DOCSLIB.ORG

Oooo Oo#Oo Oteoo

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Oooo Oo#Oo Oteoo h 14P6/175 f i ' PRACE co PAN • cc PAS REPORTS Oooo2 1 5 5 b ^ “ " o o o « o OOOM oo#oo 00* 0« 00990 00999 Witold Lipski omooo 09009 Variaits of file organization for a family 09099 of threo sets oteoo 09909 09990 _______ t75 1974 OOOO WARSZAWA O O O w CENTRUM OBLICZENIOWE POLSKIEJ AKADEMII NAUK COMPUTATION CENTRE POLISH ACADEMY OF SCIENCES 00*0 WARSAW PKIN, P. O. Box 2 2, POLAND Witold Lipski VARIANTS OP PILE ORGANIZATION POR A PA1CELY OP THREE SETS 175 Warsaw 1575 Komitat Redakcyjny A. Blikle (przewodniczący), J. Lipski (sekretarz), L. Łukaszewicz, R. Marczyński, Ł. Mardoń, A. Mazurkiewicz, Z. Pawlak, Z. Szoda (zastępca przewodniczącego), M. Warmia Pracę zgłosił Zdzisław Pawlak Mailing adirees« Witold Lipski, Jr ul. Afrykańska 14P 14, 03-946 Warszawa Ob)ic o PA. b Ina. Printed as a nanuscript Ba prawach rękopisu Bakład 700 egz. Ark. wyd. 0,75 ark. druk. 1,00. Papier offset. kl. XH, 70 g, 70 x 100. Oddano do druku w październiku 1974 r. W. D. B. Zam. nr 733/O 1 Abstract . CojepxaHHe • Streszczenie In the paper the following combinatorial problem related to file organization is considered: given three sets find an arranging of X such that each is a segment (cf.t3l). Certain theorems concerning a file organization introduced by Ghosh [21, which are connected with the above problem, are also proved. BapHaHTH opraHH3anHH MHOsceciBa Aawmtx b ciyqae ceMeRciBa Tpex u b o z s c t b B paCoie paccuaipHBaeTca npoójtewa KOMÓHHaiopHKH, cbs- 3aHHaa c opraHH3anne$ MHOxeciBa flammx, a mieHHo: no AaHiaai ipeii MBoxecTBau M ^ Mg, Mg » 1 BaflTH TaKoe ynopaflO^ieHHe MHoatecTBa X, ^to6bi Ka^woe mbokoctbo M npe,ncTaBJiajio codofi 0ipe3OK /cpaBBH c [3J /. ,D,0Ka3HBaeTCB TaKJKe aeKOTopaa ieo- peiia, cBS3aHKaa c BmneyKa3aHHoM npoCjreMOfi, a HMeBHO leopeua o opraHH33JJHBj npeAJioseHBoft romeu [2] • Warianty organizacji zbioru danych dla rodziny trzech zbiorów W artykule rozważany jest następujący problem kombinato- ryczny związany z organizacją zbioru danych: mając dane trzy zbiory M^Mg.MjSX znaleźć takie uporządkowanie zbioru X, by każdy zbiór był odcinkiem (por. [3]) . Udowodnione są również pewne twierdzenia związane z powyższym problemem doty­ czące organizacji zaproponowanej przez Ghosha [23. §0. Introduction Let X be the set of objects (records) of an information storage and retrieval system (see [7]) and let rifl£lP(X) be a family of subsets of X. We want to define a partial function Ss X —*X in such a way that each M e'TTl is a segment, i.e. M = [x,S(x),...,S|M|-1(x)J for an x£ X. By imposing certain restriction on S we define different classes of admissibility, in particular the classes of admissible, linear, cyclic, acyclic families of subsets of X, denoted by Adm(X), JL(X), ^( X ) , Ji(X) respectively (cf. ( 3,4,5]). Pile organizations based on this theory were considered , in the linear case, by Ghosh [1] and, in the general case, by Lipski and Karek C5.6] and Lipski [3,4]. These file organiza­ tions will be referred to as one-dimen3ional (1D), as opposed % " to two-dimensional (2D) organization proposed recently by Ghosh [2], as an extension of [1]. In the present paper only the case '7Y1 = is dealt with. We give, in §1, necessary and.sufficient conditions for to belong to different-classes of admissibility. Then, in §2, 2D organizations are considered. For each class of admissibility, its 2D analogon is defined, and certain theorems are proved, which extend a result of Ghosh [2, Theorem 4]. For definitions and notation the reader is referred