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Index tuning

Index tuning. Hash Index. overview. Introduction. Hash-based indexes are best for equality selections . Can efficiently support index nested joins Cannot support range searches. Static and dynamic hashing techniques exist; trade-offs similar to ISAM vs. B+ trees. Static Hashing.

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Index tuning

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  1. Index tuning Hash Index

  2. overview

  3. Introduction • Hash-basedindexes are best for equality selections. • Can efficiently support index nested joins • Cannot support range searches. • Static and dynamic hashing techniques exist; trade-offs similar to ISAM vs. B+ trees.

  4. Static Hashing • # primary pages fixed, allocated sequentially, never de-allocated; overflow pages if needed. • h(k) mod M = bucket to which data entry with key k belongs. (M = # of buckets) • Buckets contain data entries. • Long overflow chains can develop and degrade performance. • Search needs one disk I/O, insert and delete needs two I/Os

  5. Example hash function Key = ‘x1 x2 … xn’ n byte character string Have b buckets h: add x1 + x2 + ….. xn compute sum modulo b Good hash function: Expected number of keys/bucket is the same for all buckets Read Knuth Vol. 3 if you really need to select a good function.

  6. Within a bucket: Do we keep keys sorted? • Yes, if CPU time critical • & Inserts/Deletes not too frequent CS 245 Notes 5 6

  7. Next: example to illustrate inserts, overflows, deletes h(K)

  8. EXAMPLE 2 records/bucket INSERT: h(a) = 1 h(b) = 2 h(c) = 1 h(d) = 0 d a e c b 0 1 2 3 h(e) = 1

  9. d maybe move “g” up EXAMPLE: deletion Delete:ef 0 1 2 3 a b d c c e f g CS 245 Notes 5 9

  10. Rule of thumb: Try to keep space utilization between 50% and 80% Utilization = # keys used total # keys that fit • If < 50%, wasting space • If > 80%, overflows significant depends on how good hash function is & on # keys/bucket CS 245 Notes 5 10

  11. How do we cope with overflows? Periodically rehashing: reorganization Dynamic hashing • Extensible • Linear CS 245 Notes 5 11

  12. Extendible Hashing • Situation: Bucket (primary page) becomes full. Why not re-organize file by doubling# of buckets? • Reading and writing all pages is expensive! • Idea: Use directory of pointers to buckets, double # of buckets by doubling the directory, splitting just the bucket that overflowed! • Directory much smaller than file, so doubling it is much cheaper. Only one page of data entries is split. • No overflow page! • Trick lies in how hash function is adjusted!

  13. Example • Directory is array of size 4. • To find bucket for r, take last `global depth’ # bits of h(r); we denote r by h(r). • If h(r) = 5 = binary 101, it is in bucket pointed to by 01. • Insert: If bucket is full, split it (allocate new page, re-distribute). • If necessary, double the directory. (As we will see, splitting a bucket does not always require doubling; we can tell by comparing global depth with local depth for the split bucket.) • When directory doubled, global depth +1 • When a bucket is split, local depth+1

  14. Insert h(r)=20 (Causes Doubling)

  15. Points to note • 20 = binary 10100. Last 2 bits (00) tell us r belongs in A or A2. Last 3 bits needed to tell which. • Global depth of directory: Max # of bits needed to tell which bucket an entry belongs to. • Local depth of a bucket: # of bits used to determine if an entry belongs to this bucket. • When does bucket split cause directory doubling? • Before insert, local depth of bucket = global depth. Insert causes local depth to become > global depth; directory is doubled by copying it overand `fixing’ pointer to split image page. (Use of least significant bits enables efficient doubling via copying of directory!)

  16. Directory Doubling • Why use least significant bits in directory? Allows for doubling via copying!

  17. Comments on extendible hashing • If directory fits in memory, equality search answered with one disk access; else two. • 100MB file, 100 bytes/rec, 4K page size, which contains 1,000,000 records (as data entries), each page/bucket has about 40 data entries, so there are about 25,000 directory elements; chances are high that directory will fit in memory. • Directory grows in spurts, and, if the distribution of hash values is skewed, directory can grow large. • Multiple entries with same hash value cause problems!, needs to be handled specially, e.g., overflow page • Delete: If removal of data entry makes bucket empty, can be merged with `split image’. If each directory element points to same bucket as its split image, can halve directory.

  18. summarize

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