IN THIS ARTICLE WE PRESENT PRELIMINARY RESULTS OF A PROJECT IMPLEMENTED AT THE UNIVERSIDAD DEL BÍO-BÍO (UBB), CONCEPCIÓN CAMPUS, THAT SEEKS TO CONTRIBUTE TO INCREASING THE PERCEPTION OF SECURITY AMONG USERS, BY USING INFORMATION AND COMMUNICATION TECHNOLOGIES (ICTS). CURRENTLY, COMMUNITY MEMBERS OF THE CONCEPCION CAMPUS AT UBB SHOW DIFFERENT PERCEPTIONS OF INSECURITY. INITIALLY, WE PERFORM A DIAGNOSIS TO KNOW WHAT ARE THE INSECURITY PROBLEMS THAT AFFECT THE COMMUNITY, AND THE EFFECTS OF INSECURITY ON THE WELL-BEING OF THE COMMUNITY OF THE CONCEPCIÓN CAMPUS. IN THIS WAY, WE ESTABLISH THE MAIN PROBLEMS AROUND SECURITY AND EVALUATE DIFFERENT WAYS IN WHICH THE USE OF ICTS CONTRIBUTES TO IMPROVE THE INSECURITY PERCEPTION. THIS ARTICLE REPORTS A MOBILE APPLICATION PROTOTYPE, THAT ALLOWS ALERTING OF POSSIBLE UNSAFE EVENTS, TO BE USED WITHIN THE CONCEPCIÓN CAMPUS. THIS APPLICATION ALSO PERMITS TO GENERATE REPORTS OF SECURITY PROBLEMS THAT ARE PERCEIVED AT THE CAMPUS, WHICH ALLOW BOTH APPLICATION USERS AND UNIVERSITY MANAGERS TO ACQUIRE INFORMATION ON THE UNIVERSITY ENVIRONMENT IN TERMS OF SECURITY.

IN THE CONTEXT OF BIG DATA SCENARIOS, THE PRESENCE OF EXTENSIVE STATIC DATASETS IS NOT UNCOMMON. TO FACILITATE EFFICIENT QUERIES ON SUCH DATASETS, THE UTILIZATION OF MULTIPLE INDEXES, SUCH AS THE KD-TREE, BECOMES IMPERATIVE. THE CURRENT SCALE OF MANAGED POINTS MAY, HOWEVER, EXCEED THE CAPACITY OF PRIMARY MEMORY, POSING A SIGNIFICANT CHALLENGE. IN THIS ARTICLE WE INTRODUCE CKD-TREE, A COMPACT DATA STRUCTURE DESIGNED TO REPRESENT A KD-TREE EFFICIENTLY. THE STRUCTURE CKD-TREE IS ESSENTIALLY AN ENCODING OF THE SPIRAL CODE SEQUENCE OF POINTS WITHIN AN IMPLICIT KD-TREE (IKD-TREE) USING DIRECTLY ADDRESSABLE CODES (DACS). THE UNIQUE FEATURE OF CKD-TREE LIES IN ITS ABILITY TO PERFORM SPIRAL ENCODING AND DECODING OF POINTS BY RELYING SOLELY ON KNOWLEDGE OF THEIR PARENT POINTS WITHIN THE IKD-TREE. THIS INHERENT PROPERTY, COMBINED WITH DACS? DIRECT ACCESS CAPABILITY TO SEQUENCE ELEMENTS, ENABLES CKD-TREE TO TRAVERSE AND EXPLORE THE TREE WHILE DECODING ONLY THE NODES RELEVANT TO QUERIES. THE ARTICLE DETAILS THE ALGORITHMS NECESSARY FOR CREATING AND MANIPULATING A CKD-TREE, AS WELL AS ALGORITHMS FOR EVALUATING TWO FUNDAMENTAL QUERIES OVER POINTS: THE POINT QUERY AND THE RANGE QUERY . TO ASSESS THE PERFORMANCE OF CKD-TREE, A SERIES OF EXPERIMENTS ARE CONDUCTED, COMPARING IT WITH IKD-TREE AND K 2 -TREE DATA STRUCTURES. THE EVALUATION METRICS INCLUDE COMPRESSION EFFICIENCY AND EXECUTION TIME OF QUERIES. CKD-TREE ACHIEVES A COMPRESSION RATIO COMPARABLE TO THAT OF K 2 -TREE, APPROXIMATELY 70%, DEMONSTRATING HEIGHTENED EFFICIENCY, PARTICULARLY IN SCENARIOS CHARACTERIZED BY SPARSE DATA. ADDITIONALLY, CONSISTENT WITH EXPECTATIONS, K 2 -TREE EXHIBITS SUPERIOR PERFORMANCE IN QUERYING INDIVIDUAL POINTS, WHEREAS CKD-TREE OUTPERFORMS IN THE CONTEXT OF AGGREGATE DATA QUERIES, SUCH AS RANGE QUERIES.