to C3l, 0 3 » or [5]. - 6 - §1. One-Dinensional Organizations In this section we give necessary and sufficient conditions for a family £ TP(X) to be in certain classes of admissibility. We shall always assume that Mgu Mj = X and denote = Xs-For the reasons which are explained in details in [j] it is sufficient to consider (in proofs) on­ ly the families *^2» satisfying the following two conditions: (i) Each component of 'lift either consists of one element or is empty. (ii) The set of non-empty components of 9?7 is maximal possible for a class of admissibility under considera­ tion (for other families we obtain appropriate f-graphs by contraction). 7/e shall call such families basic. Let us recall (cf. Q6]) 9 that for a given Iffl^TP (X), two f-graphs ^X,S^> and <X,S^> are essentially different iff there is no bisection <j>:X — *■ X satisfying the following two conditions: (i) (\^/ x,y£ X ) ( <Cx,y> e S1 <---- <<p(x) ,<p(y)> £ S 2 ), i.e. cp is an isomorphism between <X,S/)> and <X,S2>. (ii) M 6 7TZ) cf(M) 6 TT t , i.e. ^ is an automorphism of . Theorem 1.1. ( Lip ski and Uarek 16]) Each family { , Mj} is admissible. The unique four essentially different f-graphs realizing the admissibility of a basic family are depicted in Fig. 1. I - 7 - Fig. 1. The f-graphs realizing the admissibility of {U^.Ug.M Theorem 1.2. A family {M^MgjM^} is acyclic iff IjnMjrtllj = ? » = 0 (1) The uni e three essentially different f-graphs realizing the acyclicity of a basic family are depicted in Fig. 2. Proof: If (1) does not hold then there exist 6 Hj n Mg o , Xg £ EjoMjaMj, Xje M1 a Mgn toy The contrac­ tion {•*i»M2>M3} ^ XltX2fX^ = £{x2'x3 M x1»x3l‘£x1>x2?} is evidently non-acyclic, hence {M^.Mg.Mj} is also non-acyclic ( contraction preserves the acyclicity, cf. C 3l) • The proof of the uniqueness is left to the reader. I Let us notice that (1) is equivalent to Mg a M ^ C v M/| a Kj 9 Mg v M^ n M2 ^ M^ ( 1 ) hence a family of three sets is acyclic iff one of them contains the intersection of the two others. - 8 - Pig. 2. The f-graphs realizing the acyclicity of {1L,,Mg, . Theorem 1.3. A family {M^Mg.Mj} is cyclic iff at least one of the following two conditions is satisfied: llj A MgO = 0 (2) M^AMgAMj = 0vM^rtMgAMj = 0vM^AMgAMj = 0 (3) There are two non-isomorphic types of basic families, and two essentially different f-graphs (one for each type) realizing the cyclicity of a basic family, see Fig. 3* Proof: If neither (2) nor (3) holds then there exist X q C KL, ^ Mg a , x>| f a Mg a ^ ^1 ^ ^ a M ^ , £ IL| ^ Mg a M ^ . The contraction {1L, ,Mg,M?}| £XqjXi ,Xg,Xj} = ’fx0 ,x2 ^ ' ^ O » ^ is evidently non-cyclic, hence {u^,Mg,MjJ is also non-cyclic (contraction preserves the cyclicity, cf. [3])> And so at least one of the conditions (2), (3~) must be satisfied if fit],Mg,Mj} is cyclic. The easy proof of the uniqueness is omitted. 8 - 9 - II Fig. 3. The f-graphs realizing the cyclicity of {iL^Mg.Mj}. Let us notice that (3) is equivalent to M1cM2 uM? v M2SM1uM3 v M ^ s W ^ u M g , hence a family of three sets is cyclic iff either its intersec­ tion is empty or a certain set is contained in the union of the two others. Theorem 2.4. A family [M^.Mg.Mj} is linear iff at least one of the three conditions is satisfied: M1C M 2 v Mg<= Mj v il^Mj v MgCiC, v MjCMg v MJ C M 1 (*) M1 n Mg = 0 V Mg/-» Mj = 0 v M? n M1 = 0 (5) Mg S M1 £ Mg u v n M? £ Mg S M_1 u M ^ v M1r>M2cMJcM1uM2 (6) There are three non-isomorphic basic families and four essen­ tially different f-graphs (two for the case (4)) realizing the linearity of a basic family, see Fig. 4. Proof: If our