# Linux运维基础知识-MySQL index.ppt

Indexing and Hashing,2019/7/3,Cryptography,page:2,Indexing and Hashing,Basic Concepts Ordered Indices B+-Tree Index Files B-Tree Index Files Static Hashing Dynamic Hashing Comparison of Ordered Indexing and Hashing Index Definition in SQL Multiple-Key Access,2019/7/3,Cryptography,page:3,Basic Concepts,Indexing mechanisms used to speed up access to desired data. E.g., author catalog in library Search Key - attribute to set of attributes used to look up records in a file. An index file consists of records (called index entries) of the form Index files are typically much smaller than the original file Two basic kinds of indices: Ordered indices: search keys are stored in sorted order Hash indices: search keys are distributed uniformly across “buckets” using a “hash function”.,search-key,pointer,2019/7/3,Cryptography,page:4,Index Evaluation Metrics,Access types supported efficiently. E.g., records with a specified value in the attribute or records with an attribute value falling in a specified range of values (e.g. 10000 salary 40000) Access time Insertion time Deletion time Space overhead,2019/7/3,Cryptography,page:5,Ordered Indices,In an ordered index, index entries are stored sorted on the search key value. E.g., author catalog in library Primary index: in a sequentially ordered file, the index whose search key specifies the sequential order of the file Also called clustering index The search key of a primary index is usually but not necessarily the primary key Secondary index: an index whose search key specifies an order different from the sequential order of the file. Also called non-clustering index Index-sequential file: ordered sequential file with a primary index,2019/7/3,Cryptography,page:6,Dense Index Files,Dense index — Index record appears for every search-key value in the file.,2019/7/3,Cryptography,page:7,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,2019/7/3,Cryptography,page:8,Sparse Index Files (Cont.),Compared to dense indices: Less space and less maintenance overhead for insertions and deletions. Generally slower than dense index for locating records. Good tradeoff: sparse index with an index entry for every block in file, corresponding to least search-key value in the block.,2019/7/3,Cryptography,page:9,Multilevel Index,If primary index does not fit in memory, access becomes expensive Solution: treat primary index kept 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 even outer index is too large to fit in main memory, yet another level of index can be created, and so on Indices at all levels must be updated on insertion or deletion from the file,2019/7/3,Cryptography,page:10,Multilevel Index (Cont.),2019/7/3,Cryptography,page:11,Index Update: Record 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 deletion: Dense indices – deletion of search-key: similar to file record deletion. Sparse indices – if deleted key value exists in the index, the value is replaced by 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.,2019/7/3,Cryptography,page:12,Index Update: Record Insertion,Single-level index insertion: Perform a lookup using the key value from inserted record 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 (as well as deletion) algorithms are simple extensions of the single-level algorithms,2019/7/3,Cryptography,page:13,Secondary Indices Example,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,Secondary index on balance field of account,2019/7/3,Cryptography,page:14,Primary and Secondary Indices,Indices offer substantial benefits when searching for records. BUT: Updating indices imposes overhead on database modification --when a file is modified, every index on the file must be updated, 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 micro seconds, versus about 100 nanoseconds for memory access,2019/7/3,Cryptography,page:15,B+-Tree Index Files,Disadvantage of indexed-sequential files performance degrades as file grows, since many overflow blocks get created. Periodic reorganization of entire file is required. Advantage 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 B+-trees are used extensively,B+-tree indices are an alternative to indexed-sequential files.,2019/7/3,Cryptography,page:16,B+-Tree Index Files (Cont.),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 (n–1)/2 and n–1 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) values.,A B+-tree is a rooted tree satisfying the following properties:,2019/7/3,Cryptography,page:17,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 K2 K3 . . . Kn–1,2019/7/3,Cryptography,page:18,Leaf Nodes in B+-Trees,For i = 1, 2, . . ., n–1, pointer Pi either points to a file record with search-key value Ki, or to a bucket of pointers to file records, each record having search-key value Ki. Only need bucket structure if search-key does not form a primary key. If Li, Lj are leaf nodes and i j, Li’s search-key values are less than Lj’s search-key values Pn points to next leaf node in search-key order,Properties of a leaf node:,2019/7/3,Cryptography,page:19,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 points are less than K1 For 2 i n – 1, all the search-keys in the subtree to which Pi points have values greater than or equal to Ki–1 and less than Ki All the search-keys in the subtree to which Pn points have values greater than or equal to Kn–1,2019/7/3,Cryptography,page:20,Example of a B+-tree,B+-tree for account file (n = 