R-trees. R-Trees: A Dynamic Index Structure For Spatial Searching. R-Tree. Invariants

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "R-trees. R-Trees: A Dynamic Index Structure For Spatial Searching. R-Tree. Invariants"

Transcription

1 R-Trees: A Dynamic Index Structure For Spatial Searching A. Guttman R-trees Generalization of B+-trees to higher dimensions Disk-based index structure Occupancy guarantee Multiple search paths Insertions and splits can be complex Accommodates non-point data easily 1 2 R-Tree Balanced (similar to B+ tree) Index node I is an n-dimensional rectangle of the form (I 0, I 1,..., I n-1 ) where each interval is a range [a,b] Leaf node entry: (I, tuple_id) Non-leaf node entry: (I, child_ptr) M is maximum entries per node. m M/2 is a parameter specifying the minimum number of entries per node. Invariants 1. Every leaf (non-leaf) has between m and M records (children) except for the root. 2. Root has at least two children unless it is a leaf. 3. Every index entry is the smallest rectangle that contains the children. (MBR = Minimum Bounding Rectangle). 4. All leaves appear at the same level

2 Example Example 5 6 Searching Given a search rectangle S Start at root and locate all child nodes which intersect S (via linear search). 2. Search the subtrees of those child nodes. 3. When you get to the leaves, return entries whose rectangles intersect S. Searches may require inspecting several paths. Worst case running time is not so good... Searching for R

3 Insertion I1 I2 I3 Insertion is done at the leaves Where to put new entry with rectangle R? 1. Start at root. 2. Go down the tree by choosing child whose rectangle needs the least enlargement to include R. In case of a tie, choose child with smallest area. 3. If there is room in the correct leaf node, insert it. Otherwise split the node (to be continued...) 4. Adjust the tree If the root was split into nodes N 1 and N 2, create new root with N 1 and N 2 as children. R1 R3 R2 R11 I1 I3 R8 R10 R9 I2 R8 R9 R I3 I1 I2 I3 I3 I1 I2 I3 R1 R8 R9 R10 R1 R8 R9 R10 R2 I1 R3 R11 R8 R10 R9 I2 R2 I1 R3 R11 R8 R10 R9 I

4 I3 I1 I2 I3 I3 I1 I2 I3 R1 R8 R9 R10 R1 R8 R9 R10 R2 R3 R8 R10 R2 R3 R8 R10 I1 R11 R9 I2 I1 R11 R9 I Splitting Nodes Problem: Divide M+1 entries among two nodes so that it is unlikely that the nodes are needlessly examined during a search. Solution: Minimize the probability of accessing the nodes during a query. Exhaustive algorithm. Quadratic algorithm. Linear time algorithm. Exhaustive Search Minimize the sum of probabilities of accessing the two pages by a query requires knowledge of range or number of nearest neighbors Try all possible combinations. Optimal results Bad running time!

5 Quadratic Algorithm 1. Find pair of entries E 1 and E 2 that maximizes area(j) - area(e 1 ) - area(e 2 ) where J is covering rectangle. Pick the pair with least affinity, i.e., the pair that wastes maximum space 2. Put E 1 in one group, E 2 in the other. 3. If one group has M-m+1 entries, put the remaining entries into the other group and stop. If all entries have been distributed then stop. 4. For each entry E, calculate d 1 and d 2 where d i is the area increase in covering rectangle of group i when E is added. 5. Find E with maximum d 1 - d 2 and add E to the group whose area will increase the least. Time complexity Algorithm is quadratic in M. Linear in number of dimensions ,R7 as seeds: R7, as seeds: Choose, as seeds seeds R7 R6 Minimum occupancy guarantee may force and to be assigned to

6 Linear Algorithm For each dimension, Choose the pair of entries with the largest separation (highest low value and lowest high value). Normalize by dividing by the width of entire set along that dimension. Choose the two entries (and dimension) with the largest normalized separation as the initial seeds. Randomly, but evenly divide the rest of the entries between the two groups. Algorithm is linear in M (capacity); almost no attempt at optimality. Deletion 1. Find the entry to delete and remove it from the appropriate leaf L. 2. Set N=L and Q =. (Q contains to-be-inserted entries) 3. If N is root, go to step 6. Else, let P be N s parent and E N be the entry in P that points to N. 1. If N has less than m entries, delete E N from P and add contents of N to Q. 2. If N has at least m entries then set the rectangle of E N to tightly enclose N. 4. Set N=P and repeat from step *Reinsert leaf entries from Q. Reinsert non-leaf entries from Q higher up so that all leaves are at the same level. 6. If root has 1 child, make the child the new root Space requirements (2kd + p) bytes per index entry for d dimensions k bytes per dimension p bytes for pointer Same for data entries with spatial extent (kd+p) bytes per data entry for point data Trees tend to be very wide and shallow Performance Tests CENTRAL circuit cell (1057 rectangles) Insertion test performance on last 10% inserts. Search test randomly generated rectangles that retrieve about 5% of the data. Deletion test delete every 10 th entry. Page size varies from 128 bytes to 2K M varies from 6 to

7 Insertion performance With linear-time splitting, inserts spend very little time doing splits. Growth with page size as expected. Increasing m reduces insertion cost because the minimum occupancy requirement gets used earlier in the insertion algorithm. Deletion performance Deletion cost affected by m. For large m: More nodes become under-full (occupancy < m). More reinserts take place. More possible splits. Running time is pretty bad for m = M/ Search performance Space Efficiency Stricter node fill criterion leads to smaller index. Search is relatively insensitive to splitting algorithm. Less I/O with larger pages. More CPU cost with larger pages. Smaller values of m reduce average number of entries per node, so less time is spent on search in the node