family is linear, then it is acyclic and cyclic. We obtain the conditions (4), (5), (6) by combining (1) with (2), (3) • The uniqueness is easy. I In other words a family of three sets is linear iff one of them is contained in another one, or two of them are disjoint, Fig. 4. The f-graphs realizing the linearity of or one of them contains the intersection of the two others and. is contained in their union. By Theorem 2.4. a family of three sets is linear iff it is cyclic and acyclic, though for arbitrary families it is not true (see [>]). §2. Two-Dimensional Organizations The idea of 2D organization is due to Ghosh [2]. In this section we give a definition of 2D organization which is more general than that in [2]. To each class of admissibility ^ (X) p its 2D analogon X (X) will be defined. The organization of Ghosh [2"] corresponds to the class <£2(x). Let rKTl<i'f(X) * let n be a positive integer and let f: X — » {1,2,...,n] be a function. We define: - 11 - t ± 7 ï ï <— » ( ^ M é O T ' l ) (N^/x.y eu ) ( x * y .— » f (x) * f (y) ) (f.L/Wl corresponds to the disjoint incidence domains condi­ tion in [2]s if x,y are in the same secondary array, i.e. f(x) = f(y), then there is no lliTT^ with x,yf ll), We define a family f (7n)£<P({l ,2,... ,n}) as follows: f ('W.) = [f(M): Mé-'iî?.}, where f(M) = ff(x) : xfljj* Definition 2.1. Let rïf l Ç. V(X) and let X ( x ) be a class of admissibility. TTC 6 $ 2(x) iff there is a positive integer n and a function f: X — > {l,2,...,n} such that f -L and f (7Tt)€ ÎJC({i ,2,..
Load more

Recommended publications
  • Probabilistic Databases
    Series ISSN: 2153-5418 SUCIU • OLTEANU •RÉ •KOCH M SYNTHESIS LECTURES ON DATA MANAGEMENT &C Morgan & Claypool Publishers Series Editor: M. Tamer Özsu, University of Waterloo Probabilistic Databases Probabilistic Databases Dan Suciu, University of Washington, Dan Olteanu, University of Oxford Christopher Ré,University of Wisconsin-Madison and Christoph Koch, EPFL Probabilistic databases are databases where the value of some attributes or the presence of some records are uncertain and known only with some probability. Applications in many areas such as information extraction, RFID and scientific data management, data cleaning, data integration, and financial risk DATABASES PROBABILISTIC assessment produce large volumes of uncertain data, which are best modeled and processed by a probabilistic database. This book presents the state of the art in representation formalisms and query processing techniques for probabilistic data. It starts by discussing the basic principles for representing large probabilistic databases, by decomposing them into tuple-independent tables, block-independent-disjoint tables, or U-databases. Then it discusses two classes of techniques for query evaluation on probabilistic databases. In extensional query evaluation, the entire probabilistic inference can be pushed into the database engine and, therefore, processed as effectively as the evaluation of standard SQL queries. The relational queries that can be evaluated this way are called safe queries. In intensional query evaluation, the probabilistic Dan Suciu inference is performed over a propositional formula called lineage expression: every relational query can be evaluated this way, but the data complexity dramatically depends on the query being evaluated, and Dan Olteanu can be #P-hard. The book also discusses some advanced topics in probabilistic data management such as top-kquery processing, sequential probabilistic databases, indexing and materialized views, and Monte Carlo databases.
