B+-Tree Structures and Operations
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Questions and Answers

What is the maximum number of search keys that a block can hold if n is 170?

  • 340 + 1
  • 340 (correct)
  • 170
  • 680

    • In a B+-Tree, the last pointer in the leaf nodes points to the next leaf on the left.

    False

    What is the minimum number of pointers that an inner node in a B+-Tree must have?

    n + 1

    Each block holds at least (𝑛 + 1)/2 search keys and at most _____ search keys.

    <p>n</p> Signup and view all the answers

    Match the following components of B+-Trees with their characteristics:

    <p>Leaves = Point to data blocks and hold sorted keys Root = Must use at least one pointer Inner Nodes = Pointers point to lower B-tree blocks Pointers = Directly link between blocks</p> Signup and view all the answers

    What is true about non-primary keys in a B-tree structure?

    <p>Non-primary keys can share the same value.</p> Signup and view all the answers

    In a B-tree, a non-primary key may exist in both the left and right subtrees.

    <p>True</p> Signup and view all the answers

    What defines the smallest new key value in relation to pointers in a B-tree?

    <p>Ki is the smallest new key value reachable from the (i+1)-st pointer.</p> Signup and view all the answers

    In a B-tree, non-primary keys can span multiple __________.

    <p>blocks</p> Signup and view all the answers

    Match the B-tree concepts with their descriptions:

    <p>Non-primary keys = Keys not unique and can span blocks Ki = Smallest new key value from (i+1)-st pointer Subtree = A smaller tree of nodes connected to a parent node Pointer = Reference to the next block or node in the tree</p> Signup and view all the answers

    What action is taken if there is no room in the leaf node during B-Tree insertion?

    <p>The leaf is split into two parts</p> Signup and view all the answers

    A B-Tree can have a maximum of two children per node.

    <p>False</p> Signup and view all the answers

    What is the first step in the recursive algorithm for inserting into a B-Tree?

    <p>Search corresponding leaf</p> Signup and view all the answers

    If the root node has no space during a B-Tree split, a new ______ is created.

    <p>root</p> Signup and view all the answers

    Match the following steps with their respective actions in B-Tree insertion:

    <p>Search corresponding leaf = Find where to insert the new key Split leaf = Distribute keys equally Insert key and pointer = Add key to the node Split root = Create a new root node</p> Signup and view all the answers

    What must happen when a leaf is split in a B-Tree?

    <p>A new key/pointer pair is inserted in the parent node</p> Signup and view all the answers

    In B-Trees, keys are allowed to be duplicated.

    <p>False</p> Signup and view all the answers

    What is the maximum range of values indicated for K in the B-Tree example?

    <p>10 ≤ K ≤ 28</p> Signup and view all the answers

    Which of the following is a key feature of a Key-Value Store?

    <p>Horizontal scalability</p> Signup and view all the answers

    Relational databases support single-row operations.

    <p>False</p> Signup and view all the answers

    Name one requirement for Key-Value Stores.

    <p>Horizontal scalability</p> Signup and view all the answers

    In a Key-Value Store, data is accessed using a unique ______

    <p>key</p> Signup and view all the answers

    Match the following operations with their descriptions in a Key-Value Store:

    <p>put(key, value) = Write or update a value associated with a key get(key) = Retrieve the value associated with a key delete(key) = Remove the value associated with a key No aggregation = Operations do not combine multiple records</p> Signup and view all the answers

    Which configuration setting is used to specify the ZooKeeper quorum in HBase?

    <p>hbase.zookeeper.quorum</p> Signup and view all the answers

    In HBase, a column family is defined at run-time.

    <p>False</p> Signup and view all the answers

    What is the key used to associate a customer profile in Amazon's key-value store?

    <p>customerID</p> Signup and view all the answers

    In HBase, the command Get get = new Get(Bytes.toBytes(“key1”)); is used to retrieve data associated with the ______.

    <p>key</p> Signup and view all the answers

    Match the following key-value stores with their typical identifiers:

    <p>Bigtable = No specific identifiers mentioned Apache HBase = Key: customerID Amazon Dynamo = Key: UserID Redis = No specific identifiers mentioned</p> Signup and view all the answers

    Which of the following are properties of key-value (KV) stores?

    <p>Flexible data model with column families</p> Signup and view all the answers

    Key-value stores guarantee ACID transactions.

    <p>False</p> Signup and view all the answers

    What is the purpose of a write ahead log (WAL) in KV-stores?