8 Conclusions Linear time splitting algorithm is almost as good as the others. Low node-fill requirement reduces spaceutilization but is not significantly worse than stricter node-fill requirements. R-tree can be added to relational databases. Took more than 10 years! The R*-tree: An Efficient and Robust Access Method for Points and Rectangles Norbert Beckmann, Hans-Peter Kriegel Ralf Schneider, Bernhard Seeger R*-tree Optimization on R-tree Minimize area, overlap, and margin (sum of the sides of a rectangle) Insertion at levels above leaf-1, as before at leaf-1 level, choose subtree with minimum overlap overlap(e,node) = sum of area(e entry) for all entry in node only marginally better than R-tree Split strategy M = max capacity, m = min capacity For each dimension, sort M+1 values by the lower value (use upper value to break ties) M=7,m=3 Consider groups containing the first m-1+k and the remaining M+2-m-k entries with k in [1,M-2m+2] Evaluate the area-value, margin-value, and overlap-value for each split point

9 Split strategy Area-value(split) = area(first group) + area(second group) Smaller area reduces access probability of access Margin-value(split) = margin(first group) + margin(second group) Small margin produces better packing and less overlaps Overlap-value(split) = common area of two groups Minimize common search area Choose split axis as the one containing the smallest Margin-value split Along the split axis, choose the splitting point to be the one that gives the minimum overlap-value. Use area-value to resolve ties. Forced reinserts When a split occurs at level k, sort the entries in overflowing node in a descending order based on the distance of their centroid from the node centroid Remove the first p entries and adjust the bounding rectangle of the overflowing node Reinsert the p removed entries (data or index) Empirical value for p = 30% This reduces overlap and leads to a better structure Test Data (F1) Uniform 100,000 rectangles. (F2) Cluster Centers are distributed into 640 clusters of about 1600 objects each. (F3) Parcel decompose unit square into 100,000 disjoint rectangles and increase area of each rectangle by factor of 2.5. (F4) Real-Data 120,576 rectangles from elevation lines from cartography data. (F5) Gaussian Centers follow 2-dimensional independent Gaussian distribution. (F6) Mixed-Uniform 99,000 uniformly distributed small rectangles and 1,000 uniformly distributed large rectangles. Performance Rectangle intersection query All data rectangles intersecting the query rectangle Point enclosure query All data rectangles containing the query point Rectangle enclosure query All data rectangles containing the query rectangle Spatial joins (intersection) 1K page size, M =

10 Typical Performance Data Storage utilization Spatial Join Test files: (SJ1) 1000 random rectangles from (F3) joined with (F4) (SJ2) 7500 random rectangles from (F3) joined with 7,536 rectangles from elevation lines. (SJ3) Self-join of 20,000 random rectangles from (F3) Relative performance Disk accesses Point dataset and range queries Summary of experiments Significant improvement over R-tree No test data for more than two dimensions. R*-tree is robust even for bad data distributions. R*-tree reduces # of splits and is more space efficient than other R-tree variants. R*-tree outperforms all other R-tree variants in page I/O. Problems CPU cost not calculated. Comparison with linear scan performance?

Data Warehousing und Data Mining

Data Warehousing und Data Mining Data Warehousing und Data Mining Multidimensionale Indexstrukturen Ulf Leser Wissensmanagement in der Bioinformatik Content of this Lecture Multidimensional Indexing Grid-Files Kd-trees Ulf Leser: Data

More information

Survey On: Nearest Neighbour Search With Keywords In Spatial Databases

Survey On: Nearest Neighbour Search With Keywords In Spatial Databases Survey On: Nearest Neighbour Search With Keywords In Spatial Databases SayaliBorse 1, Prof. P. M. Chawan 2, Prof. VishwanathChikaraddi 3, Prof. Manish Jansari 4 P.G. Student, Dept. of Computer Engineering&

More information

Query Processing, optimization, and indexing techniques

Query Processing, optimization, and indexing techniques Query Processing, optimization, and indexing techniques What s s this tutorial about? From here: SELECT C.name AS Course, count(s.students) AS Cnt FROM courses C, subscription S WHERE C.lecturer = Calders

More information

Big Data and Scripting. Part 4: Memory Hierarchies

Big Data and Scripting. Part 4: Memory Hierarchies 1, Big Data and Scripting Part 4: Memory Hierarchies 2, Model and Definitions memory size: M machine words total storage (on disk) of N elements (N is very large) disk size unlimited (for our considerations)

More information

Chapter 7. Multiway Trees. Data Structures and Algorithms in Java

Chapter 7. Multiway Trees. Data Structures and Algorithms in Java Chapter 7 Multiway Trees Data Structures and Algorithms in Java Objectives Discuss the following topics: The Family of B-Trees Tries Case Study: Spell Checker Data Structures and Algorithms in Java 2 Multiway

More information

Multiway Search Tree (MST)

Multiway Search Tree (MST) Multiway Search Tree (MST) Generalization of BSTs Suitable for disk MST of order n: Each node has n or fewer sub-trees S1 S2. Sm, m n Each node has n-1 or fewer keys K1 Κ2 Κm-1 : m-1 keys in ascending

More information

Multi-Way Search Trees (B Trees)

Multi-Way Search Trees (B Trees) Multi-Way Search Trees (B Trees) Multiway Search Trees An m-way search tree is a tree in which, for some integer m called the order of the tree, each node has at most m children. If n

More information

B+ Tree Properties B+ Tree Searching B+ Tree Insertion B+ Tree Deletion Static Hashing Extendable Hashing Questions in pass papers