    [Show full text]
  • Download a Copy of the 264-Page Publication
    2020 Department of Neurological Surgery Annual Report Reporting period July 1, 2019 through June 30, 2020 Table of Contents: Introduction .................................................................3 Faculty and Residents ...................................................5 Faculty ...................................................................6 Residents ...............................................................8 Stuart Rowe Lecturers .........................................10 Peter J. Jannetta Lecturers ................................... 11 Department Overview ............................................... 13 History ............................................................... 14 Goals/Mission .................................................... 16 Organization ...................................................... 16 Accomplishments of Note ................................ 29 Education Programs .................................................. 35 Faculty Biographies ................................................... 47 Resident Biographies ................................................171 Research ....................................................................213 Overview ...........................................................214 Investigator Research Summaries ................... 228 Research Grant Summary ................................ 242 Alumni: Past Residents ........................................... 249 Donations ................................................................ 259 Statistics
    [Show full text]
  • Best Answers Over Incomplete Data : Complexity and First-Order Rewritings
    Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence (IJCAI-19) Best Answers over Incomplete Data : Complexity and First-Order Rewritings Amelie´ Gheerbrant and Cristina Sirangelo Universite´ de Paris, IRIF, CNRS, F-75013 Paris, France famelie, [email protected] Abstract as if nulls were usual data values, thus merely using the stan- dard database query engine to compute certain answers. Answering queries over incomplete data is ubiqui- In general though it is a common occurrence that few if tous in data management and in many AI applica- any certain answers can be found. If there are no certain an- tions that use query rewriting to take advantage of swers, it is still useful to provide a user with some answers, relational database technology. In these scenarios with suitable guarantees. To address this need, a framework one lacks full information on the data but queries to measure how close an answer is to certainty has recently still need to be answered with certainty. The cer- been proposed [Libkin, 2018b], setting the foundations to tainty aspect often makes query answering unfeasi- both a quantitative and a qualitative approach. We focus on ble except for restricted classes, such as unions of the qualitative notion of best answers. Those are a refinement conjunctive queries. In addition often there are no, of certain answers based on comparing query answers; one or very few, certain answers, thus expensive com- that is supported by a larger set of complete interpretations is putation is in vain. Therefore we study a relax- better. Best answers are those answers for which there is no ation of certain answers called best answers.
    [Show full text]
  • 1 Tarski's Influence on Computer Science
    Tarski’s influence on computer science Solomon Feferman The following is the text of an invited lecture for the LICS 2005 meeting held in Chicago June 26-29, 2005.1 Except for the addition of references, footnotes, corrections of a few points and stylistic changes, the text is essentially as delivered. Subsequent to the lecture I received interesting comments from several colleagues that would have led me to expand on some of the topics as well as the list of references, had I had the time to do so. *********** Almost exactly eight years ago today, Anita Feferman gave a lecture for LICS 1997 at the University of Warsaw with the title, “The saga of Alfred Tarski: From Warsaw to Berkeley.” Anita used the opportunity to tell various things we had learned about Tarski while working on our biography of him. We had no idea then how long it would take to finish that work; it was finally completed in 2004 and appeared in the fall of that year under the title, Alfred Tarski: Life and Logic. The saga that Anita recounted took Tarski from the beginning of the 20th century with his birth to a middle-class Jewish family and upringing in Warsaw, through his university studies and Ph.D. at the ripe young age of 23 and on to his rise as the premier logician in Poland in the 1930s and increasing visibility on the international scene-- despite which he never succeeded in obtaining a chair as professor to match his achievements. The saga continued with Tarski coming to Harvard for a meeting in early September, 1939 when the Nazis invaded Poland on September 1st, at which point he was, in effect, stranded.