    <p>To keep a commit log as ground truth.</p> Signup and view all the answers

    In a _____ index, there is one entry for every record in the sequential file.

    <p>dense</p> Signup and view all the answers

    What is a characteristic of Sparse Index?

    <p>Has one entry for every block in sequential file</p> Signup and view all the answers

    What data structure is commonly used for indexes in KV-stores for access acceleration?

    <p>B-Trees</p> Signup and view all the answers

    Match the following index types with their descriptions:

    <p>Dense Index = One entry in index file for every record Sparse Index = One entry in index file for every block B-Trees = Balanced structures for efficient data access Write Ahead Log = Logs changes before applying to the database</p> Signup and view all the answers

    KV-stores typically support powerful query languages.

    <p>False</p> Signup and view all the answers

    Study Notes

    Big Data Systems - Key Value Stores I

    • Big Data Systems are a key topic in the course, covered in a series of lectures.
    • Different data storage and retrieval methods are emphasized.

    Timeline

    • The course schedule outlines various topics and assignments to be covered.
    • Key topics include Introduction, Organizational topics, Performance Management, Map Reduce (I and II), Data Centers, File Systems, Key Value Stores (I, II, III), Stream Processing (I and II), and Machine Learning Systems.
    • Specific dates are listed for each topic.
    • A Christmas break is included in the schedule.

    This Lecture

    • This lecture focuses on Key Value (KV) Overview and B-Trees.
    • The study of data structures and retrieval methods is included.

    Where are we?

    • A diagram visualizes the topics being addressed in the course.
    • The topics are categorized into Data Management, Operational storage and Small Writes and Reads.
    • Specific components include the Application (Application / Query Language / Analytics / Visualization, Data Processing, Data Management, File System, Virtualization / Container, OS / Scheduling, Hardware), and Big Data Systems.
    • The diagram shows a hierarchical relationship between these categories.

    Serving Requests

    • Students access the inverted index to find relevant URLs in response to a search term.
    • This is a core function of a search engine, relying on the organized, index format.
    • Requirements for a robust search engine include numerous search terms, URLs, frequent updates and interaction speed under one second

    More on Interaction

    • Today's internet applications handle vast amounts of data and user interaction.
    • Examples include Amazon's large product selection, Facebook's millions of users, and Google's extensive indexed pages.
    • These applications typically process millions to billions of items per second.

    Enter Key-Value Stores

    • Key-value stores are a type of data store that stores data as key-value pairs.
    • These stores prioritize scalability, speed, availability, and flexibility. They reduce the need for complex relational systems.
    • These stores use a basic map/hash table in a simplified implementation.

    This Lecture (OLAP / OLTP)

    • A key difference is identified between two main types of queries: OLAP and OLTP.
    • OLAP queries typically involve reading to obtain insights, and are characterixed by low query per second rates.
    • OLTP queries involve reading and writing data, and often feature large numbers of queries per second (query per second rates).
    • The current lecture focuses on how to handle OLTP-style queries at web scale.
    • Huge amounts of data at web-scale are emphasized: Petabytes to Exabytes.

    Web Scale

    • This section provides additional information on web-scale data stores vs relational systems, and a relevant YouTube video.

    DBMS (SQL) vs Key-Value Store

    • Tables representing student data and their activities illustrate the difference between SQL relational databases and key-value stores.
    • Key-value stores use raw byte access in contrast to structured schemas/data types used by relational databases.
    • Key Value stores do not use foreign keys. Important concepts such as full SQL support are missing in key-value stores.

    KV-Stores - Requirements

    • Key-value stores require high horizontal scalability (adapting to user growth, request volume and data size);
    • Robust performance for single record reads and writes and flexibility (ability to adapt to changing data definitions);
    • High reliability with the use of commodity hardware is emphasized.

    KV-Store Client Interface - Overview

    • A simplified view of the interface is presented.
    • Key-value Operations (write/update, read, delete). operations are shown, and there are no database transactions.

    KV-Store Client Interface - Example HBase

    • An example of the HBase key-value store is included, with code examples illustrating the initialization and operation of the store.

    KV-Stores in Practice

    • Well-known examples such as Bigtable, Apache HBase, Apache Cassandra, Redis, Amazon Dynamo, etc., are presented.
    • The examples highlight how different companies leverage key-value stores in their applications.

    Common Properties of KV-Stores

    • Several features about Common Elements and their associated features regarding data structures or types like the memory store, Write Ahead Log (WAL), versioning and replication are discussed.