IN THIS PAPER WE PROPOSE THE USE OF COMPACT DATA STRUCTURES TO REPRESENT AND PROCESS DATA WAREHOUSES (DWS) INTO MAIN MEMORY. COMPACT DATA STRUCTURES ARE DATA STRUCTURES THAT ALLOW COMPACTING THE DATA WITHOUT LOSING THE CAPACITY OF QUERYING THE DATA IN THEIR COMPACT FORM. A DW IS A DATA REPOSITORY TO STORE HISTORICAL DATA FOR DECISION SUPPORT, AND CONSISTS OF DIMENSIONS AND FACTS. THE DIMENSIONS ARE ABSTRACT CONCEPTS THAT GROUPS DATA WITH A SIMILAR MEANING, USUALLY, THEY ARE MODELLED AS HIERARCHIES OF LEVELS, WHICH CONTAIN ELEMENTS. THE FACTS ARE QUANTITATIVE DATA ASSOCIATED TO DIMENSIONS. A DATA CUBE IS A WAY TO RETRIEVE FACTS AT DIFFERENT LEVELS OF GRANULARITY, WHICH IS ACHIEVED BY NAVIGATION ON DIMENSIONS HIERARCHIES. SINCE A DW CAN STORE TERABYTES OF DATA, THE EFFICIENT PROCESSING OF DATA CUBES IS KEY IN OLAP (ON-LINE ANALYTICAL PROCESSING). WE SHOW THAT BY USING A COMPACT REPRESENTATION OF DWS WE CAN IMPROVE THE USE OF SPACE IN MAIN MEMORY, AND ACHIEVE BETTER PERFORMANCE FOR QUERY PROCESSING. IN THIS PAPER WE EXTEND A PREVIOUS WORK TO PROCESS AGGREGATE QUERIES WITH AGGREGATE FUNCTIONS MAX, MIN, COUNT AND AVG.

CURRENTLY, THE DETECTION OF STUDENTS WHO MAY DROP OUT FROM AN ACADEMIC PROGRAM IS A RELEVANT ISSUE FOR UNIVERSITIES, SO THERE ARE EFFORTS TO EXAMINE THE VARIABLES THAT DETERMINE STUDENTS DROP OUT. DROP OUT IS DEFINED IN DIFFERENT WAYS, HOWEVER, ALL THE STUDIES CONVERGE IN THAT FOR A STUDENT TO DROP OUT A COURSE OF STUDY, SOME VARIABLES MUST BE COMBINED. THIS STUDY PRESENTS A COMPARISON OF PERFORMANCE INDICATORS OF THE CURRENT DROP OUT MODEL OF THE UNIVERSIDAD DEL BÍO-BÍO (UBB), WHICH IS BASED ON LOGISTIC REGRESSION TECHNIQUE AND IT IS COMPARED WITH A NEW MODEL BASED ON DECISION TREES. THE NEW MODEL IS OBTAINED THROUGH DATA MINING METHODOLOGIES AND IT WAS IMPLEMENTED THROUGH THE SAP PREDICTIVE ANALYTICS TOOL. TO TRAIN, VALIDATE, AND APPLY THE MODEL, REAL DATA FROM THE UBB DATABASES WERE USED. THE COMPARISON SHOWS THAT THE PREDICTION OF STUDENT´ DROP OUT OF THE PROPOSED MODEL OBTAINS AN ACCURACY OF 86%, A PRECISION OF 97% WITH AN ERROR RATE OF 14%, BETTER INDICATORS THAN THE CURRENT VALUES DELIVERED BY THE MODEL BASED ON LOGISTIC REGRESSION. SUBSEQUENTLY, THE PREDICTION MODEL OBTAINED WAS OPTIMIZED CONSIDERING OTHER VARIABLES, IMPROVING EVEN MORE THE PREDICTION INDICATORS. HIGHER EDUCATION INSTITUTIONS SHOULD TAKE INTO ACCOUNT THE VARIABLES THAT EXPLAIN THE MOST THE PHENOMENON OF STUDENT S DROP OUT TO IMPROVE THE RETENTION OF THEIR STUDENTS.