    [Show full text]
  • Nonapplicable Nulls
    Theoretical Computer Science 46 (1986) 67-82 67 North-Holland NONAPPLICABLE NULLS Nadine LERAT and Witold LIPSKI, Jr. Laboratoire de Recherche en Informatique, E.R.A. 452 du C.N.R.S. "AI Khowarizmi", Universit~ de Paris-Sud, Centre d'Orsay, 91405 Orsay Cedex, France Communicated by M. Nivat Received December 1985 Abstract. A nonapplicable null appears in a relation whenever the value of the corresponding attribute does not exist. In order to evaluate a query on a relation r involving such null values, the information contained in r is represented by a set of null-free instances, then the query on r--expressed in a user-friendly query language (Generalized Relational Calculus)---is translated into a set of queries on the null-free instances. Conversely, we define the operations on relations with nulls (Generalized Relational Algebra) and we proved an extension of Codd's completeness theorem. Introduction It often happens in database practice that we are not able to provide the value of an attdbutennot just because we do not know this value, but rather because (we know that) the attribute does not apply, i.e., this value simply does not exist. Typically, a special symbol, called a nonexistent null or nonapplicable null, is inserted in such a situation into the appropriate field in the database. One should make a clear distinction between nonapplicable nulls and the usual 'existential nulls' denoting 'value exists but is not known'. Indeed, these two cases of nulls have a completely different flavor and it should be stressed that a situation necessitating the use of a nonapplicable null has nothing to do with information incompleteness.
    [Show full text]
  • My Six Encounters with Victor Marek — a Personal Account
    My Six Encounters with Victor Marek — a Personal Account Mirosław Truszczynski´ Department of Computer Science, University of Kentucky, Lexington, KY 40506, USA [email protected] 1 Introduction Co-editing the volume dedicated to Victor Marek in honor of his 65th birthday turned into an occasion to reflect on the influence Victor has had on my life. Since 1985, we have worked together day in and day out, and over the years we have grown to be friends (I hope he sees it the same way). However, the story starts about 10 years earlier, and whenever I think about it, it invariably boils down to what I call six encounters. In 1973, I entered the Warsaw University of Technology and had to attend lectures on the foundations of mathematics. While in high school, I had never heard about the subject but was soon under its spell. There was clarity and elegance in it and, to my (pleasant) surprise, also questions that went beyond mathematics into the realm of phi- losophy. To be sure, it was not easy, and for a while I feared I could fail to master the subject. Fortunately, I learned that there was an excellent problem book. Owing to the color of its cover, it was known as the ”black book” among my fellow students. It helped me a lot. In fact, for a while it was indispensable! The authors were Victor Marek and Janusz Onyszkiewicz [1]. Such was my first, albeit indirect, encounter with Victor. It quite possibly saved a young aspiring mathematician. (By the way, there is also an English edition of the book [2].
    [Show full text]
  • Ooo Ooto •Oooo
    PRACE IPI PAN • ICS PAS REPORTS o o oO . 1 Q Tomasz Imielinski, Witold Lipski, jr ooto O O O f O A systematic approach 0 0 0 O O *° relational O # # database theory 90900 00900 OOO ----------------------------------------------------------------------------- 457 •oooo0#000 INSTYTUT PODSTAW INFORMATYKI POLSKIEI AKADEMII NAUK INSTITUTE OF COMPUTER SCIENCE POLISH ACADEMY OF SCIENCES ooooo 00-901 W A R SA W , P. O. Box 22, P O L A N D Tomasz Imieliński, Witold Lipski, A SYSTEMATIC APPROACH TO RELATIONAL DATABASE THEORY. 457 Warsaw, January 1982 Rada Redakcyjna A. Blikle (przewodniczący), S. Bylka, J. Lipski (sekretarz), W. Lipski, L. Łukaszewicz, R. Marczyński, A. Mazurkiewicz, T. Nowicki, Z. Szoda, M. Warsrus (zastępca przewodniczącego) Pracę zgłosił Andrzej Blikle Mailing addresses: Tomasz Imieliński Witold Lipski Institute of Computer Science Polish Academy of Sciences P.O. Box 22 00-901 Warszawa PKiH iss : : 0138 - 0648 J? X. f ' r , \ ! D 4 ? z \ ’ L1»• o , • *<w PB Printed as a manucsript Ha prawach rękopisu Nakład 700 egz. Ark. Wyd. 1,25; ark. druk. 1,75, Papier offset, kl. III, 70 g, 70 x 100. Oddano do druku w atyczniu 1982 r. W. D. H. Zaa. nr Sygn. J d k 2 ć |.k 5 ł nr inw. Abstract • COJ(0P*®HM , streszczenie In an attempt to eliminate motivational inconsistencies, we propose a new approach to relational database theory. Basically, a database schema is treated as a relational view defined over certain atomic, selfexplainable relations, constituting wnat we call a conceptual schema. In this new framework, we revisit some basic notions of the relational database theory, such as dependencies and schema equivalence.
