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Chapter 4: Transaction Management. Title: Efficient Locking for Concurrent Operations on B-Trees Authors: Philip L. Lehman, S. Bing Yao Pages: 334-354. Efficient Locking for Concurrent Operations on B-Trees. Problem Problem Statement Why is this problem important?

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Chapter 4: Transaction Management

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Chapter 4 transaction management

Chapter 4: Transaction Management

  • Title: Efficient Locking for Concurrent Operations on B-Trees

  • Authors:Philip L. Lehman, S. Bing Yao

  • Pages: 334-354


Efficient locking for concurrent operations on b trees

Efficient Locking for Concurrent Operations on B-Trees

  • Problem

    • Problem Statement

    • Why is this problem important?

    • Why is this problem hard?

  • Approaches

    • Approach description, key concepts

    • Contributions (novelty, improved)

    • Assumptions


Problem statement

Problem Statement

  • Given

    • Data on secondary storage devices

    • Database index

  • Find: Efficient Locking

    • Locking mechanisms for search, insertion, and deletion

  • Objectives

    • The mechanisms are safe from concurrent operations

  • Constraints

    • Many processes are allowed to operate on the data simultaneously.

    • Each process do not share its primary memory.

    • Disk page is the smallest unit of read and write.

    • Locks should not prevent other processes from reading the locked page.


Why is this problem important

Why is this problem important?

  • B-tree or B*-tree is widely used as a data structure for storing large files of information on secondary storage devices.

  • Most databases are manipulated concurrently by several processes.


Why is this problem hard

Why is this problem Hard?

  • Locking root may reduce concurrency.

  • Depending upon nodes

    • parent – child

    • Insert / split may go up many levels

    • split / insert conflicts with read, insert

  • Concurrent operation on B*-tree is erroneous.

A, B, C: blocks of primary storage

x, y, z: variables in the primary storage


Novelty of contribution

Novelty of Contribution

  • Related Work

    • Naïve approach to concurrent B-tree problem fails.

    • Using semaphore locks entire sub-tree affected by updates.

    • B*-tree

      • Locks are applied mostly in lower sections of tree.

  • Contributions

    • Uses a small (constant) # of locks at any time

    • Locks only prevent multiple update access.


Principles of b link tree

Principles of Blink-tree

  • Add a single ‘link’ pointer field to each node.

  • The link provides an additional method for reaching a node.

  • The split two nodes are joined by a link pointer, and are functionally essentially the same as a single node.

  • The link pointer serves as a ‘temporary fix’ that allows correct concurrent operation.

  • Additionally, the Blink-tree enables serial search, i.e., retrieving nodes in the same level (e.g., retrieving only leaves).

Reference: A Guttman ‘R-tree a dynamic index structure for spatial searching’, 1984


Example of b link tree

Example of Blink-tree


Search insertion algorithms

Search, Insertion Algorithms

  • Search

    • If a current node is to split, the search algorithm rectifies the error by following the link pointer of the newly split node.

  • Insertion

    • The insertion may cause

      splitting a node. (= unsafe)

    • Lock a node before modification.

Example: Splitting node a into node a’ and b’


Locking efficiency

Locking Efficiency

  • The insertion algorithm uses at most a constant # of locks (three) for any process at any time.

    • Split  chaining across the level of nodes containing the father to find the correct insertion position  Three nodes are locked for the duration of one operation.

  • This type of locking occurs rarely in a Blink-tree

    • Extremely small collision probability

Example: Splitting node a into node a’ and b’


Validation methodology

Validation Methodology

  • Correctness Proof

    • Theorem 1: Deadlock Freedom. The system can’t produce deadlock.

      • Impose an order: bottom to top / left to right

      • Locks are placed by the inserter according to a well-ordering

      • As long as inserter follow the well-ordering, it never places a lock on any node below a locked node, nor on any node to the left.

    • Theorem 2: All put operations correctly modify tree structure.

      • Classify put operations into three types.

      • Prove the correctness of first case and show consecutive put operations is equivalent to one change.

    • Theorem 3: Interaction Theorem. Actions of an insertion process don’t impair correctness of actions of other processes.

      • Classify three possible types of insertion.

      • Apply lemma 3 to several aspects separately.

  • Livelock: one process runs indefinitely.

    • extremely unlikely problem


Class exercise 1 2

Class Exercise 1/2

  • How can we resolve the erroneous behavior of B*-tree using Blink-tree?

A, B, C: blocks of primary storage

x, y, z: variables in the primary storage


Class exercise 2 2

Class Exercise 2/2

  • Can insert lead to deadlock? Livelock?

  • Many nodes have 2 pointers pointing to them,

    • One from parent

    • One from left sibling

      Which one is created first?

  • In the figure (b), why the

    right link was created first?

Example: Splitting node a into node a’ and b’


Summary

Summary

  • Paper’s focus

    • Blink-tree – implementations and correctness

  • Ideas

    • Link provides an additional method to reach a node.

    • The split two nodes work as a single node by the link.

  • Contributions

    • Locking scheme is simpler (no read-locks).

    • A constant # of nodes are locked.

  • Analytical Validation

    • Correctness proofs


Assumptions rewrite today

Assumptions, Rewrite today

  • Assumptions

    • Many processes can operate on data simultaneously.

    • A process is allowed to lock and unlock a disk page.

  • Rewrite today

    • Compare with newer methods

      • T-tree

    • Experimental evaluation - Simulation

      • Measure lock efficiency


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