1. Chapter 4: Transaction Management
Title: Efficient Locking for Concurrent Operations on B-Trees
Authors: Philip L. Lehman, S. Bing Yao
Pages:

2. 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

3. Problem Statement Given Find: Efficient Locking Objectives Constraints
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.

4. 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.

5. 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

6. 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.

7. 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

8. Example of Blink-tree

9. Search, Insertion Algorithms
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’

10. 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’

11. 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

12. 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

13. 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’

14. Summary Paper’s focus Ideas Contributions Analytical Validation
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

15. Assumptions, Rewrite today
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