CSE 4/562 - Database Systems


CSE 4/562 – Database Systems

February 19, 2018
$150 $50
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

Data Organization

Index Types

A hierarchy of decisions lead to data at the leaves.
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


Bad question orders lead to poor performance!
Each access to a binary tree node is a random access.
Which Dimension
Why limit ourselves to asking about one dimension?

Worst-Case Tree?

$O(N)$ with the tree laid out left/right-deep

Best-Case Tree?

$O(\log N)$ with the tree perfectly balanced

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

How do you handle updates?

B+Tree = ISAM + Updates


  • 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