B+ Tree Properties B+ Tree Searching B+ Tree Insertion B+ Tree Deletion Static Hashing Extendable Hashing Questions in pass papers B+ Tree and Hashing B+ Tree Properties B+ Tree Searching B+ Tree Insertion B+ Tree Deletion Static Hashing Extendable Hashing Questions in pass papers B+ Tree Properties Balanced Tree Same height for paths

More information

Vector storage and access; algorithms in GIS. This is lecture 6

Vector storage and access; algorithms in GIS. This is lecture 6 Vector storage and access; algorithms in GIS This is lecture 6 Vector data storage and access Vectors are built from points, line and areas. (x,y) Surface: (x,y,z) Vector data access Access to vector

More information

Data Mining. Cluster Analysis: Advanced Concepts and Algorithms

Data Mining. Cluster Analysis: Advanced Concepts and Algorithms Data Mining Cluster Analysis: Advanced Concepts and Algorithms Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 1 More Clustering Methods Prototype-based clustering Density-based clustering Graph-based

More information

Previous Lectures. B-Trees. External storage. Two types of memory. B-trees. Main principles

Previous Lectures. B-Trees. External storage. Two types of memory. B-trees. Main principles B-Trees Algorithms and data structures for external memory as opposed to the main memory B-Trees Previous Lectures Height balanced binary search trees: AVL trees, red-black trees. Multiway search trees:

More information

Spatial Partitioning and Indexing Responsible persons: Claudia Dolci, Dante Salvini, Michael Schrattner, Robert Weibel

Spatial Partitioning and Indexing Responsible persons: Claudia Dolci, Dante Salvini, Michael Schrattner, Robert Weibel Geographic Information Technology Training Alliance (GITTA) presents: Spatial Partitioning and Indexing Responsible persons: Claudia Dolci, Dante Salvini, Michael Schrattner, Robert Weibel Content 1.

More information

Problem. Indexing with B-trees. Indexing. Primary Key Indexing. B-trees. B-trees: Example. primary key indexing

Problem. Indexing with B-trees. Indexing. Primary Key Indexing. B-trees. B-trees: Example. primary key indexing Problem Given a large collection of records, Indexing with B-trees find similar/interesting things, i.e., allow fast, approximate queries Anastassia Ailamaki http://www.cs.cmu.edu/~natassa 2 Indexing Primary

More information

Tree-Based Indexes for Image Data

Tree-Based Indexes for Image Data Tree-Based Indexes for Image Data Leonard Brown Le Gruenwald The University of Oklahoma School of Computer Science Norman, OK, 73019 lbrown@cs.ou.edu gruenwal@cs.ou.edu Abstract As in conventional DataBase

More information

CSE 326: Data Structures B-Trees and B+ Trees

CSE 326: Data Structures B-Trees and B+ Trees Announcements (4//08) CSE 26: Data Structures B-Trees and B+ Trees Brian Curless Spring 2008 Midterm on Friday Special office hour: 4:-5: Thursday in Jaech Gallery (6 th floor of CSE building) This is

More information

Physical Data Organization

Physical Data Organization Physical Data Organization Database design using logical model of the database - appropriate level for users to focus on - user independence from implementation details Performance - other major factor

More information

Suppose you are accessing elements of an array: ... or suppose you are dereferencing pointers:

Suppose you are accessing elements of an array: ... or suppose you are dereferencing pointers: CSE 100: B-TREE Memory accesses Suppose you are accessing elements of an array: if ( a[i] < a[j] ) {... or suppose you are dereferencing pointers: temp->next->next = elem->prev->prev;... or in general

More information

Analysis of Algorithms I: Binary Search Trees

Analysis of Algorithms I: Binary Search Trees Analysis of Algorithms I: Binary Search Trees Xi Chen Columbia University Hash table: A data structure that maintains a subset of keys from a universe set U = {0, 1,..., p 1} and supports all three dictionary

More information

Chapter 18 Indexing Structures for Files. Indexes as Access Paths

Chapter 18 Indexing Structures for Files. Indexes as Access Paths Chapter 18 Indexing Structures for Files Indexes as Access Paths A single-level index is an auxiliary file that makes it more efficient to search for a record in the data file. The index is usually specified

More information

Indexing Spatio-temporal Archives

Indexing Spatio-temporal Archives The VLDB Journal manuscript No. (will be inserted by the editor) Indexing Spatio-temporal Archives Marios Hadjieleftheriou 1, George Kollios 2, Vassilis J. Tsotras 1, Dimitrios Gunopulos 1 1 Computer Science

More information

BIRCH: An Efficient Data Clustering Method For Very Large Databases

BIRCH: An Efficient Data Clustering Method For Very Large Databases BIRCH: An Efficient Data Clustering Method For Very Large Databases Tian Zhang, Raghu Ramakrishnan, Miron Livny CPSC 504 Presenter: Discussion Leader: Sophia (Xueyao) Liang HelenJr, Birches. Online Image.

More information

MODULE 15 Clustering Large Datasets LESSON 34

MODULE 15 Clustering Large Datasets LESSON 34 MODULE 15 Clustering Large Datasets LESSON 34 Incremental Clustering Keywords: Single Database Scan, Leader, BIRCH, Tree 1 Clustering Large Datasets Pattern matrix It is convenient to view the input data

More information

B-Trees. Algorithms and data structures for external memory as opposed to the main memory B-Trees. B -trees

B-Trees. Algorithms and data structures for external memory as opposed to the main memory B-Trees. B -trees B-Trees Algorithms and data structures for external memory as opposed to the main memory B-Trees Previous Lectures Height balanced binary search trees: AVL trees, red-black trees. Multiway search trees:

More information

Efficient visual search of local features. Cordelia Schmid

Efficient visual search of local features. Cordelia Schmid Efficient visual search of local features Cordelia Schmid Visual search change in viewing angle Matches 22 correct matches Image search system for large datasets Large image dataset (one million images

