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When inserting or deleting a key value, the crabbing protocol takes these actions: It follows the same protocol as for searching until it reaches the desired leaf node Up to this point, it obtains only shared locks It locks the leaf node in exclusive mode and inserts or deletes the key value If it needs to split a node or coalesce it with its siblings, or redistribute key values between siblings, the crabbing protocol locks the parent of the node in exclusive mode After performing these actions, it releases the locks on the node and siblings If the parent requires splitting, coalescing, or redistribution of key values, the protcol retains the lock on the parent, and splitting, coalescing, or redistribution propagates further in the same manner Otherwise, it releases the lock on the parent The protocol gets its name from the way in which crabs advance by moving sideways, moving the legs on one side, then the legs on the other, and so on alternately The progress of locking while the protocol both goes down the tree and goes back up (in case of splits, coalescing, or redistribution) proceeds in a similar crab-like manner Once a particular operation releases a lock on a node, other operations can access that node There is a possibility of deadlocks between search operations coming down the tree, and splits, coalescing or redistribution propagating up the tree The system can easily handle such deadlocks by restarting the search operation from the root, after releasing the locks held by the operation The second technique achieves even more concurrency, avoiding even holding the lock on one node while acquiring the lock on another node, by using a modi ed version of B+ -trees called B-link trees; B-link trees require that every node (including internal nodes, not just the leaves) maintain a pointer to its right sibling This pointer is required because a lookup that occurs while a node is being split may have to search not only that node but also that node s right sibling (if one exists) We shall illustrate this technique with an example later, but we rst present the modi ed procedures of the B-link-tree locking protocol Lookup Each node of the B+ -tree must be locked in shared mode before it is accessed A lock on a nonleaf node is released before any lock on any other node in the B+ -tree is requested If a split occurs concurrently with a lookup, the desired search-key value may no longer appear within the range of values represented by a node accessed during lookup In such a case, the search-key value is in the range represented by a sibling node, which the system locates by following the pointer to the right sibling However, the system locks leaf nodes following the two-phase locking protocol, as Section 1673 describes, to avoid the phantom phenomenon Insertion and deletion The system follows the rules for lookup to locate the leaf node into which it will make the insertion or deletion It upgrades the shared-mode lock on this node to exclusive mode, and performs the insertion.

The McGraw Hill Companies, 2001

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functional dependency ( F D ) is a constraint about two or more columns o f a table X deter mines Y(X Y) if there exists at most one value o f 7 for every value o f X The word func tion c o m e s from mathematics where a function gives one value For example, Social Secu rity number determines city (StdSSN > StdCity) in the university database table if there is at most o n e city value for every Social Security number A column appearing o n the lefthand side o f an F D is called a determinant or, alternatively, an L H S for left-hand side In this example, StdSSN is a determinant You can also think about functional dependencies as identifying potential candidate keys B y stating thatX > Y, i f X a n d Fare placed together in a table without other columns, X is a candidate key Every determinant (LHS) is a candidate k e y if it is placed in a table with the other columns that it determines For example, if StdSSN, StdCity, and StdClass are placed in a table together and StdSSN - StdCity and StdSSN - StdClass then StdSSN is a candidate key If there are n o other candidate keys, a determinant will b e c o m e the primary key if it does not allow null values

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