A DATA WAREHOUSE (DW) IS A DATA REPOSITORY THAT ORGANIZES AND PHYSICALLY INTEGRATES DATA FROM MULTIPLE SOURCES UNDER SPECIAL KINDS OF SCHEMAS. A DW IS COMPOSED BY A SET OF DIMENSIONS THAT REFLECT THE WAY THE DATA IS STRUCTURED, AND THE FACTS THAT CORRESPOND TO QUANTITATIVE DATA RELATED WITH THE DIMENSIONS. A DIMENSION SCHEMA IS A HIERARCHICAL GRAPH OF CATEGORIES. A DIMENSION INSTANCE IS STRICT IF EVERY ELEMENT OF THE DIMENSION HAS A UNIQUE ANCESTOR ELEMENT IN EACH OF THE ANCESTOR CATEGORIES. THIS PROPERTY IS CRUCIAL FOR THE EFFICIENCY OF THE SYSTEM SINCE IT ALLOWS FOR THE CORRECT COMPUTATION OF AGGREGATE QUERIES USING PRE-COMPUTED VIEWS. A DIMENSION INSTANCE MAY BECOME NON-STRICT AFTER UPDATE OPERATIONS. WHEN THIS HAPPENS, THE INSTANCE CAN BE MINIMALLY REPAIRED IN SEVERAL WAYS. IN THIS PAPER WE CHARACTERIZE CONSISTENT ANSWERS TO AGGREGATE QUERIES BY MEANS OF SMALLEST RANGES THAT CONTAIN THE ANSWERS OBTAINED FROM EVERY MINIMAL REPAIR. WE ALSO INTRODUCE THE NOTION OF CANONICAL DIMENSION WHICH CAPTURES INFORMATION ABOUT ALL THE MINIMAL REPAIRS. WE USE THIS DIMENSION TO APPROXIMATE CONSISTENT QUERY ANSWERS.

CONSISTENT QUERY ANSWERING IS AN INCONSISTENCY TOLERANT APPROACH TO OBTAINING SEMANTICALLY CORRECT ANSWERS FROM A DATABASE THAT MAY BE INCONSISTENT WITH RESPECT TO ITS INTEGRITY CONSTRAINTS. IN THIS WORK WE FORMALIZE THE NOTION OF CONSISTENT QUERY ANSWER FOR SPATIAL DATABASES AND SPATIAL SEMANTIC INTEGRITY CONSTRAINTS. IN ORDER TO DO THIS, WE FIRST CHARACTERIZE CONFLICTING SPATIAL DATA, AND NEXT, WE DEFINE ADMISSIBLE INSTANCES THAT RESTORE CONSISTENCY WHILE STAYING CLOSE TO THE ORIGINAL INSTANCE. IN THIS WAY WE OBTAIN A REPAIR SEMANTICS, WHICH IS USED AS AN INSTRUMENTAL CONCEPT TO DEFINE AND POSSIBLY DERIVE CONSISTENT QUERY ANSWERS. WE THEN CONCENTRATE ON A CLASS OF SPATIAL DENIAL CONSTRAINTS AND SPATIAL QUERIES FOR WHICH THERE EXISTS AN EFFICIENT STRATEGY TO COMPUTE CONSISTENT QUERY ANSWERS. THIS STUDY APPLIES INCONSISTENCY TOLERANCE IN SPATIAL DATABASES, RISING RESEARCH ISSUES THAT SHIFT THE GOAL FROM THE CONSISTENCY OF A SPATIAL DATABASE TO THE CONSISTENCY OF QUERY ANSWERING.

