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  1. CSCI 5708: Query Processing I Pusheng Zhang University of Minnesota Email: Feb 3, 2004

  2. Outline • Basic Steps in Query Processing • Measures of Query Cost • Strategies for relational operations and Cost Analysis • Select Operation • External Sorting • Join Operation • Other Operations • Evaluation of Expressions

  3. Basic Steps in Query Processing FIGURE 15.1 PP 494 Statistics about Data

  4. Basic Steps in Query Processing (Cont.) • Scanning, Parsing, and Validating • translate the query into its internal form. This is then translated into relational algebra. • Parser checks syntax, verifies relations • Evaluation • The query-execution engine takes a query-evaluation plan, executes that plan, and returns the answers to the query.

  5. Basic Steps in Query Processing : Optimization • A relational algebra expression may have many equivalent expressions • E.g.,  SALARY < 50K ( SALARY (EMPLOYEE)) is equivalent to  SALARY ( SALARY < 50K (EMLOYEE)) • Each relational algebra operation can be evaluated using one of several different algorithms • Correspondingly, a relational-algebra expression can be evaluated in many ways. • Annotated expression specifying detailed evaluation strategy is called an evaluation-plan. • E.g., can use an index on SALARY to find employees with SALARY < 50k, • or can perform complete relation scan and discard employees with SALARY  50k

  6. Basic Steps: Optimization (Cont.) • Query Optimization: Amongst all equivalent evaluation plans choose the one with lowest cost. • Cost is estimated using statistical information from the database catalog • e.g. number of tuples in each relation, size of tuples, etc. • In query processing we study • How to measure query costs • Algorithms for evaluating relational algebra operations • How to combine algorithms for individual operations in order to evaluate a complete expression • In query optimization • We study how to optimize queries, that is, how to find an evaluation plan with lowest estimated cost. • Heuristic rules and systematically estimating

  7. Measures of Query Cost • Cost is generally measured as total elapsed time for answering query • Many factors contribute to time cost • disk accesses, CPU, or even network communication • Typically disk access is the predominant cost, and is also relatively easy to estimate. Measured by taking into account • Number of seeks * average-seek-cost • Number of blocks read * average-block-read-cost • Number of blocks written * average-block-write-cost • Cost to write a block is greater than cost to read a block • data is read back after being written to ensure that the write was successful

  8. Measures of Query Cost (Cont.) • For simplicity we just use number of block transfers from disk as the cost measure • We ignore the difference in cost between sequential and random I/O for simplicity • We also ignore CPU/communication costs for simplicity • I/O cost DEPENDS on • Search criteria: point/range query on a ordering / other fields • File structures: heap, sorted, hashed • Index types: primary, clustering, secondary, B+ tree, multilevel, … • Other factors: e.g., buffering, disk placement, materialization, overflow / free space mgmt, … • We do not include cost to writing output to disk in our cost formulae

  9. Catalog Information for Cost Estimation • nr: number of tuples in a relation r. • br: number of blocks containing tuples of r. • sr: size of a tuple of r. • bfr: blocking factor of r — i.e., the number of tuples of r that fit into one block. • d(A, r): number of distinct values that appear in r for attribute A. • sl(A,r): selectivity (fraction of records satisfying an equality condition in r for attribute A. • sc(A,r): selection cardinality of attribute A of relation r; average number of records that satisfy equality on A • x: number of index levels • e = Pr[a record in overflow area] * E(overflow chain length)

  10. Selection Operation • File scan – search algorithms that locate and retrieve records that fulfill a selection condition. • Algorithm S1 (linear search). Scan each file block and test all records to see whether they satisfy the selection condition. • Cost estimate (number of disk blocks scanned) = br • br denotes number of blocks containing records from relation r • If selection is on a key attribute, cost = (br /2) • stop on finding record • Linear search can be applied regardless of • selection condition or • ordering of records in the file, or • availability of indices

  11. Selection Operation (Cont.) • S2 (binary search). Applicable if selection is an equality comparison on the attribute on which file is ordered. • Assume that the blocks of a relation are stored contiguously • Cost estimate (number of disk blocks to be scanned): • log2(br) — cost of locating the first tuple by a binary search on the blocks •  sc(A,r) / bfr  - 1 — Plus number of other blocks containing records that satisfy selection condition • If selection is on a key attribute, cost = log2(br)

  12. Selections (cont.) • Index scan – search algorithms that use an index • selection condition must be on search-key of index. • S3a (primary index, equality). Retrieve a single record that satisfies the corresponding equality condition • Cost = x + 1 • S3b (hash key). Retrieve a single record • Cost = e + 1 • S4 (primary index, comparison). (Relation is sorted on A) • For A  V(r) use index to find first tuple  v and scan relation sequentially from there. Rough cost = x + (br/2), • For AV (r) just scan relation sequentially till first tuple > v; do not use index.

  13. Selection (cont.) • S5 (equality on clustering index to retrieve multiple records) • Cost = x + sc(A,r) / bfr • S6a (equality on search-key of secondary index). • Retrieve a single record if the search-key is a candidate key • Cost = x + 1 • Retrieve multiple records if search-key is not a candidate key • Cost = x + number of records retrieved • Can be very expensive! • each record may be on a different block • one block access for each retrieved record • worst cost = x + sc(A,r)

  14. Selections (cont.) • S6b (secondary index, comparison). • For A  V(r) use index to find first index entry  v and scan index sequentially from there, to find pointers to records. • For AV (r) just scan leaf pages of index finding pointers to records, till first entry > v • In either case, retrieve records that are pointed to • requires an I/O for each record • Linear file scan may be cheaper if many records are to be fetched!

  15. Implementation of Complex Selections • Conjunction: 1 2. . . n(r) • S7 (conjunctive selection using one index). • Select a combination of i and algorithms S2 through S6 that results in the least cost fori (r). • Test other conditions on tuple after fetching it into memory buffer. • S8 (conjunctive selection using multiple-key index). • Use appropriate composite (multiple-key) index if available. • S9 (conjunctive selection by intersection of identifiers). • Requires indices with record pointers. • Use corresponding index for each condition, and take intersection of all the obtained sets of record pointers. • Then fetch records from file • If some conditions do not have appropriate indices, apply test in memory.

  16. Algorithms for Complex Selections • Disjunction:1 2 . . . n(r). • S10 (disjunctive selection by union of identifiers). • Applicable if all conditions have available indices. • Otherwise use linear scan. • Use corresponding index for each condition, take union of all the obtained sets of record pointers, and eliminate duplicates • Fetch data from file • Negation: (r) • Use linear scan on file • If very few records satisfy , and an index is applicable to  • Find satisfying records using index and fetch from file