More information

DATABASE DESIGN - 1DL400

DATABASE DESIGN - 1DL400 DATABASE DESIGN - 1DL400 Spring 2015 A course on modern database systems!! http://www.it.uu.se/research/group/udbl/kurser/dbii_vt15/ Kjell Orsborn! Uppsala Database Laboratory! Department of Information

More information

THE concept of Big Data refers to systems conveying

THE concept of Big Data refers to systems conveying EDIC RESEARCH PROPOSAL 1 High Dimensional Nearest Neighbors Techniques for Data Cleaning Anca-Elena Alexandrescu I&C, EPFL Abstract Organisations from all domains have been searching for increasingly more

More information

Cluster Analysis for Optimal Indexing

Cluster Analysis for Optimal Indexing Proceedings of the Twenty-Sixth International Florida Artificial Intelligence Research Society Conference Cluster Analysis for Optimal Indexing Tim Wylie, Michael A. Schuh, John Sheppard, and Rafal A.

More information

Balanced search trees

Balanced search trees Lecture 8 Balanced search trees 8.1 Overview In this lecture we discuss search trees as a method for storing data in a way that supports fast insert, lookup, and delete operations. (Data structures handling

More information

Indexing and Retrieval of Historical Aggregate Information about Moving Objects

Indexing and Retrieval of Historical Aggregate Information about Moving Objects Indexing and Retrieval of Historical Aggregate Information about Moving Objects Dimitris Papadias, Yufei Tao, Jun Zhang, Nikos Mamoulis, Qiongmao Shen, and Jimeng Sun Department of Computer Science Hong

More information

Multi-dimensional index structures Part I: motivation

Multi-dimensional index structures Part I: motivation Multi-dimensional index structures Part I: motivation 144 Motivation: Data Warehouse A definition A data warehouse is a repository of integrated enterprise data. A data warehouse is used specifically for

More information

Data Mining Cluster Analysis: Advanced Concepts and Algorithms. ref. Chapter 9. Introduction to Data Mining

Data Mining Cluster Analysis: Advanced Concepts and Algorithms. ref. Chapter 9. Introduction to Data Mining Data Mining Cluster Analysis: Advanced Concepts and Algorithms ref. Chapter 9 Introduction to Data Mining by Tan, Steinbach, Kumar 1 Outline Prototype-based Fuzzy c-means Mixture Model Clustering Density-based

More information

I/O-Efficient Spatial Data Structures for Range Queries

I/O-Efficient Spatial Data Structures for Range Queries I/O-Efficient Spatial Data Structures for Range Queries Lars Arge Kasper Green Larsen MADALGO, Department of Computer Science, Aarhus University, Denmark E-mail: large@madalgo.au.dk,larsen@madalgo.au.dk

More information

CUBE INDEXING IMPLEMENTATION USING INTEGRATION OF SIDERA AND BERKELEY DB

CUBE INDEXING IMPLEMENTATION USING INTEGRATION OF SIDERA AND BERKELEY DB CUBE INDEXING IMPLEMENTATION USING INTEGRATION OF SIDERA AND BERKELEY DB Badal K. Kothari 1, Prof. Ashok R. Patel 2 1 Research Scholar, Mewar University, Chittorgadh, Rajasthan, India 2 Department of Computer

More information

QuickDB Yet YetAnother Database Management System?

QuickDB Yet YetAnother Database Management System? QuickDB Yet YetAnother Database Management System? Radim Bača, Peter Chovanec, Michal Krátký, and Petr Lukáš Radim Bača, Peter Chovanec, Michal Krátký, and Petr Lukáš Department of Computer Science, FEECS,

More information

Richard G. Newell, Mark Easterfield & David G. Theriault Smallworld Systems Ltd, 8-9 Bridge Street, Cambridge, England CB2 1UA

Richard G. Newell, Mark Easterfield & David G. Theriault Smallworld Systems Ltd, 8-9 Bridge Street, Cambridge, England CB2 1UA INTEGRATION OF SPATIAL OBJECTS IN A GIS Richard G. Newell, Mark Easterfield & David G. Theriault Smallworld Systems Ltd, 8-9 Bridge Street, Cambridge, England CB2 1UA ABSTRACT A GIS is distinguished from

More information

Announcements. CSE332: Data Abstractions. Lecture 9: B Trees. Today. Our goal. M-ary Search Tree. M-ary Search Tree. Ruth Anderson Winter 2011

Announcements. CSE332: Data Abstractions. Lecture 9: B Trees. Today. Our goal. M-ary Search Tree. M-ary Search Tree. Ruth Anderson Winter 2011 Announcements CSE2: Data Abstractions Project 2 posted! Partner selection due by 11pm Tues 1/25 at the latest. Homework due Friday Jan 28 st at the BEGINNING of lecture Lecture 9: B Trees Ruth Anderson

More information

Ag + -tree: an Index Structure for Range-aggregation Queries in Data Warehouse Environments

Ag + -tree: an Index Structure for Range-aggregation Queries in Data Warehouse Environments Ag + -tree: an Index Structure for Range-aggregation Queries in Data Warehouse Environments Yaokai Feng a, Akifumi Makinouchi b a Faculty of Information Science and Electrical Engineering, Kyushu University,

More information

Redundant Bit Vectors for the Audio Fingerprinting Server. John Platt Jonathan Goldstein Chris Burges

Redundant Bit Vectors for the Audio Fingerprinting Server. John Platt Jonathan Goldstein Chris Burges Redundant Bit Vectors for the Audio Fingerprinting Server John Platt Jonathan Goldstein Chris Burges Structure of Talk. Problem Statement 2. Problems with Existing Techniques 3. Bit Vectors 4. Partitioning