A DATABASE INSTANCE CAN BECOME INCONSISTENT WITH RESPECT TO ITS INTEGRITY CONSTRAINTS (ICS), FOR INSTANCE, AFTER UPDATE OPERATIONS. WHEN THIS HAPPENS, IT IS POSSIBLE TO COMPUTE THE REPAIRS OF THE DATABASE. A MINIMAL REPAIR IS A NEW DATABASE INSTANCE THAT SATISFIES THE ICS, IS OBTAINED BY APPLYING UPDATE OPERATIONS OVER THE ORIGINAL INSTANCE, AND DIFFERS MINIMALLY FROM THE ORIGINAL INSTANCE. WE CAN EVALUATE QUERIES OVER THE REPAIRS, AN ANSWER TO A CONJUNCTIVE QUERY IS CONSISTENT IF IT IS AN ANSWER IN EVERY REPAIR. THE REPAIRS OF DATABASE INSTANCES CAN BE SPECIFIED BY REPAIR PROGRAMS. MOREOVER, WE CAN COMPUTE CONSISTENT ANSWERS TO QUERIES BY EVALUATING QUERY PROGRAMS TOGETHER WITH THE REPAIR PROGRAMS UNDER THE STABLE MODEL SEMANTICS. THE USE OF LOGIC PROGRAMS DOES NOT EXCEED THE INTRINSIC COMPLEXITY OF CONSISTENT QUERY ANSWERING. NEVERTHELESS, FOR A CERTAIN CLASS OF CONJUNCTIVE QUERIES AND ICS IT IS POSSIBLE TO USE THE ALTERNATIVE WELL-FOUNDED SEMANTICS (WFS) TO EVALUATE QUERIES. WE PRESENT CQA-WF, A SYSTEM THAT ALLOWS THE COMPUTATION OF CONSISTENT ANSWERS TO CONJUNCTIVE QUERIES OVER INCONSISTENT DATABASES WITH RESPECT TO FUNCTIONAL DEPENDENCIES (FDS). CQA-WF EVALUATES LOGIC PROGRAMS UNDER THE WFS. THE WFS HAS LOWER DATA COMPLEXITY THAN THE STABLE MODELS SEMANTICS.

SUSTAINABLE AGRICULTURE IS CURRENTLY BEING CHALLENGED UNDER CLIMATE CHANGE SCENARIOS SINCE EXTREME ENVIRONMENTAL PROCESSES DISRUPT AND DIMINISH GLOBAL FOOD PRODUCTION. FOR EXAMPLE, DROUGHT-INDUCED INCREASES IN PLANT DISEASES AND RAINFALL CAUSED A DECREASE IN FOOD PRODUCTION. MACHINE LEARNING AND AGRICULTURAL BIG DATA ARE HIGH-PERFORMANCE COMPUTING TECHNOLOGIES THAT ALLOW ANALYZING A LARGE AMOUNT OF DATA TO UNDERSTAND AGRICULTURAL PRODUCTION. MACHINE LEARNING AND AGRICULTURAL BIG DATA ARE HIGH-PERFORMANCE COMPUTING TECHNOLOGIES THAT ALLOW THE PROCESSING AND ANALYSIS OF LARGE AMOUNTS OF HETEROGENEOUS DATA FOR WHICH INTELLIGENT IT AND HIGH-RESOLUTION REMOTE SENSING TECHNIQUES ARE REQUIRED. HOWEVER, THE SELECTION OF ML ALGORITHMS DEPENDS ON THE TYPES OF DATA TO BE USED. THEREFORE, AGRICULTURAL SCIENTISTS NEED TO UNDERSTAND THE DATA AND THE SOURCES FROM WHICH THEY ARE DERIVED. THESE DATA CAN BE STRUCTURED, SUCH AS TEMPERATURE AND HUMIDITY DATA, WHICH ARE USUALLY NUMERICAL (E.G., FLOAT); SEMI-STRUCTURED, SUCH AS THOSE FROM SPREADSHEETS AND INFORMATION REPOSITORIES, SINCE THESE DATA TYPES ARE NOT PREVIOUSLY DEFINED AND ARE STORED IN NO-SQL DATABASES; AND UNSTRUCTURED, SUCH AS THOSE FROM FILES SUCH AS PDF, TIFF, AND SATELLITE IMAGES, SINCE THEY HAVE NOT BEEN PROCESSED AND THEREFORE ARE NOT STORED IN ANY DATABASE BUT IN REPOSITORIES (E.G., HADOOP). THIS STUDY PROVIDES INSIGHT INTO THE DATA TYPES USED IN AGRICULTURAL BIG DATA ALONG WITH THEIR MAIN CHALLENGES AND TRENDS. IT ANALYZES 43 PAPERS SELECTED THROUGH THE PROTOCOL PROPOSED BY KITCHENHAM AND CHARTERS AND VALIDATED WITH THE PRISMA CRITERIA. IT WAS FOUND THAT THE PRIMARY DATA SOURCES ARE DATABASES, SENSORS, CAMERAS, GPS, AND REMOTE SENSING, WHICH CAPTURE DATA STORED IN PLATFORMS SUCH AS HADOOP, CLOUD COMPUTING, AND GOOGLE EARTH ENGINE. IN THE FUTURE, DATA LAKES WILL ALLOW FOR DATA INTEGRATION ACROSS DIFFERENT PLATFORMS, AS THEY PROVIDE REPRESENTATION MODELS OF OTHER DATA TYPES AND THE RELATIONSHIPS BETWEEN THEM, IMPROVING