    Common Non-Features of KV-Stores

    • Certain features are missing in key-value stores such as integrity constraints, transactional guarantees (ACID properties), powerful query languages and materialized views.

    Simple Index

    • Students access data via a simple index structure. The sequential file is often sorted by primary key, storing key-pointer pairs.
    • Index types include dense indices (one entry for each record) and sparse indices (one entry per block).

    B-Trees

    • B-Trees are a more sophisticated data structure for improved access acceleration .
    • They consist of multiple levels of blocks with particular rules about capacity (often minimum half full), and balancing.
    • No overflow blocks are needed. The hierarchical structure is emphasized.

    Structure

    • Details about the structure of B-Trees (balanced, multiple levels, specific parameters) are presented.

    Definition of B+-Trees

    • B-Trees structure is important to know (sorted leaves, specific pointers, various types of blocks in different levels).

    Example Configuration

    • An illustrative example of B-tree configuration with parameters and relationships is highlighted.

    Alternative Definition

    • Alternate descriptions of structure parameters (at least n-keys, at most 2n-keys, and n+1 pointers) are reviewed.

    Examples of Leaves

    • Full and partially filled leaf node examples are presented.

    Examples of Inner Nodes

    • An inner node's configuration is described in terms of keys, number of pointers and their function in tree traversal.

    Example B+-Tree

    • An example of a complete B+-tree with specific values and structure.

    Applications of B+-Trees

    • Various index role applications within B-Tree indices are presented (dense index, sparse index, primary key, unique keys).
    • Various ways search operation is conducted through B-tree operations is presented.

    Searching in B-Trees

    • Algorithms to locate a given key value are explained (recursive traversal through the tree, comparing keys at each node, movement down the tree).

    Example: Searching in B-Trees (60 and 53 searching)

    • Searching examples are provided (specific search sequences in a tree, following rules). The examples provide concrete illustrations.

    Range Queries

    • Searching for a range of keys are described, and how B-trees can help locate all keys included in the range, using various key techniques (e.g. BETWEEN).

    Example: Searching in B-Trees (10 <= K <= 28)

    • Explanation of range queries. The searching mechanism in the tree, and how to follow rules to identify values.

    B-Tree Insertion

    • Algorithms for inserting a new key value in a B-tree, the relevant operations are explained.

    Inserting into a B-Tree

    • Recursion algorithms, overflow checks for split and handling operations for adding new node key values are highlighted.

    Example of B-Tree Insertion (60 and 61 insertions)

    • The mechanism of insertion (following rules, overflow, ascending up the tree to parent node when required for maintaining balanced structure), as applied to several examples.

    Example of B-Tree Insertion

    • Several examples illustrating the insertion mechanisms (filling, splitting of nodes and maintaining the B-Tree structure)

    Deletion Cost

    • Cost analysis of deleting key values in a B-Tree, are discussed and explained.

    Deleting from a B-Tree

    • Recursion algorithms for deleting a node in B-Tree; underflow, merge and steal mechanisms, maintaining minimum key and parent adjustment.

    Example of B-Tree Deletion (12)

    • Example demonstrating the deletion of a specific key value (12) in a B-Tree and the adjustment that might be needed based on the rules followed.

    Example of B-Tree Deletion (15)

    • Example of deleting a key in a B-Tree, underflow handling, the procedures involved to adjust values to maintain the B-Tree structure are highlighted.

    Deletion Cost

    • Cost analysis and complexity of data deletion operation in B-Tree.

    Deleting from B-Trees - Variation

    • Special considerations for B-tree deletions.

    B-Tree Variations

    • Special considerations.

    B-Trees for Non-Primary Keys

    • Differences in handling non-primary keys in the B-Tree structure and how it changes the search mechanism are explained, and illustrated using relevant examples.

    B-Tree Variations: B*-Tree

    • The B* and B# variations, with emphasis on managing overflow during insertion (different methods for distributing across all leaves and better utilization and maintenance).

    Next Part

    • A preview for a subsequent lecture. Next lectures to be covered will include Key Value Stores part II, LSM Tree and the concept of distributed architectures.

    Thank you for your attention!

    • Questions and contact details are provided

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    Big Data Systems - Key Value Stores I PDF

    Description

    Test your knowledge on B+-Tree structures, including properties, behavior during insertions, and relationships between keys and pointers. This quiz covers essential concepts related to B+-Trees and their components, offering questions about maximum search keys and node behavior.

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