    [Show full text]
  • Best Answers Over Incomplete Data: Complexity and First-Order Rewritings
    Best Answers over Incomplete Data : Complexity and First-Order Rewritings Amélie Gheerbrant, Cristina Sirangelo To cite this version: Amélie Gheerbrant, Cristina Sirangelo. Best Answers over Incomplete Data : Complexity and First- Order Rewritings. the Twenty-Eighth International Joint Conference on Artificial Intelligence (IJCAI 2019), Aug 2019, Macao, China. hal-02971723 HAL Id: hal-02971723 https://hal.archives-ouvertes.fr/hal-02971723 Submitted on 19 Oct 2020 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. Best Answers over Incomplete Data : Complexity and First-Order Rewritings Amelie´ Gheerbrant and Cristina Sirangelo Universite´ de Paris, IRIF, CNRS, F-75013 Paris, France famelie, [email protected] Abstract as if nulls were usual data values, thus merely using the stan- dard database query engine to compute certain answers. Answering queries over incomplete data is ubiqui- In general though it is a common occurrence that few if tous in data management and in many AI applica- any certain answers can be found. If there are no certain an- tions that use query rewriting to take advantage of swers, it is still useful to provide a user with some answers, relational database technology.
    [Show full text]
  • FINDING a MANHATTAN PATH and RELATED PROBLEMS by Witold
    FINDING A MANHATTAN PATH AND RELATED PROBLEMS by Witold Lipski, Jr. This work was supported in part by the University of Illinois. FINDING A MANHATTAN PATH AND RELATED PROBLEMS Witold Lipski, Jr. Coordinated Science Laboratory University of Illinois at Urbana-Champaign Urbana, IL 61801, USA Abstract. Let S be a set of n horizontal and vertical segments on the plane, and let s, t € S. A Manhattan path (of length k) from s to t is an alternating sequence of horizontal and vertical segments s = r^,r.,...,r^ = t where r^ 2 intersects r^+ p 0 < i < k. We give an 0 (nlog n) algorithm to find, for a given t, a tree of shortest Manhattan paths from all s € S to t. We also determine a maximum set of crossings (intersections of segments) with no two on the same segment, as well as a maximum set of nonintersecting segments, 3/2 2 both in 0(n log n) time. The latter algorithm is applied to decomposing, 3/2 2 in 0(n log n) time, a hole-free union of n rectangles with sides parallel to the coordinate axes into the minimal number of disjoint rectangles. All 2 the algorithms require O(nlogn) space, and for all of them the factor log n can be improved to lognloglogn, at the cost of some complication of the basic data structure used. Keywords and phrases: computational geometry, horizontal and vertical segments, segment tree, Manhattan path, minimal decomposition into disjoint rectangles. On leave from the Institute of Computer Science, Polish Academy of Sciences, P.
    [Show full text]
  • The Relational Model of Data and Cylindric Algebras
    JOURNAL OF COMPUTER AND SYSTEM SCIENCES 28,8&102 (1984) The Relational Model of Data and Cylindric Algebras TOMASZ IMIELI~KI AND WITOLD LIPSKI, JR. Institute of Computer Science, Polish Academy of Sciences P.O. Box 22, 00-901 Warsaw PKiN, Poland Received August 24, 1982; revised April 25, 1983 It is shown how the theory of cylindric algebras (a notion introduced by Tarski and others as a tool in the algebraization of the first order predicate calculus) can give a new insight into Codd’s relational model of data. The relational algebra of Codd can be embedded in a natural way into a cylindric algebra where the join operation becomes the usual set-theoretical inter- section. It is shown, by using known facts from the theory of cylindric algebras, that a version of the relational algebra is not finitely axiomatizable and that the equivalence problem for certain relational expressions is undecidable. A duality between the project-join and select- union operator pairs is also briefly discussed. 1. INTRODUCTION A general classification of query languages which turned out to be convenient in database theory and practice is that into nonprocedural and procedural languages. A query in a nonprocedural language expresses what we want without necessarily saying how to obtain it. A query in a procedural language explicitly specifies the actions that should be taken, or procedures to be invoked, to obtain the response. While no practical query language is either purely procedural or purely nonprocedural, it is clear that nonprocedural languages are more convenient for the user, whereas procedural languages are easier to implement.
