CPSC 3100 Scientific Programming

CPSC 3100 Scientific Programming

CpSc 3220 File and Database Processing Lecture 17 Indexed Files Sequential File Organization For sequential processing of entire file Records ordered by a search-key Easy Insert for Sequential File Organization

Indexed Files: Basic Concepts Indexing mechanisms can speed up access to desired data. Search Key - attribute used to look up records in a file. An index file consists of records (called index entries) of the form search-key pointer Index files are typically much smaller than Data files Stored in search-key order. From Database Concepts, Silberschatz,

et al. Ordered Indices Ordered index: index entries are stored sorted on the search key value Primary index: in a sequentially ordered file, the index whose search key specifies the sequential order of the file. The search key of a primary index is usually but not necessarily a unique key to the Data File Secondary index: an index whose search key specifies an order different from the sequential order of the file. Index-sequential file: ordered sequential file with a primary

index. From Database Concepts, Silberschatz, et al. Dense Index Files Dense index Index record appears for every search-key value in the file. E.g. index on ID attribute of instructor relation From Database Concepts, Silberschatz, et al.

Dense Index Files (Cont.) Dense Indices can be kept on non-unique data fields Example, dense index on dept_name, with instructor file sorted on dept_name From Database Concepts, Silberschatz, et al. Sparse Index Files Sparse Index: contains index records for only some search-key values. Applicable when records are sequentially ordered on search-key

To locate a record with search-key value K we: Find index record with largest search-key value < K Search file sequentially starting at the record to which the index record points From Database Concepts, Silberschatz, et al. Multilevel Index If a dense primary index does not fit in memory, access becomes expensive.

Solution: keep primary index on disk as a sequential file and construct a sparse index on it. outer index a sparse index of primary index inner index the primary index file If outer index is too large to fit in main memory, another level of index can be created. Indices at all levels must be updated on insertion or deletion from the file. From Database Concepts, Silberschatz, et al.

Multilevel Index From Database Concepts, Silberschatz, et al. Index Update: Deletion If deleted record was the only record in the file with its particular search-key value, the search-key is deleted from the index also.

Single-level index entry deletion: Dense indices deletion of search-key is similar to file record deletion. Sparse indices If an entry for the search key exists in the index, it is deleted by replacing the entry in the index with the next search-key value in the file (in search-key order). If the next search-key value already has an index entry, the entry is deleted instead of being replaced. From Database Concepts, Silberschatz, et al. Index Update: Insertion

Single-level index insertion: Perform a lookup using the search-key value appearing in the record to be inserted. Dense indices if the search-key value does not appear in the index, insert it. Sparse indices if index stores an entry for each block of the file, no change needs to be made to the index unless a new block is created. If a new block is created, the first search-key value appearing in the new block is inserted into the index. Multilevel insertion and deletion: algorithms

are simple extensions of the single-level algorithms From Database Concepts, Silberschatz, et al. Secondary Indices Frequently, one wants to find all the records whose values in a certain field (which is not the search-key of the primary index) satisfy some condition. Example 1: In the instructor relation stored sequentially by ID, we may want to find all instructors in a particular department Example 2: as above, but where we want to find all instructors with a

specified salary or with salary in a specified range of values We can have a secondary index with an index record for each search-key value From Database Concepts, Silberschatz, et al. Secondary Indices Example Secondary index on salary field of instructor

Index record points to a bucket that contains pointers to all the actual records with that particular search-key value. Secondary indices have to be dense From Database Concepts, Silberschatz, et al. Primary and Secondary Indices Indices offer substantial benefits for CRUD file processing. Updating indices can be expensive, Sequential scan using primary index is efficient, but a

sequential scan using a secondary index is expensive Each record access may fetch a new block from disk Block fetch requires about 5 to 10 milliseconds, versus about 100 nanoseconds for memory access From Database Concepts, Silberschatz, et al. B -Tree Index Files +

An alternative to indexed-sequential files. Advantages of B+-tree index files: automatically reorganizes itself with small, local, changes, in the face of insertions and deletions. Reorganization of entire file is not required to maintain performance. (Minor) disadvantage of B+-trees: extra insertion and deletion overhead, space overhead. Advantages of B+-trees outweigh disadvantages and B+-trees are used extensively B+-trees are a variant of B-trees A discussion of B-trees can be found at

http://en.wikipedia.org/wiki/B-tree Example of B -Tree + A B+-tree is a rooted tree with the following properties: All paths from root to leaf are of the same length Each node that is not a root or a leaf has between n/2 and n children. A leaf node has between (n1)/2)/2 and n1)/2 values Special cases: If the root is not a leaf, it has at least 2 children.

