Indexes
+CSE 4/562 – Database Systems
+February 19, 2018
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| $150 | +$50 | +
| Index ToC |
+ No Index ToC Summary |
+
Today's Focus
+ ++ $\sigma_C(R)$ and $(\ldots \bowtie_C R)$ +
+(Finding records in a table really fast)
+ + +Indexing Strategies
+ +-
+
- Rearrange the data. +
- Put things in a predictable location or a specific order. +
- ("clustering" the data) +
- Wrap the data. +
- Record where specific data values live +
- ("indexing" the data). +
Data Organization
+ +-
+
- Unordered Heap +
- No organization at all. $O(N)$ reads. +
- (Secondary) Index +
- Index structure over unorganized data. $O(\ll N)$ random reads for some queries. +
- Clustered (Primary) Index +
- Index structure over clustered data. $O(\ll N)$ sequential reads for some queries. +
Data Organization
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+ Data Organization
+
+ Index Types
+-
+
- Tree-Based +
- A hierarchy of decisions lead to data at the leaves. + +
- Hash-Based +
- A hash function puts data in predictable locations. + +
- CDF-Based (new) +
- A more complex function predicts where data lives. +
Tree-Based Indexes
+ + +Tree-Based Indexes
+ + +Challenges
+ +-
+
- Balance +
- Bad question orders lead to poor performance! + +
- IO +
- Each access to a binary tree node is a random access. + +
- Which Dimension +
- Why limit ourselves to asking about one dimension? +
Worst-Case Tree?
+Best-Case Tree?
+Binary Trees are Bad for IO
+Every step of binary search is a random access
+Every tree node access is a random access
+Random access IO is bad.
+Idea: Load a bunch of binary tree nodes together.
+Binary Tree: $1$ separator & $2$ pointers
+$log_2(N)$ Deep
+$K$-ary Tree: $(K-1)$ separators & $K$ pointers
+$log_K(N)$ Deep
+Important: You still need to do binary search on each node of a $K$-ary tree, but now you're doing random access on memory (or cache) instead of disk (or memory)
+ISAM Trees
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+ How do you handle updates?
+B+Tree = ISAM + Updates
+Challenges
+ +-
+
- Finding space for new records +
- Keeping the tree balanced as new records are added +
Idea 1: Reserve space for new records
+Just maintaining open space won't work forever...
+Rules of B+Trees
+ +-
+
- Keep space open for insertions in inner/data nodes. +
- ‘Split’ nodes when they’re full + +
- Avoid under-using space +
- ‘Merge’ nodes when they’re under-filled +
Maintain Invariant: All Nodes ≥ 50% Full
+(Exception: The Root)
+
Deletions reverse this process (at 50% fill).
Next Class: Hash- and CDF-Based Indexes
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