DIMENSIONS IN DATA WAREHOUSES (DWS) ARE SET OF ELEMENTS CONNECTED BY A HIERARCHICAL RELATIONSHIP. USUALLY, DIMENSIONS ARE REQUIRED TO BE STRICT AND COVERING TO SUPPORT SUMMARIZATIONS AT DIFFERENT LEVELS OF GRANULARITY. A DIMENSION IS STRICT IF ALL THEY ROLLUP RELATIONS ARE FUNCTIONS, AND IS COVERING IF EVERY ELEMENT IN A CATEGORY IS CONNECTED WITH AN ELEMENT IN ITS ANCESTOR CATEGORIES. WE PRESENT THE DATA WAREHOUSE FIXER (DWF), A SYSTEM THAT RESTORES CONSISTENCY OF DIMENSIONS THAT FAIL TO SATISFY THEIR STRICTNESS CONSTRAINTS. THE SYSTEM CHECKS CONSISTENCY, COMPUTES MINIMAL REPAIRS FOR INCONSISTENT DIMENSIONS BY IMPLEMENTING DATALOG PROGRAMS WITH NEGATION AND WEAK CONSTRAINTS, AND ALSO FIXES INCONSISTENT DIMENSIONS.

DIMENSIONS IN DATA WAREHOUSES (DWS) ARE USUALLYMODELED AS A HIERARCHICAL SET OF CATEGORIES CALLED THE DIMENSIONSCHEMA. TO GUARANTEE SUMMARIZABILITY, THIS IS, THE CAPABILITY OFUSING PRE-COMPUTED ANSWERS AT LOWER LEVELS TO COMPUTE ANSWERSAT HIGHER LEVELS, A DIMENSION IS REQUIRED TO BE STRICT AND COVERING,MEANING THAT EVERY ELEMENT OF THE DIMENSION MUST BE CONNECTEDTO A UNIQUE ANCESTOR IN EACH OF ITS ANCESTOR CATEGORIES. IN PRACTICE,ROLLUP RELATIONS OF DIMENSIONS NEED TO BE RECLASSI?ED TO CORRECTERRORS OR TO ADAPT THE DATA TO CHANGES. AFTER THESE OPERATIONS THEDIMENSION MAY BECOME NON-STRICT. A MINIMAL R-REPAIR IS A NEWDIMENSION THAT IS STRICT AND COVERING, IS OBTAINED FROM THE ORIGINALDIMENSION THROUGH A MINIMUM NUMBER OF CHANGES, AND KEEPSTHE SET OF RECLASSI?CATIONS. IN THE GENERAL CASE ?NDING AN R-REPAIRFOR A DIMENSION IS NP-COMPLETE. WE PRESENT EF?CIENT POLYNOMIALTIME ALGORITHMS TO COMPUTE A SINGLE R-REPAIR FOR DIMENSIONS THATCONTAIN ONE CON?ICTING LEVEL AND BECOME INCONSISTENT AFTER ONERECLASSI?CATION OF ELEMENTS.

