1 Overview of Storage and Indexing Yanlei Diao UMass Amherst Feb 13, 2007 Slides Courtesy of R. Ramakrishnan and J. Gehrke.
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1 Overview of Storage and Indexing Yanlei Diao UMass Amherst Feb 13, 2007 Slides Courtesy of R. Ramakrishnan and J. Gehrke
2 DBMS Architecture Disk Space Manager DB Access Methods Buffer Manager Query Parser Query Rewriter Query Optimizer Query Executor Lock Manager Log Manager
3 Data on External Storage Disks: Can retrieve random pages at (almost) fixed cost But reading several consecutive pages is much faster than reading them in random order. Tapes: Can only read pages in sequence Slower but cheaper than disks; used for archival storage Page: Unit of information read from or written to disk Size of page: DBMS parameter, 4KB, 8KB Disk space manager: Abstraction: a collection of pages. Allocate/de-allocate a page. Read/write a page. Page I/O: Pages read from disk and pages written to disk Dominant cost of database operations
4 Access Methods Access methods: routines to manage various disk-based data structures. Files of records Various kinds of indexes File of records: Important abstraction of external storage in a DBMS! Record id (rid) is sufficient to physically locate a record Indexes: Auxiliary data structures Given a value in the index search key field(s), find the record ids of records with this value
5 Buffer Management Architecture: Data is read into memory for processing Data is written to disk for persistent storage Buffer manager stages pages between external storage and main memory buffer pool. Access method layer makes calls to the buffer manager.
6 Access Methods Many alternatives exist, each ideal for some situations, and not so good for others: Heap (unorder) files: Suitable when typical access is a file scan retrieving all records. Sorted Files: Best if records are retrieved in order of the sorting attribute(s), or only a `range’ of records is needed. Indexes: Data structures to organize records via trees or hashing. Like sorted files, they speed up searches for a subset of records, based on values in certain (“search key”) fields Updates are much faster than in sorted files.
7 Indexes An index on a file speeds up selections on the search key field(s) for the index. Any subset of the fields of a relation can be the search key for an index on the relation. Search key is not the same as key (minimal set of fields that uniquely identify a record in a relation). An index contains a collection of data entries, and supports efficient retrieval of all data entries k* with a given key value k. Data entry (in an index) versus data record (in a file). Given a data entry k*, we can find record(s) with the key k in at most one disk I/O. (Details soon …)
8 B+ Tree Indexes Leaf pages contain data entries : Leaf pages are chained using prev & next pointers Data entries are sorted by the search key value Non-leaf Pages (Sorted by search key) Leaf
9 B+ Tree Indexes Non-leaf pages have index entries; only used to direct searches P 0 K 1 P 1 K 2 P 2 K m P m index entry Non-leaf Pages (Sorted by search key) Leaf
10 Example B+ Tree Equality selection: find 28*? 29*? Range selection: find all > 15* and < 30* Insert/delete: Find the data entry in a leaf, then change it. Need to adjust the parent sometimes. And the change sometimes bubbles up the tree. 2*3* Root 17 30 14*16* 33*34* 38* 39* 135 7*5*8*22*24* 27 27*29* Entries <= 17Entries > 17 Data entries in leaf nodes are sorted.
11 Hash-Based Indexes Good for equality selections. A hash index is a collection of buckets. Bucket = primary page plus zero or more overflow pages. Buckets contain data entries. h 1 2 3 … … … … … … N-1 Search key value k Hashing function h : h ( k ) = bucket of data entries that may contain the search key value k. No need for “index entries” in this scheme.
12 Alternatives for Data Entry k* in Index In a data entry k* we can store: Alt1: Data record with key value k Alt2: Alt3: Choice of an alternative for data entries is orthogonal to an indexing technique used. Indexing techniques: B+ tree, hashing Every indexing technique can be combined with any alternative.
13 Alternative 1 for Data Entries Alternative 1: Index structure itself is a file organization for data records (instead of a Heap or sorted file). At most one index on a given collection of data records can use Alternative 1. Otherwise, data records are duplicated, leading to redundant storage and potential inconsistency. If data records are very large, # of pages containing data entries is high. Size of the index structure to direct searches (e.g., non-leaf nodes in B+ tree) can also be large.
