition of a hypergraph H where I H = I. It is straightforward to see that ghw(I H ) coincides with the classical notion (cf., [13]) of generalised hypertree width of a hypergraph H, and IGHW k is the class of incidence graphs I H of all hypergraphs H of generalised hypertree width k.…”

Section: Connectedness For Red Nodesmentioning

confidence: 80%

“…We use the same notation as [13] for decompositions of hypergraphs, but we write bag(t) and cover(t) instead of χ(t) and λ(t), respectively, and we formalise them with respect to incidence graphs rather than hypergraphs. Definition 2.3.…”

Section: Generalised Hypertree Decompositionsmentioning

confidence: 99%

“…Note that there are different concepts of "tree-likeness" for hypergraphs. Berge-acyclicity is a rather restricted one; it is subsumed by the more general concept of α-acyclic hypergraphs, which coincides with the hypergraphs of generalised hypertree width 1 (cf., [14,15,13]).…”

Section: Introductionmentioning

confidence: 99%

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Counting Homomorphisms from Hypergraphs of Bounded Generalised Hypertree Width: A Logical Characterisation

Scheidt¹,

Schweikardt²

2023

Preprint

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We introduce the 2-sorted counting logic GC k that expresses properties of hypergraphs. This logic has available k variables to address hyperedges, an unbounded number of variables to address vertices of a hypergraph, and atomic formulas E(e, v) to express that vertex v is contained in hyperedge e.We show that two hypergraphs H, H satisfy the same sentences of the logic GC k if, and only if, they are homomorphism indistinguishable over the class of hypergraphs of generalised hypertree width at most k. Here, H, H are called homomorphism indistinguishable over a class C if for every hypergraph G ∈ C the number of homomorphisms from G to H equals the number of homomorphisms from G to H . This result can be viewed as a generalisation (from graphs to hypergraphs) of a result by Dvořák (2010) stating that any two (undirected, simple, finite) graphs H, H are indistinguishable by the k+1-variable counting logic C k+1 if, and only if, they are homomorphism indistinguishable over the class of graphs of tree-width at most k.

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Section: Connectedness For Red Nodesmentioning

confidence: 80%

Section: Generalised Hypertree Decompositionsmentioning

confidence: 99%

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Counting Homomorphisms from Hypergraphs of Bounded Generalised Hypertree Width: A Logical Characterisation

Scheidt¹,

Schweikardt²

2023

Preprint

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“…For a fixed k, we denote by GHW(k ) the class of CQs of ghw at most k. In contrast to the case of general CQs, the evaluation problem for CQs in GHW(k ) can be solved in polynomial time [12]. Notice that each CQ in CQ[k] is also in GHW(k ), but not viceversa.…”

Section: Bounded Gen Hypertree-widthmentioning

confidence: 99%

Regularizing conjunctive features for classification

Barceló

Baumgärtner

Dalmau

et al. 2021

Journal of Computer and System Sciences

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“…For cyclic queries, the situation is more complicated and different notions of width have been explored [33]. From a practical point of view, algorithms withÕ(n d + r ) complexity all follow the same high-level approach.…”

Section: Part 2: Optimal Join Algorithmsmentioning

confidence: 99%

Optimal Join Algorithms Meet Top-k

Tziavelis

Gatterbauer

Riedewald

2020

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

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Top-k queries have been studied intensively in the database community and they are an important means to reduce query cost when only the "best" or "most interesting" results are needed instead of the full output. While some optimality results exist, e.g., the famous Threshold Algorithm, they hold only in a fairly limited model of computation that does not account for the cost incurred by large intermediate results and hence is not aligned with typical database-optimizer cost models. On the other hand, the idea of avoiding large intermediate results is arguably the main goal of recent work on optimal join algorithms, which uses the standard RAM model of computation to determine algorithm complexity. This research has created a lot of excitement due to its promise of reducing the time complexity of join queries with cycles, but it has mostly focused on full-output computation. We argue that the two areas can and should be studied from a unified point of view in order to achieve optimality in the common model of computation for a very general class of top-k-style join queries. This tutorial has two main objectives. First, we will explore and contrast the main assumptions, concepts, and algorithmic achievements of the two research areas. Second, we will cover recent, as well as some older, approaches that emerged at the intersection to support efficient ranked enumeration of join-query results. These are related to classic work on k-shortest path algorithms and more general optimization problems, some of which dates back to the 1950s. We demonstrate that this line of research warrants renewed attention in the challenging context of ranked enumeration for general join queries.

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Hypertree Decompositions

Cited by 54 publications

References 144 publications

Counting Homomorphisms from Hypergraphs of Bounded Generalised Hypertree Width: A Logical Characterisation

Counting Homomorphisms from Hypergraphs of Bounded Generalised Hypertree Width: A Logical Characterisation

Regularizing conjunctive features for classification

Optimal Join Algorithms Meet Top-k

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