WE PRESENT EFFICIENT ALGORITHMS TO COMPUTE SIMPLE AND COMPLEX MAP ALGEBRA OPERATIONS OVER RASTER DATA STORED IN MAIN MEMORY, USING THE K2-ACC COMPACT DATA STRUCTURE. RASTER DATA CORRESPOND TO NUMERICAL DATA THAT REPRESENT ATTRIBUTES OF SPATIAL OBJECTS, SUCH AS TEMPERATURE OR ELEVATION MEASURES. COMPACT DATA STRUCTURES ALLOW EFFICIENT DATA STORAGE IN MAIN MEMORY AND QUERY THEM IN THEIR COMPRESSED FORM. A K2-ACC IS A SET OF K2-TREES, ONE FOR EVERY DISTINCT NUMERIC VALUE IN THE RASTER MATRIX. WE DEMONSTRATE THAT MAP ALGEBRA OPERATIONS CAN BE COMPUTED EFFICIENTLY USING THIS COMPACT DATA STRUCTURE. IN FACT, SOME MAP ALGEBRA OPERATIONS PERFORM OVER FIVE ORDERS OF MAGNITUDE FASTER COMPARED WITH ALGORITHMS WORKING OVER UNCOMPRESSED DATASETS.

WE PRESENT EFFICIENT ALGORITHMS TO COMPUTE TWO SPATIAL QUERIES OVER POINTS STORED IN COMPACT DATA STRUCTURES. THE FORMER IS THE K-NEAREST NEIGHBORS QUERY (KNN) WHICH GIVEN A POINT Q GETS THE K-NEAREST POINTS TO Q. THE LATTER QUERY IS THE K-CLOSEST PAIR QUERY (KCPQ), WHICH OBTAINS THE K-PAIRS OF CLOSEST NEIGHBORS BETWEEN TWO SET OF POINTS R AND S ON THE SAME SPATIAL PLANE. THERE ARE SEVERAL EFFICIENT IMPLEMENTATIONS OF THESE QUERIES, WHICH WORK MAINLY WITH DATA STORED IN SECONDARY MEMORY. HOWEVER, THESE IMPLEMENTATIONS DO NOT SCALE WELL OVER LARGE DATASETS. OUR ALGORITHMS COMPUTE THE QUERIES OVER LARGE DATASETS OF POINTS STORED IN COMPACT DATA STRUCTURES, IN MAIN MEMORY. COMPACT DATA STRUCTURES ARE STRUCTURES THAT ALLOW EFFICIENTLY STORAGE DATA IN MAIN MEMORY AND QUERY THEM IN THEIR COMPRESSED FORM. WE USE THE -TREE COMPACT STRUCTURE TO REPRESENT POINTS OF INTEREST. THROUGH EXPERIMENTATION OVER SYNTHETIC AND REAL DATASETS, WE SHOW THAT BY USING THE -TREE WE CAN WORK WITH LARGE DATASETS IN MAIN MEMORY, AND THAT THE KNN AND KCPQ SPATIAL DATA QUERIES CAN BE EFFICIENTLY COMPUTED OVER THE COMPACT DATA STRUCTURES. WE ALSO IMPLEMENT A JAVA LIBRARY THAT IS AVAILABLE FOR THE ACADEMIC AND INDUSTRIAL COMMUNITY.

IN THIS PAPER, WE PRESENT TWO ALGORITHMS TO OBTAIN THE CONVEX HULL OF A SET OF POINTS THAT ARE STORED IN THE COMPACT DATA STRUCTURE CALLED K2-TREE. THIS PROBLEM CONSISTS IN GIVEN A SET OF POINTS P IN THE EUCLIDEAN SPACE OBTAINING THE SMALLEST CONVEX REGION (POLYGON) CONTAINING P. TRADITIONAL ALGORITHMS TO COMPUTE THE CONVEX HULL DO NOT SCALE WELL FOR LARGE DATABASES, SUCH AS SPATIAL DATABASES, SINCE THE DATA DOES NOT RESIDE IN MAIN MEMORY. WE USE THE K2-TREE COMPACT DATA STRUCTURE TO REPRESENT, IN MAIN MEMORY, EFFICIENTLY A BINARY ADJACENCY MATRIX REPRESENTING POINTS OVER A 2D SPACE. THIS STRUCTURE ALLOWS AN EFFICIENT NAVIGATION IN A COMPRESSED FORM. THE EXPERIMENTATIONS PERFORMED OVER SYNTHETICAL AND REAL DATA SHOW THAT OUR PROPOSED ALGORITHMS ARE MORE EFFICIENT. IN FACT THEY PERFORM OVER FOUR ORDER OF MAGNITUDE COMPARED WITH ALGORITHMS WITH TIME COMPLEXITY OF O(NLOGN).

