Explaining Query Answer Completeness and Correctness with Minimal Pattern Covers Fatma-Zohra Hannou, Bernd Amann, Mohamed-Amine Baazizi

Explaining Query Answer Completeness and Correctness with Minimal Pattern Covers Fatma-Zohra Hannou, Bernd Amann, Mohamed-Amine Baazizi To cite this version: Fatma-Zohra Hannou, Bernd Amann, Mohamed-Amine Baazizi. Explaining Query Answer Complete- ness and Correctness with Minimal Pattern Covers. 2019. hal-01982575 HAL Id: hal-01982575 https://hal.archives-ouvertes.fr/hal-01982575 Preprint submitted on 15 Jan 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Explaining Query Answer Completeness and Correctness with Minimal Pattern Covers Fatma-Zohra Hannou Bernd Amann Mohamed-Amine Baazizi Sorbonne Universite,´ CNRS, Sorbonne Universite,´ CNRS, Sorbonne Universite,´ CNRS, LIP6 LIP6 LIP6 Paris, France Paris, France Paris, France [email protected] [email protected] Mohamed- [email protected] ABSTRACT returns complete answers and, in some cases, for annotat- Information incompleteness is a major data quality issue ing the query answers with some completeness meta-data. which is amplified by the increasing amount of data col- Despite these efforts, reasoning about data completeness re- lected from unreliable sources. Assessing the completeness mains tricky due to the complexity of exhaustively repre- of data is crucial for determining the quality of the data it- senting and deriving information about available and miss- self, but also for verifying the validity of query answers over ing data in large datasets. incomplete data. While there exists an important amount In many situations, datasets and query results are ex- of work on modeling data completeness, deriving this com- plicitly or implicitly depend on some complete reference pleteness information has not received much attention. In (or master) datasets to describe their expected full extent. this work, we tackle the issue of efficiently describing and in- For instance, sensor databases are usually construed within ferring knowledge about data completeness w.r.t. to a com- a spatio-temporal reference delimiting the coverage of the plete reference data set and study the use of a pattern alge- captured data. It is also believed according to [9] that 80 bra for summarizing the completeness and validity of query % of enterprises maintain master data with their analyti- answers. We describe an implementation and experiments cal databases (customers informations, product) . In other with a real-world dataset to validate the effectiveness and data-centric applications, a reference is defined by domain the efficiency of our approach. experts during database design and updated when neces- sary. Finally, it may also sometimes be useful to use an PVLDB Reference Format: existing table or query result as a reference for deriving a Fatma-Zohra HANNOU, Bernd AMANN and Mohamed-Amine comprehensive representation about available and missing BAAZIZI. Explaining Query Answer Completeness and Correct- information in some specific context. ness with Minimal Pattern Covers. PVLDB, 12(xxx): xxxx-yyyy, 2019. DOI: https://doi.org/10.14778/xxxxxxx.xxxxxxx Representing information completeness. To understand the importance of using reference datasets for assessing data completeness, consider the database in Table 2 which depicts 1. INTRODUCTION an example of a sensor database. The table Energy reports Information incompleteness is a major data quality issue on daily energy measurements for some locations specified that is exacerbated by the growing number of applications, by floor (fl) and room (ro). This database is endowed collecting data from distributed, open, and unreliable en- with a spatial reference MAP describing all locations in vironments. Sensor networks and data integration are sig- some building and a calendar CAL indicating the expected nificant examples in which data incompleteness naturally temporal coverage (Table 1). Observe that both reference arises due to hardware or software failures, data incompat- data sets are not necessarily validated master data but might ibility, missing data access authorizations etc. In all these have been built by an expert for a specific analysis task. situations, querying and analyzing data can lead to deriving partial or incorrect answers. Extensive effort has been Table 1: Reference tables devoted to representing and querying incomplete databases MAP fl ro CAL we da [11, 8, 3, 7, 13, 16]. The common characteristics of these f1 r1 w1 × approaches is the use of some intensional or extensional in- f1 r2 Mon w2 formation about completeness for deciding whether a query f2 r1 Tue This work is licensed under the Creative Commons Attribution- For various reasons, the current database misses some val- NonCommercial-NoDerivatives 4.0 International License. To view