More information

PERFORMANCE COMPARISON OF SPATIAL INDEXING STRUCTURES FOR DIFFERENT QUERY TYPES NEELABH PANT. Presented to the Faculty of the Graduate School of

PERFORMANCE COMPARISON OF SPATIAL INDEXING STRUCTURES FOR DIFFERENT QUERY TYPES NEELABH PANT. Presented to the Faculty of the Graduate School of PERFORMANCE COMPARISON OF SPATIAL INDEXING STRUCTURES FOR DIFFERENT QUERY TYPES by NEELABH PANT Presented to the Faculty of the Graduate School of The University of Texas at Arlington in Partial Fulfillment

More information

File Management. Chapter 12

File Management. Chapter 12 Chapter 12 File Management File is the basic element of most of the applications, since the input to an application, as well as its output, is usually a file. They also typically outlive the execution

More information

Indexing the Trajectories of Moving Objects in Networks

Indexing the Trajectories of Moving Objects in Networks Indexing the Trajectories of Moving Objects in Networks Victor Teixeira de Almeida Ralf Hartmut Güting Praktische Informatik IV Fernuniversität Hagen, D-5884 Hagen, Germany {victor.almeida, rhg}@fernuni-hagen.de

More information

7. Indexing. Contents: Single-Level Ordered Indexes Multi-Level Indexes B + Tree based Indexes Index Definition in SQL.

7. Indexing. Contents: Single-Level Ordered Indexes Multi-Level Indexes B + Tree based Indexes Index Definition in SQL. ECS-165A WQ 11 123 Contents: Single-Level Ordered Indexes Multi-Level Indexes B + Tree based Indexes Index Definition in SQL 7. Indexing Basic Concepts Indexing mechanisms are used to optimize certain

More information

DISTANCE-BASED INDEXING FOR HIGH-DIMENSIONAL METRIC SPACES *

DISTANCE-BASED INDEXING FOR HIGH-DIMENSIONAL METRIC SPACES * DISTANCE-BASED INDEXING FOR HIGH-DIMENSIONAL METRIC SPACES * Tolga Bozkaya Department of Computer Engineering & Science Case Western Reserve University email: bozkaya@alpha.ces.cwru.edu Meral Ozsoyoglu

More information

From Last Time: Remove (Delete) Operation

From Last Time: Remove (Delete) Operation CSE 32 Lecture : More on Search Trees Today s Topics: Lazy Operations Run Time Analysis of Binary Search Tree Operations Balanced Search Trees AVL Trees and Rotations Covered in Chapter of the text From

More information

BINARY SEARCH TREE PERFORMANCE

BINARY SEARCH TREE PERFORMANCE BINARY SEARCH TREE PERFORMANCE Operation Best Time Average Time Worst Time (on a tree of n nodes) Find Insert Delete O(lg n)?? O(lg n)?? O(n) Fastest Running Time The find, insert and delete algorithms

More information

An Adaptive Index Structure for High-Dimensional Similarity Search

An Adaptive Index Structure for High-Dimensional Similarity Search An Adaptive Index Structure for High-Dimensional Similarity Search Abstract A practical method for creating a high dimensional index structure that adapts to the data distribution and scales well with

More information

Chapter 23: Advanced Data Types and New Applications. Overview

Chapter 23: Advanced Data Types and New Applications. Overview Chapter 23: Advanced Data Types and New Applications Copyright: Silberschatz, Korth and Sudarshan 1 Overview! Temporal Data! Spatial and Geographic Databases! Multimedia Databases! Mobility and Personal

More information

Chapter 7. Indexes. Objectives. Table of Contents

Chapter 7. Indexes. Objectives. Table of Contents Chapter 7. Indexes Table of Contents Objectives... 1 Introduction... 2 Context... 2 Review Questions... 3 Single-level Ordered Indexes... 4 Primary Indexes... 4 Clustering Indexes... 8 Secondary Indexes...

More information

Effective Complex Data Retrieval Mechanism for Mobile Applications

Effective Complex Data Retrieval Mechanism for Mobile Applications , 23-25 October, 2013, San Francisco, USA Effective Complex Data Retrieval Mechanism for Mobile Applications Haeng Kon Kim Abstract While mobile devices own limited storages and low computational resources,

More information

CSE 326, Data Structures. Sample Final Exam. Problem Max Points Score 1 14 (2x7) 2 18 (3x6) 3 4 4 7 5 9 6 16 7 8 8 4 9 8 10 4 Total 92.

CSE 326, Data Structures. Sample Final Exam. Problem Max Points Score 1 14 (2x7) 2 18 (3x6) 3 4 4 7 5 9 6 16 7 8 8 4 9 8 10 4 Total 92. Name: Email ID: CSE 326, Data Structures Section: Sample Final Exam Instructions: The exam is closed book, closed notes. Unless otherwise stated, N denotes the number of elements in the data structure

More information

GiST. Amol Deshpande. March 8, 2012. University of Maryland, College Park. CMSC724: Access Methods; Indexes; GiST. Amol Deshpande.