If the root is a leaf (that is, there are no other nodes in the tree), it can have between 0 and (n 1)/2) values. B -Tree Node Structure + Typical node Ki are the search-key values

Pi are pointers to children (for non-leaf nodes) or pointers to records or buckets of records (for leaf nodes). The search-keys in a node are ordered K1)/2 < K2 < K3 < . . . < Kn1)/2 (Initially assume no duplicate keys, address duplicates later) Leaf Nodes in B+-Trees Properties of a leaf node: For i = 1)/2, 2, . . ., n1)/2, pointer Pi points to a file record with search-key value Ki, If Li, Lj are leaf nodes and i < j, Lis search-key values are less

than or equal to Ljs search-key values Pn points to next leaf node in search-key order Non-Leaf Nodes in B -Trees + Non leaf nodes form a multi-level sparse index on the leaf nodes. For a non-leaf node with m pointers: All the search-keys in the subtree to which P1)/2 points are less than K1)/2 For 2 i n 1)/2, all the search-keys in the subtree to which Pi

points have values greater than or equal to Ki1)/2 and less than Ki All the search-keys in the subtree to which Pn points have values greater than or equal to Kn1)/2 Example of B -tree + B+-tree for instructor file (n = 6)

Leaf nodes must have between 3 and 5 values ((n1)/2)/2 and n 1)/2, with n = 6). Non-leaf nodes other than root must have between 3 and 6 children ((n/2 and n with n =6). Root must have at least 2 children. Query on B -Trees + Find record with search-key value V: C=root

While C is not a leaf node { Let i be least value such that V Ki. If no such i exists set C = last non-null pointer in C Else { if (V= Ki ) Set C = Pi +1 else set C = Pi} } Let i be least value s.t. Ki = V If there is such a value i follow pointer Pi to the desired record. Else no record with search-key value k exists. Queries on B Trees +-

If there are K search-key values in the file, the height of the tree is no more than logn/2(K). A node is generally the same size as a disk block, typically 4 kilobytes and n is typically around 1)/200 (40 bytes per index entry). With 1)/2 million search key values and n = 1)/200 at most log50(1)/2,000,000) = 4 nodes are accessed in a lookup. Contrast this with a balanced binary tree with 1)/2 million search key values around 20 nodes are accessed in a lookup

above difference is significant since every node access may need a disk I/O, costing around 20 milliseconds Editing B -Trees: Insertion + Find the leaf node in which the search-key value would appear If the search-key value is not present, then add the record to the main file If there is room in the leaf node, insert (key-value, pointer) pair in

the leaf node Otherwise, split the node (along with the new (key-value, pointer) entry) as discussed in the next slide. Insertion in B+-Trees Splitting a leaf node: take the n (search-key value, pointer) pairs (including the one being inserted) in sorted order. Place the first n/2 in the original node, and the rest in a new node. let the new node be p, and let k be the least key value in p. Insert (k,p) in the parent of the node being split.

If the parent is full, split it and propagate the split further up. Splitting of nodes proceeds upwards till a node that is not full is found. In the worst case the root node may be split increasing the height of the tree by 1)/2. Result of splitting node containing Brandt, Califieri and Crick on inserting Adams Next step: insert entry with (Califieri,pointer-to-new-node) into parent Example of B+-Tree Insertion

B+-Tree before and after insertion of Adams Another B -Tree Insertion + B+-Tree before and after insertion of Lamport Deletion in B -Trees: + Find the record to be deleted, and remove it from the main file Remove (search-key value, pointer) from the leaf node

If the node has too few entries due to the removal, and the entries in the node and a sibling fit into a single node, then merge siblings: Insert all the search-key values in the two nodes into a single node (the one on the left), and delete the other node. Delete the pair (Ki1)/2, Pi), where Pi is the pointer to the deleted node, from its parent, recursively using the above procedure. Deletion in B -Trees (contd) + Otherwise, if the node has too few entries due to the

removal, but the entries in the node and a sibling do not fit into a single node, then redistribute pointers: Redistribute the pointers between the node and a sibling such that both have more than the minimum number of entries. Update the corresponding search-key value in the parent of the node. The node deletions may cascade upwards till a node which has n/2 or more pointers is found. If the root node has only one pointer after deletion, it is deleted and the sole child becomes the root. Examples of B+-Tree Deletion

Before and after deleting Srinivasan Deleting Srinivasan causes merging of under-full leaves B+-Tree Deletion (Cont.) Deletion of Singh and Wu from result of previous example Leaf containing Singh and Wu became underfull, and borrowed a value Kim

from its left sibling Search-key value in the parent changes as a result B+-tree Deletion (Cont.) Before and after deletion of Gold from earlier example Node with Gold and Katz became underfull, and was merged with its sibling Parent node becomes underfull, and is merged with its sibling

Value separating two nodes (at the parent) is pulled down when merging Root node then has only one child, and is deleted B -Tree File Organization + Index file degradation problem is solved by using B +-Tree indices. Data file degradation problem is solved by using B+-Tree File Organization. The leaf nodes in a B+-tree file organization store records, instead of pointers. Leaf nodes are still required to be half full

Since records are larger than pointers, the maximum number of records that can be stored in a leaf node is less than the number of pointers in a nonleaf node. Insertion and deletion are handled in the same way as insertion and deletion of entries in a B+-tree index. For Next Time We will talk about Hashing Read the File Organization paper that is in the Course Materials section of our Blackboard site

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