3),2019/7/3,Cryptography,page:21,Example of B+-tree,Leaf nodes must have between 2 and 4 values ((n–1)/2 and n –1, with n = 5). Non-leaf nodes other than root must have between 3 and 5 children ((n/2 and n with n =5). Root must have at least 2 children.,B+-tree for account file (n = 5),2019/7/3,Cryptography,page:22,Observations about B+-trees,Since the inter-node connections are done by pointers, “logically” close blocks need not be “physically” close. The non-leaf levels of the B+-tree form a hierarchy of sparse indices. The B+-tree contains a relatively small number of levels Level below root has at least 2* n/2 values Next level has at least 2* n/2 * n/2 values etc. If there are K search-key values in the file, the tree height is no more than logn/2(K) thus searches can be conducted efficiently. Insertions and deletions to the main file can be handled efficiently, as the index can be restructured in logarithmic time (as we shall see).,2019/7/3,Cryptography,page:23,Queries on B+-Trees,Find all records with a search-key value of k. N=root Repeat Examine N for the smallest search-key value k. If such a value exists, assume it is Ki. Then set N = Pi Otherwise k Kn–1. Set N = Pn Until N is a leaf node If for some i, key Ki = k follow pointer Pi to the desired record or bucket. Else no record with search-key value k exists.,2019/7/3,Cryptography,page:24,Queries on B+-Trees (Cont.),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 100 (40 bytes per index entry). With 1 million search key values and n = 100 at most log50(1,000,000) = 4 nodes are accessed in a lookup. Contrast this with a balanced binary tree with 1 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,2019/7/3,Cryptography,page:25,Updates on B+-Trees: Insertion,Find the leaf node in which the search-key value would appear If the search-key value is already present in the leaf node Add record to the file If the search-key value is not present, then add the record to the main file (and create a bucket if necessary) 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.,2019/7/3,Cryptography,page:26,Updates on B+-Trees: Insertion (Cont.),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.,Result of splitting node containing Brighton and Downtown on inserting Clearview Next step: insert entry with (Downtown,pointer-to-new-node) into parent,2019/7/3,Cryptography,page:27,Updates on B+-Trees: Insertion (Cont.),B+-Tree before and after insertion of “Clearview”,2019/7/3,Cryptography,page:28,Redwood,Insertion in B+-Trees (Cont.),Splitting a non-leaf node: when inserting (k,p) into an already full internal node N Copy N to an in-memory area M with space for n+1 pointers and n keys Insert (k,p) into M Copy P1,K1, …, K n/2-1,P n/2 from M back into node N Copy Pn/2+1,K n/2+1,…,Kn,Pn+1 from M into newly allocated node N’ Insert (K n/2,N’) into parent N Read pseudocode in book!,Downtown Mianus Perryridge,,,,,Downtown,,,,,Mianus,,,,,2019/7/3,Cryptography,page:29,Updates on B+-Trees: Deletion,Find the record to be deleted, and remove it from the main file and from the bucket (if present) Remove (search-key value, pointer) from the leaf node if there is no bucket or if the bucket has become empty 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 (Ki–1, Pi), where Pi is the pointer to the deleted node, from its parent, recursively using the above procedure.,2019/7/3,Cryptography,page:30,Updates on B+-Trees: Deletion,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.,2019/7/3,Cryptography,page:31,Examples of B+-Tree Deletion,Deleting “Downtown” causes merging of under-full leaves leaf node can become empty only for n=3!,Before and after deleting “Downtown”,2019/7/3,Cryptography,page:32,Examples of B+-Tree Deletion (Cont.),Before and After deletion of “Perryridge” from result of previous example,2019/7/3,Cryptography,page:33,Examples of B+-Tree Deletion (Cont.),Leaf with “Perryridge” becomes underfull (actually empty, in this special case) and merged with its sibling. As a result “Perryridge” node’s parent became underfull, and was merged with its sibling Value separating two nodes (at parent) moves into merged node Entry deleted from parent Root node then has only one child, and is deleted,2019/7/3,Cryptography,page:34,Example of B+-tree Deletion (Cont.),Parent of leaf containing Perryridge became underfull, and borrowed a pointer from its left sibling Search-key value in the parent’s parent changes as a result,Before and after deletion of “Perryridge” from earlier example,2019/7/3,Cryptography,page:35,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.,2019/7/3,Cryptography,page:36,B+-Tree File Organization (Cont.),Good space utilization important since records use more space than pointers. To improve space utilization, involve more sibling nodes in redistribution during splits and merges,Example of B+-tree File Organization,2019/7/3,Cryptography,page:37,Indexing Strings,Variable length strings as keys Variable fanout Use space utilization as criterion for splitting, not number of pointers Prefix compression Key values at internal nodes can be prefixes of full key Keep enough characters to distinguish entries in the subtrees separated by the key value E.g. “Silas” and “Silberschatz” can be separated by “Silb” Keys in leaf node can be compressed by sharing common prefixes,2019/7/3,Cryptography,page:38,B-Tree Index Files,Similar to B+-tree, but B-tree allows search-key values to appear only once; eliminates redundant storage of search keys