THE HAUSDORFF DISTANCE BETWEEN TWO SETS OF POINTS A AND B CORRESPONDS TO THE LARGEST OF THE DISTANCES BETWEEN EACH OBJECT X ? A AND ITS NEAREST NEIGHBOR IN B. THE HAUSDORFF DISTANCE HAS SEVERAL APPLICATIONS, SUCH AS COMPARING MEDICAL IMAGES OR COMPARING TWO TRANSPORT ROUTES. THERE ARE DIFFERENT ALGORITHMS TO COMPUTE THE HAUSDORFF DISTANCE, SOME OPERATE WITH THE SETS OF POINTS IN MAIN MEMORY AND OTHERS IN SECONDARY MEMORY. ON THE OTHER HAND, TO FACE THE CHALLENGE OF INDEXING LARGE SETS OF POINTS IN MAIN MEMORY, THERE ARE COMPACT DATA STRUCTURES SUCH AS K 2 -TREE WHICH, BY MINIMIZING STORAGE, CAN BE EFFICIENTLY CONSULTED. AN EFFICIENT ALGORITHM (HDK2) THAT ALLOWS THE CALCULATION OF THE HAUSDORFF DISTANCE IN THE COMPACT STRUCTURE K 2 -TREE IS PRESENTED IN THIS ARTICLE. THIS ALGORITHM ACHIEVES AN EFFICIENT SOLUTION IN BOTH TIME AND SPACE. THROUGH A SERIES OF EXPERIMENTS, THE PERFORMANCE OF OUR ALGORITHM WAS EVALUATED TOGETHER WITH OTHERS PROPOSED IN LITERATURE UNDER SIMILAR CONDITIONS. THE RESULTS ALLOW TO CONCLUDE THAT HDK2 HAS A BETTER PERFORMANCE IN RUNTIME THAN SUCH ALGORITHMS

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).

THE TYPICAL PROBLEMS OF THE REQUIREMENTS ELICITATION STAGE INCREASE WHEN STAKEHOLDERS ARE WORKING ON A GLOBAL SOFTWARE DEVELOPMENT PROJECT. IN ORDER TO FULFIL THE CHALLENGE OF SUCCESSFULLY CARRYING OUT THE REQUIREMENTS ELICITATION PROCESS IN A GSD ENVIRONMENT, REQUIREMENTS SPECIALISTS NEED SUITABLE PREPARATION. AN IMPROVEMENT IN THIS PREPARATION NECESSITATES AN UPDATE OF THE CONTENTS, TECHNIQUES AND TOOLS USED IN THE TEACHING OF THE REQUIREMENTS ELICITATION PROCESS. IN THIS PAPER WE DISCUSS THESE ISSUES, SHOW A LIST OF KNOWLEDGE AND SKILLS WHICH ARE DESIRABLE FOR REQUIREMENTS ELICITATION ENGINEERS IN GSD (OBTAINED FROM A REVIEW OF LITERATURE), AND WE ALSO PROPOSE A SIMULATOR ENVIRONMENT WITH WHICH TO DEVELOP CERTAIN SKILLS THAT ARE APPROPRIATE FOR STUDENTS AND ENGINEERS IN GSD REQUIREMENTS ELICITATION.

THIS PAPER PRESENTS THE SUCCINCT MOVING OBJECT INDEX (SMO - INDEX) THAT PURSUES EFFICIENCY IN STORAGE AND TIME OF QUERY PROCESSING FOR TIMESTAMP AND INTERVAL QUERIES. THE DATA STRUCTURE STORES DATA AND INDEX TOGETHER IN A COMPACT MANNER REDUCING THE NEED OF USING EXTERNAL MEMORY. IT IS BASED ON A K2-TREE TO STORE SNAPSHOTS OF OBJECTS LOCATION AT SOME TIME INSTANTS, AND ON A COMPACT REPRESENTATION OF THE MOVEMENT OF OBJECTS BETWEEN CONSECUTIVE SNAPSHOTS. THE EXPERIMENTAL EVALUATION SHOWS THAT THE SMO-INDEX OVERCOMES MVR-TREE IN SPACE USED AND TIME COST WHEN OBJECTS CONSTANTLY MOVE AT SIMILAR SPEED.