    [Show full text]
  • Query Processing on Probabilistic Data: a Survey
    Foundations and Trends R in Databases Vol. 7, No. 3-4 (2015) 197–341 c 2017 G. Van den Broeck and D. Suciu DOI: 10.1561/1900000052 Query Processing on Probabilistic Data: A Survey Guy Van den Broeck Dan Suciu University of California University of Washington Los Angeles Seattle Contents 1 Introduction 198 2 Probabilistic Data Model 203 2.1 Possible Worlds Semantics . 204 2.2 Independence Assumptions . 205 2.3 Query Semantics . 212 2.4 Beyond Independence: Hard Constraints . 215 2.5 Beyond Independence: Soft Constraints . 218 2.6 From Soft Constraints to Independence . 225 2.7 Related Data Models . 229 3 Weighted Model Counting 236 3.1 Three Variants of Model Counting . 236 3.2 Relationships Between the Three Problems . 241 3.3 First-Order Model Counting . 243 3.4 Algorithms and Complexity for Exact Model Counting . 249 3.5 Algorithms for Approximate Model Counting . 252 4 Lifted Query Processing 258 4.1 Extensional Operators and Safe Plans . 260 4.2 Lifted Inference Rules . 265 4.3 Hierarchical Queries . 269 ii iii 4.4 The Dichotomy Theorem . 271 4.5 Negation . 278 4.6 Symmetric Databases . 281 4.7 Extensions . 284 5 Query Compilation 292 5.1 Compilation Targets . 293 5.2 Compiling UCQ . 300 5.3 Compilation Beyond UCQ . 311 6 Data, Systems, and Applications 313 6.1 Probabilistic Data . 313 6.2 Probabilistic Database Systems . 315 6.3 Applications . 318 7 Conclusions and Open Problems 321 Acknowledgements 323 References 324 Abstract Probabilistic data is motivated by the need to model uncertainty in large databases. Over the last twenty years or so, both the Database community and the AI community have studied various aspects of probabilistic relational data.
    [Show full text]
  • Remembering Professor Helena Rasiowa
    Remembering Professor Helena Rasiowa Victor W. Marek Department of Computer Science University of Kentucky Mathematicians, also often computer scientists, discuss and point to their genealogy. I do not mean here the dukes and counts among their forbears, but rather scientists of the past, their advisors, and the advisors of those, and all the way to the beginning of science in the late medieval and renaissance eras. There is a site, at the North Dakota State University, where the relevant information is stored and the information needed to produce directed graph of genealogy of a mathematician can be collected. It so happens that the genealogical information of Professor Helena Ra- siowa and mine are similar - for we had the same advisor, Professor Andrzej Mostowski, a great logician, a student of Kazimierz Kuratowski and Alfred Tarski. I guess the \parentage" could not be better in Warsaw. There was a significant age difference, in fact the very first lecture at Warsaw University, Mathematics, I took (this happened in October 1960) happened to be a class in Algebra and Professor Rasiowa was a lecturer. This fact does not qualify me to write about Professor Rasiowa. But during 22 years at Warsaw University (in different roles; first as a student, then as a teaching assistant, graduate student, and faculty) I interacted with Professor Rasiowa, although I never worked in her scientific group. Her younger collab- orators Cecylia (Ina) Rauszer, and Andrzej Skowron were coauthors, an much later, already after we moved to United States, I became a coauthor of Professor Rasiowa. While working at Warsaw University, there were no direct scientific con- tacts with Professor Rasiowa - I focused on the research as done at Professor Mostowski group, but, in the hindsight, there were some signs that logic, and more precisely, foundations of mathematics, are becoming more applied (which was the direction pushed by Professor Rasiowa and her group).
    [Show full text]