ON-LINE ANALYTICAL PROCESSING (OLAP) DIMENSIONS ARE USUALLY MODELED AS A SET OF ELEMENTS CONNECTED BY A HIERARCHICAL RELATIONSHIP. TO ENSURE SUMMARIZABILITY, A DIMENSION IS REQUIRED TO BE STRICT, THAT IS, EVERY ELEMENT OF THE DIMENSION MUST HAVE A UNIQUE ANCESTOR IN EACH OF ITS ANCESTOR CATEGORIES. IN PRACTICE, ELEMENTS IN A DIMENSION ARE OFTEN RECLASSIFIED, MEANING THAT THEIR ROLLUPS ARE CHANGED. AFTER THIS OPERATION THE DIMENSION MAY BECOME NON-STRICT. TO FIX THIS PROBLEM, WE PROPOSE TO COMPUTE A SET OF MINIMAL R-REPAIRS FOR THE NEW NON-STRICT DIMENSION. EACH MINIMAL R-REPAIR IS A STRICT DIMENSION THAT KEEPS THE RESULT OF THE RECLASSIFICATION, AND IS OBTAINED BY PERFORMING A MINIMUM NUMBER OF INSERTIONS AND DELETIONS TO THE DIMENSION GRAPH. WE SHOW THAT, ALTHOUGH IN THE GENERAL CASE FINDING AN R-REPAIR IS NP-COMPLETE, FOR REAL-WORLD HIERARCHY SCHEMAS, COMPUTING SUCH REPAIRS CAN BE DONE IN POLYNOMIAL TIME. FURTHER, WE PROPOSE EFFICIENT HEURISTIC-BASED ALGORITHMS FOR COMPUTING R-REPAIRS, AND DISCUSS THEIR COMPUTATIONAL COMPLEXITY. WE ALSO PERFORM EXPERIMENTS OVER SYNTHETIC AND REAL-WORLD DIMENSIONS TO SHOW THE PLAUSIBILITY OF OUR APPROACH.

A DIMENSION IN A DATA WAREHOUSE (DW) IS AN ABSTRACT CONCEPT THAT GROUPS DATA THAT SHARE A COMMON SEMANTIC MEANING. THE DIMENSIONS ARE MODELED USING A HIERARCHICAL SCHEMA OF CATEGORIES. A DIMENSION IS CALLED STRICT IF EVERY ELEMENT OF EACH CATEGORY HAS EXACTLY ONE ANCESTOR IN EACH PARENT CATEGORY, AND COVERING IF EACH ELEMENT OF A CATEGORY HAS AN ANCESTOR IN EACH PARENT CATEGORY. IF A DIMENSION IS STRICT AND COVERING WE CAN USE PRE-COMPUTED RESULTS AT LOWER LEVELS TO ANSWER QUERIES AT HIGHER LEVELS. THIS CAPABILITY OF COMPUTING SUMMARIES IS VITAL FOR EFFICIENCY PURPOSES. NEVERTHELESS, WHEN DIMENSIONS ARE NOT STRICT/COVERING IT IS IMPORTANT TO KNOW THEIR STRICTNESS AND COVERING CONSTRAINTS TO KEEP THE CAPABILITY OF OBTAINING CORRECT SUMMARIZATIONS. REAL WORLD DIMENSIONS MIGHT FAIL TO SATISFY THESE CONSTRAINTS, AND, IN THESE CASES, IT IS IMPORTANT TO FIND WAYS TO FIX THE DIMENSIONS (CORRECT THEM) OR FIND WAYS TO GET CORRECT ANSWERS TO QUERIES POSED ON INCONSISTENT DIMENSIONS. A MINIMAL REPAIR IS A NEW DIMENSION THAT SATISFIES THE STRICTNESS AND COVERING CONSTRAINTS, AND THAT IS OBTAINED FROM THE ORIGINAL DIMENSION THROUGH A MINIMUM NUMBER OF CHANGES. THE SET OF MINIMAL REPAIRS CAN BE USED AS A TOOL TO COMPUTE ANSWERS TO AGGREGATE QUERIES IN THE PRESENCE OF INCONSISTENCIES. HOWEVER, COMPUTING ALL OF THEM IS NP-HARD. IN THIS PAPER, INSTEAD OF TRYING TO FIND ALL POSSIBLE MINIMAL REPAIRS, WE DEFINE A SINGLE COMPATIBLE REPAIR THAT IS CONSISTENT WITH RESPECT TO BOTH STRICTNESS AND COVERING CONSTRAINTS, IS CLOSE TO THE INCONSISTENT DIMENSION, CAN BE COMPUTED EFFICIENTLY AND CAN BE USED TO COMPUTE APPROXIMATE ANSWERS TO AGGREGATE QUERIES. IN ORDER TO DEFINE THE COMPATIBLE REPAIR WE DEFINED THE NOTION OF EXTENDED DIMENSION THAT SUPPORTS SETS OF ELEMENTS IN CATEGORIES.