14 Alternatives 2, 3 for Data Entries Alternatives 2 and 3: Data entries,, typically much smaller than data records. Index structure used to direct search is much smaller than with Alternative 1. So, better than Alternative 1 with large data records, especially if search keys are small. Alternative 3 more compact than Alternative 2 In the presence of multiple K* entries! Alternative 3 leads to variable sized data entries, even if search keys are of fixed length. Variable sizes records/data entries are hard to manage.
15 Index Classification Primary index vs. secondary index: If search key contains the primary key, then called primary index. Other indexes are called secondary indexes. Unique index: Search key contains a candidate key. No data entries can have the same search key value. Recall: Key? Primary key? Candidate key?
16 Index Classification (Contd.) Clustered index: order of data records is the same as, or `close to’, order of (sorted) data entries. Alternative 1 implies clustered Alternatives 2 and 3 are clustered only if data records are sorted on the search key field. A data file can be clustered on at most one search key. Retrieving data records: fast, with one or a few I/Os. Why? Unclustered index: Multiple unclustered indexes on a data file. Retrieving data records: can be slow, toughing many pages.
17 Clustered vs. Unclustered Indexes Suppose that Alternative (2) is used for data entries, and data records are stored in a Heap file. To build a clustered index, first sort the Heap file (with some free space on each page for future inserts). Overflow pages may be needed for inserts. (Thus, order of data records is `close to’, but not identical to, the sort order.)
18 Index Classification (Contd.) Dense index : contains (at least) one data entry for every search key value that appears in a record in the indexed file Alternatives 1, 2, 3 Sparse index : contains one entry for each page of records in the indexed file. Sparse index has to be clustered! Alternative 1? Alternative 2? Alternative 3?
19 Cost Model for Our Analysis We ignore CPU costs, for simplicity: B: The number of data pages R: Number of records per page D: (Average) time to read or write disk page I/O cost: Measuring # of page I/O’s ignores pre-fetching of a sequence of pages; thus, approximate I/O cost. Average-case analysis, based on simplistic assumptions. * Good enough to show the overall trends!
20 Comparing File Organizations Heap files (random order; insert at eof) Sorted files, sorted on Clustered B+ tree file, Alternative (1), search key Unclustered B + tree index on a heap file, search key Unclustered hash index on a heap file, search key
21 Operations to Compare Scan: Fetch all records from disk Equality search: e.g. (age, sal) = (24, 50K) Range selection: e.g. (age, sal) [(22, 20K), (30, 200K)] Insert a record Delete a record
22 Assumptions in Our Analysis Heap Files: Equality selection on key; exactly one match. Sorted Files: Files compacted after deletions. Indexes: Alt (2), (3): size of data entry = 10% size of data record Hash: No overflow chains. 80% page occupancy => File size = 1.25 data size B+Tree: 67% occupancy (typical): implies file size = 1.5 data size Balanced with fanout F (133 typical) at each non-leaf level
23 Assumptions (contd.) Scans: Leaf nodes of a tree-index are chained. Index data entries plus actual file scanned for unclustered indexes. Range searches: We use tree indexes to restrict the set of data records fetched, but ignore hash indexes.
24 Cost of Operations * Several assumptions underlie these (rough) estimates!
25 Cost of Operations * Several assumptions underlie these (rough) estimates! # of leaf pages: B*0.1/67%=0.15B; Cost of index I/O: 0.15BD # of data entries on a leaf page: R*10*0.67=6.7R; Cost of data I/O: 0.15B*6.7R*D=BDR Key: unclustered B+tree, one I/O per data entry! # of data entry pages: B*0.1/80%=0.125B; Cost of index I/O: 0.125BD # of data entries on a hash page: R*10*0.80=8R; Cost of data I/O: 0.125B*8R*D=BDR Key: unclustered hash index, one I/O per data entry!
26 Summary Many alternative access methods exist, each appropriate in some situation. Index is a collection of data entries plus a way to quickly find entries with given key values. If selection queries are frequent, building an index is important. Hash-based indexes only good for equality search. Tree-based indexes best for range search; also good for equality search.
27 Summary (Contd.) Data entries can be actual data records, pairs, or pairs. Choice orthogonal to indexing technique used to locate data entries with a given key value. Can have several indexes on a given file of data records, each with a different search key. Indexes can be classified as clustered vs. unclustered, primary vs. secondary, etc. Differences have important consequences for utility/performance.