Chapter 4: Transaction Management

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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

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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

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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.

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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.

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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

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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.

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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
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Example of Blink-tree
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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
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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
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Validation Methodology

• Correctness Proof
• Theorem 1 Deadlock Freedom. The system cant
  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 dont 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

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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

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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
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Summary

• Papers 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

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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