COMPACT DATA STRUCTURES ARE DATA STRUC-TURES THAT ALLOW COMPACTING DATA WITHOUT LOSING THEABILITY OF QUERYING THEM IN THEIR COMPACT FORM. WEPRESENT ALGORITHMS TO EXTEND THE FUNCTIONALITY OF THECOMPACT DATA STRUCTURE CMHD (COMPACT REPRESEN-TATION OF MULTIDIMENSIONAL DATA ON HIERARCHICAL DO-MAINS), WHICH ALLOWS THE COMPUTATION OF AGGREGATEQUERIES WITH SUM FUNCTION ON MULTIDIMENSIONAL MATRICES.WE IMPLEMENT THE REST OF AGGREGATE FUNCTIONS, I.E., FUNC-TIONS MIN,MAX,COUNT AND AVG. WE USE THE CMHD OVERDATA WAREHOUSES (DWS), THAT ARE COLLECTION OF DATAORGANIZED TO SUPPORT THE DECISION-MAKING PROCESS. THEIMPROVEMENT OF E?CIENCY OF QUERY PROCESSING IN DWS ISA VERY IMPORTANT ISSUE. THEREFORE, VARIOUS E?ORTS HAVEBEEN MADE IN THAT DIRECTION, SUCH AS MATERIALIZATION OFVIEWS, USE OF INDEXES, AMONG OTHERS. WE SHOW THROUGHEXPERIMENTATION OVER DWS WITH SYNTHETIC DATA, THAT BYUSING A COMPACT REPRESENTATION OF DWS, WE CAN ACHIEVEBETTER PERFORMANCE IN PROCESSING AGGREGATE QUERIES.

LIBRO: INTERNATIONAL CONFERENCE ON EXTENDING DATABASE TECHNOLOGY ISBN: 978-3-540-23305-3

DIMENSIONS IN DATA WAREHOUSES (DWS) ARE MODELED USING A HIERARCHICAL SCHEMA OF CATEGORIES. A DIMENSION SHOULD SATISFY A SET OF CONSTRAINTS TO ENSURE THAT QUERIES CAN BE ANSWERED EFFICIENTLY USING PRE-COMPUTED ANSWERS. FOR MANY REASONS A DIMENSION MIGHT BECOME INCONSISTENT AND THERE MIGHT BE SEVERAL WAYS TO FIX IT. IN ORDER TO REPRESENT THIS UNCERTAINTY, WE INTRODUCE THE CONCEPT OF EXTENDED DIMENSIONS, THAT IS, DIMENSIONS WHERE CATEGORIES CONTAIN SETS OF ELEMENTS WHICH ALLOW TO REPRESENT AMBIGUITY. IN THIS ARTICLE WE FORMALIZE EXTENDED DIMENSIONS AND A SUITABLE WAY TO ANSWER QUERIES FROM THEM.