GiST. Amol Deshpande. March 8, 2012. University of Maryland, College Park. CMSC724: Access Methods; Indexes; GiST. Amol Deshpande. CMSC724: ; Indexes; : Generalized University of Maryland, College Park March 8, 2012 Outline : Generalized : Generalized : Why? Most queries have predicates in them Accessing only the needed records key

More information

Databases and Information Systems 1 Part 3: Storage Structures and Indices

Databases and Information Systems 1 Part 3: Storage Structures and Indices bases and Information Systems 1 Part 3: Storage Structures and Indices Prof. Dr. Stefan Böttcher Fakultät EIM, Institut für Informatik Universität Paderborn WS 2009 / 2010 Contents: - database buffer -

More information

Classifying Large Data Sets Using SVMs with Hierarchical Clusters. Presented by :Limou Wang

Classifying Large Data Sets Using SVMs with Hierarchical Clusters. Presented by :Limou Wang Classifying Large Data Sets Using SVMs with Hierarchical Clusters Presented by :Limou Wang Overview SVM Overview Motivation Hierarchical micro-clustering algorithm Clustering-Based SVM (CB-SVM) Experimental

More information

Data Structures for Moving Objects

Data Structures for Moving Objects Data Structures for Moving Objects Pankaj K. Agarwal Department of Computer Science Duke University Geometric Data Structures S: Set of geometric objects Points, segments, polygons Ask several queries

More information

A. V. Gerbessiotis CS Spring 2014 PS 3 Mar 24, 2014 No points

A. V. Gerbessiotis CS Spring 2014 PS 3 Mar 24, 2014 No points A. V. Gerbessiotis CS 610-102 Spring 2014 PS 3 Mar 24, 2014 No points Problem 1. Suppose that we insert n keys into a hash table of size m using open addressing and uniform hashing. Let p(n, m) be the

More information

SPEEDING UP BULK-LOADING OF QUADTREES

SPEEDING UP BULK-LOADING OF QUADTREES l0 SPEEDING UP BULK-LOADING OF QUADTREES GÍSLI R. HJALTASON HANAN SAMET YORAM J. SUSSMANN COMPUTER SCIENCE DEPARTMENT AND CENTER FOR AUTOMATION RESEARCH AND INSTITUTE FOR ADVANCED COMPUTER STUDIES UNIVERSITY

More information

Clustering. Danilo Croce Web Mining & Retrieval a.a. 2015/201 16/03/2016

Clustering. Danilo Croce Web Mining & Retrieval a.a. 2015/201 16/03/2016 Clustering Danilo Croce Web Mining & Retrieval a.a. 2015/201 16/03/2016 1 Supervised learning vs. unsupervised learning Supervised learning: discover patterns in the data that relate data attributes with

More information

! Overview! Measures of Query Cost! Selection Operation! Sorting! Join Operation! Other Operations! Evaluation of Expressions

! Overview! Measures of Query Cost! Selection Operation! Sorting! Join Operation! Other Operations! Evaluation of Expressions Chapter 13: Query Processing Chapter 13: Query Processing! Overview! Measures of Query Cost! Selection Operation! Sorting! Join Operation! Other Operations! Evaluation of Expressions Basic Steps in Query

More information

Generalizing Database Access Methods

Generalizing Database Access Methods Generalizing Database Access Methods by Ming Zhou A thesis presented to the University of Waterloo in fulfilment of the thesis requirement for the degree of Master of Mathematics in Computer Science Waterloo,

More information

Database 2 Lecture II. Alessandro Artale

Database 2 Lecture II. Alessandro Artale Free University of Bolzano Database 2. Lecture II, 2003/2004 A.Artale (1) Database 2 Lecture II Alessandro Artale Faculty of Computer Science Free University of Bolzano Room: 221 artale@inf.unibz.it http://www.inf.unibz.it/

More information

Approximation Algorithms

Approximation Algorithms Approximation Algorithms or: How I Learned to Stop Worrying and Deal with NP-Completeness Ong Jit Sheng, Jonathan (A0073924B) March, 2012 Overview Key Results (I) General techniques: Greedy algorithms

More information

Chapter 13: Query Processing. Basic Steps in Query Processing

Chapter 13: Query Processing. Basic Steps in Query Processing Chapter 13: Query Processing! Overview! Measures of Query Cost! Selection Operation! Sorting! Join Operation! Other Operations! Evaluation of Expressions 13.1 Basic Steps in Query Processing 1. Parsing

More information

Data Management for Data Science

Data Management for Data Science Data Management for Data Science Database Management Systems: Access file manager and query evaluation Maurizio Lenzerini, Riccardo Rosati Dipartimento di Ingegneria informatica automatica e gestionale

More information

15.1 Introduction The Disk-based Environment B-tree Definition B-tree Query B-tree Insertion B-tree Deletion

15.1 Introduction The Disk-based Environment B-tree Definition B-tree Query B-tree Insertion B-tree Deletion 15 B Trees Donghui Zhang Northeastern University 15.1 Introduction............................................ 15-1 15.2 The Disk-based Environment........................ 15-2 15.3 The B-tree..............................................

More information

Large Databases. mjf@inesc-id.pt, jorgej@acm.org. Abstract. Many indexing approaches for high dimensional data points have evolved into very complex

Large Databases. mjf@inesc-id.pt, jorgej@acm.org. Abstract. Many indexing approaches for high dimensional data points have evolved into very complex NB-Tree: An Indexing Structure for Content-Based Retrieval in Large Databases Manuel J. Fonseca, Joaquim A. Jorge Department of Information Systems and Computer Science INESC-ID/IST/Technical University

More information

MATHEMATICAL ENGINEERING TECHNICAL REPORTS. The Best-fit Heuristic for the Rectangular Strip Packing Problem: An Efficient Implementation

MATHEMATICAL ENGINEERING TECHNICAL REPORTS. The Best-fit Heuristic for the Rectangular Strip Packing Problem: An Efficient Implementation MATHEMATICAL ENGINEERING TECHNICAL REPORTS The Best-fit Heuristic for the Rectangular Strip Packing Problem: An Efficient Implementation Shinji IMAHORI, Mutsunori YAGIURA METR 2007 53 September 2007 DEPARTMENT