a copy ues that are pinpointed in grayscale in the Energy table. of this license, visit http://creativecommons.org/licenses/by-nc-nd/4.0/. For Assume that an analyst wants to gain a full knowledge about any use beyond those covered by this license, obtain permission by emailing the segments of the data that are available or missing. To [email protected]. Copyright is held by the owner/author(s). Publication rights facilitate her understanding of the data, the analyst would licensed to the VLDB Endowment. like a summarized version of the completeness information Proceedings of the VLDB Endowment, Vol. 12, No. xxx ISSN 2150-8097. and may opt for a pattern-based representation like the one DOI: https://doi.org/10.14778/xxxxxxx.xxxxxxx presented in Table 3. This figure shows two tables PE and 1 directly from the patterns of the input data. To illustrate Table 2: Data table this idea, consider Q1 which retrieves all measures referring Energy fl ro we da kWh to week w2: t0 f1 r1 w1 Mon 10 Q1 : select ∗ from Energy where we = 'w2 ' ; t1 f1 r1 w1 Tue 12 t2 f1 r1 w2 Mon 10 By evaluating Q1 over PE and PE respectively, we obtain m0 f1 r1 w2 Tue ? Table Q1(PE) and table Q1(PE): Q1 produces a complete t f1 r2 w1 Mon 8 3 answer for floor f2 while the first tuple in Q (P ) indicates t f1 r2 w1 Tue 10 1 E 4 that no answer is returned for room r2 during week w2: m1 f1 r2 w2 Mon ? m2 f1 r2 w2 Tue ? Q1(PE) fl ro we da Q1(PE) fl ro we da t5 f2 r1 w1 Mon 12 f2 ∗ ∗ ∗ ∗ r2 w2 ∗ t6 f2 r1 w1 Tue 7 f1 r1 ∗ Mon f1 r1 w2 Tue t7 f2 r1 w2 Mon 8 t8 f2 r1 w2 Tue 8 The pattern completeness model can also play a crucial role for validating the correctness of aggregation queries an- PE capturing the available and the missing information of swers. When such queries are applied on incomplete data, table Energy respectively. More exactly, table PE contains the values resulting from aggregating incomplete partitions pattern tuples that capture all partitions which are complete are simply incorrect and there is means to notify this fact w.r.t. the reference. For instance, pattern tuple p0 indicates to the user. To illustrate the role of the pattern model in that all measurements pertaining to week w1 are available, detecting potential problems with aggregation queries, con- whatever the values of floor, room or day are. Pattern p3 sider Q2 which sums the energy consumption over all day in table PE reports that no measure can be found for room values. r2 and week w2. This representation is compact as it only reports on the largest possible partitions that are complete Q2 : select f l , ro , we , sum(kWh) as kWh (resp. missing) in the data. It is also covering as it re- from Energy ports on every possible maximal complete (resp. missing) group by f l , ro , we partition of the data. Without this presentation, the analyst This query returns both valid and non-valid answers pro- might have to issue several queries without any guarantee of duced by complete and incomplete partitions respectively. deriving an exhaustive information about completeness that Incomplete partitions producing incorrect results can easily the pattern representation offers in a rather natural manner. be identified by patterns for which the value of the attribute day is a constant instead of ∗. These "incompleteness" patterns are separated from the correct partitions in Q2(PE) Table 3: Completeness pattern tables of Energy and Q2(PE). PE fl ro we da Q (P ) fl ro we PE fl ro we da 2 E Q (P ) fl ro we p0 ∗ ∗ w1 ∗ ∗ ∗ w1 2 E p3 ∗ r2 w2 ∗ ∗ r2 w2 p1 f2 ∗ ∗ ∗ f2 ∗ ∗ p4 f1 r1 ∗ Tue f1 r1 ∗ p2 f1 r1 ∗ Mon f1 r1 ∗ Analyzing information completeness. Pattern tables can Annotating query results. Completeness pattern tables become very large due to randomness of missing information also can be used for rewriting aggregation queries to au- and may not be easily analyzed by hand. Querying pattern tomatically annotate the produced results. For example, tables with SQL turns out to be a convenient means for Table 4 shows the annotated result of query Q2 where com- extracting and reasoning about data completeness. In our pleteness information is directly extracted from P2 and P¯2. example, if an analyst wants to identify the floors where all measures are available, she could issue the following query on PE and notice that, since p1 is the only pattern satisfying Table 4: Annotated Query Answer the predicate of Q0, the only floor satisfying her criteria is f2. Result Q2 fl ro we kWh annot f1 r1 w1 22 ok Q0 : select f l from PE f1 r1 w2 10 incorr where ro= ' ∗ ' and we=' ∗ ' and da=' ∗ ' f1 r2 w1 18 ok Querying pattern tables have another interesting applica- f2 r1 w1 19 ok tion when it comes to extracting completeness information of f2 r1 w2 16 ok query answers obtained from incomplete input tables.

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