## Weighted hypertree decompositions and optimal query plans (2004)

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Venue: | In Proc. of PODS’04 |

Citations: | 8 - 2 self |

### BibTeX

@INPROCEEDINGS{Scarcello04weightedhypertree,

author = {Francesco Scarcello},

title = {Weighted hypertree decompositions and optimal query plans},

booktitle = {In Proc. of PODS’04},

year = {2004},

pages = {210--221}

}

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### Abstract

Hypertree width [22, 25] is a measure of the degree of cyclicity of hypergraphs. A number of relevant problems from different areas, e.g., the evaluation of conjunctive queries in database theory or the constraint satisfaction in AI, are tractable when their underlying hypergraphs have bounded hypertree width. However, in practical contexts like the evaluation of database queries, we have more information besides the structure of queries. For instance, we know the number of tuples in relations, the selectivity of attributes and so on. In fact, all commercial query-optimizers are based on quantitative methods and do not care about structural properties. In this paper, we define the notion of weighted hypertree decomposition, in order to combine structural decomposition methods with quantitative approaches. Weighted hypertree decompositions are equipped with cost functions, that can be used for modelling many

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Citation Context ...irm this intuition. 2. HYPERTREE DECOMPOSITIONS AND NORMAL FORMS We next recall some basic definitions of hypergraphs and hypertree decompositions. For detailed descriptions of the latter notion, see =-=[22, 25]-=-. A hypergraph H is a pair (V,H), where V is a set of vertices and H is a set of hyper-edges such that for each h ∈ H, h ⊆ V .For the sake of simplicity, we always denote V and H by var(H) and edges(H... |

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Citation Context ...ion, one of the major problems studied in the field of AI, and there has been a lot of recent interaction between the areas of query optimization and constraint satisfaction (see Vardi’s survey paper =-=[44]-=-). In this paper, we adopt the logical representation of a relational database [42, 1], where data tuples are identified with logical ground atoms, and conjunctive queries are represented as datalog r... |

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Citation Context ...ability results also hold for some further restrictions of the class of NF bounded-width hypertree decompositions, such as the bounded-width decompositions in reduced normal form, recently defined in =-=[17]-=-. 5. MINIMAL DECOMPOSITIONS AND OPTIMAL QUERY PLANS: SOME EXPERIMENTS In this section, we exploit the previous results for the efficient evaluation of database queries and we carry out some experiment... |

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Citation Context ... and so on), may be employed for v ∗ and e ∗ . In particular, in our experiments with such minimal hypertree decompositions reported in Section 5, we adopt the standard techniques described, e.g., in =-=[16, 18]-=-. ✷ Clearly, all this powerful weighting functions would be of limited practical applicability, without a polynomial time algorithm for the computation of minimal hypertree decompositions. Surprisingl... |

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Citation Context ...necessarily complete. Nevertheless, this property can be easily guaranteed by adding a fresh variable to each query atom. The algorithmcost-k-decomp, available at the hypertree decomposition homepage =-=[41]-=-, also deals with these issues, by suitably modifying the query and then filtering such fresh variables, in its output phase. Example 5.1 Consider again the following conjunctive query Q1,s{S,X,X’,C,F... |