More information

Clustering UE 141 Spring 2013

Clustering UE 141 Spring 2013 Clustering UE 141 Spring 013 Jing Gao SUNY Buffalo 1 Definition of Clustering Finding groups of obects such that the obects in a group will be similar (or related) to one another and different from (or

More information

Smart-Sample: An Efficient Algorithm for Clustering Large High-Dimensional Datasets

Smart-Sample: An Efficient Algorithm for Clustering Large High-Dimensional Datasets Smart-Sample: An Efficient Algorithm for Clustering Large High-Dimensional Datasets Dudu Lazarov, Gil David, Amir Averbuch School of Computer Science, Tel-Aviv University Tel-Aviv 69978, Israel Abstract

More information

Efficient Updates for OLAP Range Queries on Flash Memory

Efficient Updates for OLAP Range Queries on Flash Memory Efficient Updates for OLAP Range Queries on Flash Memory Mitzi McCarthy and Zhen He Department of Computer Science and Computer Engineering, La Trobe University, VIC 3086, Australia Email: m.mccarthy@latrobe.edu.au;

More information

ICS 434 Advanced Database Systems

ICS 434 Advanced Database Systems ICS 434 Advanced Database Systems Dr. Abdallah Al-Sukairi sukairi@kfupm.edu.sa Second Semester 2003-2004 (032) King Fahd University of Petroleum & Minerals Information & Computer Science Department Outline

More information

Data storage Tree indexes

Data storage Tree indexes Data storage Tree indexes Rasmus Pagh February 7 lecture 1 Access paths For many database queries and updates, only a small fraction of the data needs to be accessed. Extreme examples are looking or updating

More information

root node level: internal node edge leaf node CS@VT Data Structures & Algorithms 2000-2009 McQuain

root node level: internal node edge leaf node CS@VT Data Structures & Algorithms 2000-2009 McQuain inary Trees 1 A binary tree is either empty, or it consists of a node called the root together with two binary trees called the left subtree and the right subtree of the root, which are disjoint from each

More information

MIDAS: Multi-Attribute Indexing for Distributed Architecture Systems

MIDAS: Multi-Attribute Indexing for Distributed Architecture Systems MIDAS: Multi-Attribute Indexing for Distributed Architecture Systems George Tsatsanifos (NTUA) Dimitris Sacharidis (R.C. Athena ) Timos Sellis (NTUA, R.C. Athena ) 12 th International Symposium on Spatial

More information

Chapter 4 Index Structures

Chapter 4 Index Structures Chapter 4 Index Structures Having seen the options available for representing records, we must now consider how whole relations, or the extents of classes, are represented. It is not sufficient 4.1. INDEXES

More information

The DC-Tree: A Fully Dynamic Index Structure for Data Warehouses

The DC-Tree: A Fully Dynamic Index Structure for Data Warehouses Published in the Proceedings of 16th International Conference on Data Engineering (ICDE 2) The DC-Tree: A Fully Dynamic Index Structure for Data Warehouses Martin Ester, Jörn Kohlhammer, Hans-Peter Kriegel

More information

3. The Junction Tree Algorithms

3. The Junction Tree Algorithms A Short Course on Graphical Models 3. The Junction Tree Algorithms Mark Paskin mark@paskin.org 1 Review: conditional independence Two random variables X and Y are independent (written X Y ) iff p X ( )

More information

A Storage and Access Architecture for Efficient Query Processing in Spatial Database Systems

A Storage and Access Architecture for Efficient Query Processing in Spatial Database Systems A Storage and Access Architecture for Efficient Query Processing in Spatial Database Systems Thomas Brinkhoff, Holger Horn, Hans-Peter Kriegel, Ralf Schneider Institute for Computer Science, University

More information

Enterprise Miner - Decision tree 1

Enterprise Miner - Decision tree 1 Enterprise Miner - Decision tree 1 ECLT5810 E-Commerce Data Mining Technique SAS Enterprise Miner -- Decision Tree I. Tree Node Setting Tree Node Defaults - define default options that you commonly use

More information

EE602 Algorithms GEOMETRIC INTERSECTION CHAPTER 27

EE602 Algorithms GEOMETRIC INTERSECTION CHAPTER 27 EE602 Algorithms GEOMETRIC INTERSECTION CHAPTER 27 The Problem Given a set of N objects, do any two intersect? Objects could be lines, rectangles, circles, polygons, or other geometric objects Simple to

More information

Environmental Remote Sensing GEOG 2021

Environmental Remote Sensing GEOG 2021 Environmental Remote Sensing GEOG 2021 Lecture 4 Image classification 2 Purpose categorising data data abstraction / simplification data interpretation mapping for land cover mapping use land cover class

More information

CSCI Trees. Mark Redekopp David Kempe

CSCI Trees. Mark Redekopp David Kempe 1 CSCI 104 2-3 Trees Mark Redekopp David Kempe 2 Properties, Insertion and Removal BINARY SEARCH TREES 3 Binary Search Tree Binary search tree = binary tree where all nodes meet the property that: All

More information

The DC-tree: A Fully Dynamic Index Structure for Data Warehouses

The DC-tree: A Fully Dynamic Index Structure for Data Warehouses The DC-tree: A Fully Dynamic Index Structure for Data Warehouses Martin Ester, Jörn Kohlhammer, Hans-Peter Kriegel Institute for Computer Science, University of Munich Oettingenstr. 67, D-80538 Munich,

More information

Providing Diversity in K-Nearest Neighbor Query Results

Providing Diversity in K-Nearest Neighbor Query Results Providing Diversity in K-Nearest Neighbor Query Results Anoop Jain, Parag Sarda, and Jayant R. Haritsa Database Systems Lab, SERC/CSA Indian Institute of Science, Bangalore 560012, INDIA. Abstract. Given

More information

Operating Systems: Internals and Design Principles. Chapter 12 File Management Seventh Edition By William Stallings

Operating Systems: Internals and Design Principles. Chapter 12 File Management Seventh Edition By William Stallings Operating Systems: Internals and Design Principles Chapter 12 File Management Seventh Edition By William Stallings Operating Systems: Internals and Design Principles If there is one singular characteristic

More information

(20 pts) Exercise on Page 546 in Elmasri and Navathe.

