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? Why is this problem hard? Approaches Approach description, key concepts Contributions (novelty, improved) Assumptions

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.

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? 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 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 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 Blink-tree

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’

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 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 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 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 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

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