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Inverse Algorithms Complementary algorithms are a broad class of algorithms, of which inverse algorithms are a subset. An algorithm can be considered a mathematical function that transforms a system from a certain initial state to a certain final state. Given an algorithm F that transforms a system from the initial state S0 to the final state S1, let there be a complementary algorithm G that transforms the system from the initial state S1 to the final state S0. Mathematically, you could describe algorithms F and G like this: F(S0) = S1 G(S1) = S0 You can deduce two things, if G exists: that F is an invertible algorithm, and that G is the inverse of F, if F is applied to the system when the initial state is S0. The following equation shows explicitly that G is the inverse of F: G(F(S0)) = S0 This equation tells you that the effect of applying first F and then G to a system in the initial state S0 causes the system to end up in the state S0. You need a simpler way to denote the is-inverse-of relationship. In math textbooks, the inverse of a function F is usually called F-1. The problem with this convention, as pointed out by many people over the years, including Feynman,7 is that it uses the same notation to describe the inverse of F and the reciprocal of F, which is 1/F. To avoid any confusion in this book, I ll use the function Inverse to indicate the inverse of an algorithm. To show that G is the inverse of F, I ll simply use this equation: G = Inverse(F)

Oracle handles the shrinking operation internally as an insert/delete operation. Since you are only moving data and not modifying it, triggers on the tables will not fire when you perform the shrink operations. When you shrink a table to compact space, the indexes on the table remain usable after the shrinking operation.

A tablespace must both be locally managed as well as use Automatic Segment Space Management for its segments to be eligible for segment-shrinking operations.

You can use simple SQL commands to shrink segments. The segment-shrinking operation compacts fragmented space in the segments and optionally frees the space.

Given two algorithms F and G, you can state that G = Inverse(F), for a given initial system state S0, if G(F(S0)) = S0.

Before shrinking the segments, you must first enable row movement for any segment that you want to shrink. You can enable row movement by using the ENABLE ROW MOVEMENT clause of the ALTER TABLE command, as shown here: SQL> ALTER TABLE test ENABLE ROW MOVEMENT; Of course, if you ve already specified the ENABLE ROW MOVEMENT clause at table-creation time, you won t need to issue any commands to enable row movement before starting the segment-shrinking operation. By default, row movement is disabled at the segment level. There are two phases in a segment-shrinking operation: Compaction phase: During the compaction phase, the rows in a table are compacted and moved toward the left side of the segment. You thus make the segment dense, but the HWM remains where it was. The recovered space isn t immediately released back as free space. You can continue to issue DML statements and queries on a segment while it is being shrunk. Oracle holds locks only on the packets of the rows involved in the DML operations. If you have any long-running queries, Oracle can read from all the blocks that have technically been reclaimed during the shrinking operation. Of course, this capability is dependent on the time interval you specified for your undo retention parameter. Adjustment of the HWM/releasing-space phase: In the second phase, which lasts for a very short period of time, Oracle lowers the HWM and releases the recovered free space under the old HWM back to the parent tablespace. Oracle locks the object in an exclusive mode while the HWM is being lowered, meaning that you can t issue any INSERT, UPDATE, or DELETE DML statements against the segment.

During the compacting phase, the object is online and available, but during the second phase, the object becomes briefly unavailable, due to Oracle s exclusive locking of the segment.