(20 pts) Exercise on Page 546 in Elmasri and Navathe. CS 440 Assignment #4 Solution (total = 150 pts., due on March 4 th, Thursday 11:30pm) (20 pts) Exercise 14.15 on Page 546 in Elmasri and Navathe. A PARTS file with Part# as the key field includes records

More information

Well-Separated Pair Decomposition for the Unit-disk Graph Metric and its Applications

Well-Separated Pair Decomposition for the Unit-disk Graph Metric and its Applications Well-Separated Pair Decomposition for the Unit-disk Graph Metric and its Applications Jie Gao Department of Computer Science Stanford University Joint work with Li Zhang Systems Research Center Hewlett-Packard

More information

ISSUES IN SPATIAL DATABASES AND GEOGRAPHIC INFORMATION SYSTEMS (GIS) HANAN SAMET

ISSUES IN SPATIAL DATABASES AND GEOGRAPHIC INFORMATION SYSTEMS (GIS) HANAN SAMET ISSUES IN SPATIAL DATABASES AND GEOGRAPHIC INFORMATION SYSTEMS (GIS) HANAN SAMET COMPUTER SCIENCE DEPARTMENT AND CENTER FOR AUTOMATION RESEARCH AND INSTITUTE FOR ADVANCED COMPUTER STUDIES UNIVERSITY OF

More information

Lecture 1: Data Storage & Index

Lecture 1: Data Storage & Index Lecture 1: Data Storage & Index R&G Chapter 8-11 Concurrency control Query Execution and Optimization Relational Operators File & Access Methods Buffer Management Disk Space Management Recovery Manager

More information

Chapter 4: Non-Parametric Classification

Chapter 4: Non-Parametric Classification Chapter 4: Non-Parametric Classification Introduction Density Estimation Parzen Windows Kn-Nearest Neighbor Density Estimation K-Nearest Neighbor (KNN) Decision Rule Gaussian Mixture Model A weighted combination

More information

CS188 Spring 2011 Section 3: Game Trees

CS188 Spring 2011 Section 3: Game Trees CS188 Spring 2011 Section 3: Game Trees 1 Warm-Up: Column-Row You have a 3x3 matrix of values like the one below. In a somewhat boring game, player A first selects a row, and then player B selects a column.

More information

Record Storage, File Organization, and Indexes

Record Storage, File Organization, and Indexes Record Storage, File Organization, and Indexes ISM6217 - Advanced Database Updated October 2005 1 Physical Database Design Phase! Inputs into the Physical Design Phase " Logical (implementation) model

More information

Laboratory Module 8 B Trees

Laboratory Module 8 B Trees Purpose: understand the notion of B trees to build, in C, a B tree 1 2-3 Trees 1.1 General Presentation Laboratory Module 8 B Trees When working with large sets of data, it is often not possible or desirable

More information

Indexing Method for Multidimensional Vector Data

Indexing Method for Multidimensional Vector Data DOI: 10.2298/CSIS120702022T Indexing Method for Multidimensional Vector Data Justin Terry and Bela Stantic Institute for Integrated and Intelligent Systems Griffith University, Queensland 4222, Australia

More information

External Sorting. Why Sort? 2-Way Sort: Requires 3 Buffers. Chapter 13

External Sorting. Why Sort? 2-Way Sort: Requires 3 Buffers. Chapter 13 External Sorting Chapter 13 Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke 1 Why Sort? A classic problem in computer science! Data requested in sorted order e.g., find students in increasing

More information

Multidimensional Indexes

Multidimensional Indexes Chapter 5 Multidimensional Indexes All the indox structures discussed so far are one dimensional] that is, they assume a single search key, and they retrieve records that match a given searchkey value.

More information

Mining Social Network Graphs

Mining Social Network Graphs Mining Social Network Graphs Debapriyo Majumdar Data Mining Fall 2014 Indian Statistical Institute Kolkata November 13, 17, 2014 Social Network No introduc+on required Really? We s7ll need to understand

More information

International Journal of Advance Research in Computer Science and Management Studies

International Journal of Advance Research in Computer Science and Management Studies Volume 3, Issue 11, November 2015 ISSN: 2321 7782 (Online) International Journal of Advance Research in Computer Science and Management Studies Research Article / Survey Paper / Case Study Available online

More information

Symbol Tables. IE 496 Lecture 13

Symbol Tables. IE 496 Lecture 13 Symbol Tables IE 496 Lecture 13 Reading for This Lecture Horowitz and Sahni, Chapter 2 Symbol Tables and Dictionaries A symbol table is a data structure for storing a list of items, each with a key and

More information

Performance Evaluation of Main-Memory R-tree Variants

Performance Evaluation of Main-Memory R-tree Variants Performance Evaluation of Main-Memory R-tree Variants Sangyong Hwang 1, Keunjoo Kwon 1, Sang K. Cha 1, Byung S. Lee 2 1. Seoul National University {syhwang, icdi, chask}@kdb.snu.ac.kr 2. University of

More information

Binary Search Trees 3/20/14

Binary Search Trees 3/20/14 Binary Search Trees 3/0/4 Presentation for use ith the textbook Data Structures and Algorithms in Java, th edition, by M. T. Goodrich, R. Tamassia, and M. H. Goldasser, Wiley, 04 Binary Search Trees 4

More information