Database System Principles
18.7 Tree Locking Protocol
CS257 Section 1 Spring 2012
Dhruv Jalota
ID: 115
Index
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Motivation
B-Tree
Protocol
Why it works
Example
Precedence graph
Proof
Motivation
• Data elements are not hierarchically stored by
containment but rather they are DISJOINT.
• A B-TREE is the ideal data structure to
represent such a database since traversal to
reach any data element would require
beginning at the root.
• Two-phase locking in such a situation makes
concurrent use of DB by transactions
impossible
B-TREE details
• Basic DS:
- Keeps records in sorted order
- Uses partially full blocks to speed up insertion
and deletion
Locking structure:
- Granularity is at node level. Smaller is not
beneficial and entire tree is infeasible!
Tree protocol
• Transaction’s first lock can be any node
• Subsequent locks only if currently locked
parent
• Nodes unlocked any time
• Cannot relock if released node, even if parent
is still held
• (As we can see – NOT 2PL)
Why it works
• Implies a serial order on transactions in
schedule
• Define Ti < S Tj (order of precedence)
• In schedule S, Ti and Tj lock common nodes,
but Ti locks first
Example
• Figure 18.30 from text book.
• And figure 18.31
Precedence graph
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Figure 18.32 from text book.
T1 < S T2
T3 < S T2
Acyclic graph means any topological order is
an equivalent serial schedule
• Thus, (T1, T3, T2) = (T3, T1, T2)
• This is because nodes are touched in same
order.
Proof for acyclic precedence graph
giving equivalent schedules
• If two transactions lock several elements in
common, then they are all locked in the same
order
• Figure 18.33