# NAME

Set::Relation::V1 - Bundled original implementation of Set::Relation role

# VERSION

This document describes Set::Relation::V1 version 0.13.4 for Perl.

# SYNOPSIS

See the SYNOPSIS of Set::Relation, which represents this file also.

# DESCRIPTION

Set::Relation::V1 provides the original complete implementation of the Set::Relation and Set::Relation::Mutable roles. It is their first working proof of concept or prototype or reference implementation. Early lessons learned while making this implementation did subsequently lead to the creation of Set::Relation::V2, which kept the same interface but reworked the internals in several large ways to improve execution performance and other resource efficiencies. This older version is kept in parallel to having the newer one, as a baseline for benchmarking the reworked internals as well as for learning from.

## Matters of Mutability

Now, while a relation value is conceptually immutable, the Set::Relation::V1 class allows you to mutate a Set::Relation::V1 object under some circumstances as a convenience to users, in a similar manner to how you can mutate a Perl Hash or Array by inserting or deleting its elements. By default, a newly created Set::Relation::V1 object is mutable, that is its identity is said to not be frozen; but when you perform certain operations with one, it will become immutable, gaining a frozen identity, and this change can not be reversed, though you can clone said object to get an un-frozen duplicate.

There are 3 main ways to make a Set::Relation::V1 object immutable. The first is explicitly, by invoking its `freeze_identity`

method. The second is implicitly, by invoking its `which`

method *(this one may be reconsidered on users' request)*; this also happens to be done indirectly any time a tuple-representing Hash is given to a Set::Relation routine. The third is if another Set::Relation::V1 object is constructed that is given the first object as a tuple attribute value; this was done rather than cloning the input object under the assumption that most of the time you wouldn't want to mutate the input object afterwards, for efficiency.

## Matters of Performance

Set::Relation::V1 by itself is strictly an in-memory data structure, same as Perl's built-in arrays and hashes. Its design focuses on providing correct-behaving features in a relatively simple manner.

Performance is made as good as possible, using multiple design techniques, while not becoming too complicated. Set::Relation::V1 keeps a variety of indexes automatically and makes a trade-off of being willing to use more RAM (by storing multiple copies of data in hashed form, at least 3 copies total) in order to get better CPU performance.

Loosely speaking, each Set::Relation::V1 object is a Perl hash-ref with one element per tuple, where the hash value is the tuple itself as a Perl hash-ref and the key is a unique hash / serialization of the entire deep value of said tuple.

This basic structure means that fundamental operations of taking a whole arbitrary tuple and querying whether or not it is in the relation is an O(1) / constant-time operation, same as testing the existence of a key in a Perl hash; likewise, inserting a tuple into or deleting a tuple from a relation is also an O(1) / constant-time operation.

All basic set operations, like relational union or difference, are all O(N) / linear-time due to that basic structure alone. When comparing 2 input relations for a set operation, only the smaller one needs to be fully (at the worst) or partially scanned, and the other does not; the scan produces a list of tuples to search for, and each search for a tuple in the second relation is O(1). Similarly, many basic relational operations like projection and extension are 0(N). No such operations are in polynomial-time such as O(N^2); that would simply be unacceptable.

Set::Relation::V1 also automatically generates more indexes to help with the general cases of relational joins or semijoins where the arguments have some but not all attributes in common (the common ones only providing the join criteria). Without the extra indexes, a generic join would be in polynomial time since it would have to pair up every tuple of one argument with every one of another to see if parts of each tuple match. However, this is changed to linear time by first creating (or reusing) an index on each argument that is a hash of just the portion of the tuple attributes that overlap with the other argument. Creating each index is also linear time. So then using those indexes, doing an ordinary join or semijoin then has the same performance characteristics as relational union or difference.

Now to be more accurate concerning relational join operations, finding out what set of tuples in each input match each other is always a linear time operation like relational intersection (what is actually happening on the indexes), but producing the result set of tuples is an O(N*M) operation. Now if the attributes overlapped between both inputs are superkeys of each input, then producing the result set reduces to linear / O(N) time; otherwise it is appropriately slower since the then multiple tuples on each side of a match are then cartesian joined. If the main operation is a semijoin, that is always O(N) since we are actually just filtering one input by the other, not joining them for a result.

Of course, a regular cartesian product, a join between 2 relations having no attributes in common, can't be helped by an index (and generates none), and so does have O(N*M) performance all the time. This can't be helped since we know that the result will always have a cardinality that is the multiplication of input relations' cardinalities.

For the various few more complicated operators provided by Set::Relation::V1, which are conceptually defined in terms of simpler operators, their performance is generally based on what they are defined in terms of.

To keep things simple, creation of indexes (besides the single fundemental one) is strictly automatic and you can not explicitly add or remove an index on a Set::Relation::V1 object. Creation is just done the first time the indexes would be *used*, so they only happen say if you do a regular join or such operation. Once an index is created, it is automatically kept up to date by any Set::Relation::V1 mutator methods; the design of said indexes also makes it such that keeping them up to date during tuple inserts or deletes is also O(1) per index.

To keep things simple, when new Set::Relation::V1 objects are generated from relational operations, that new object starts out with no indexes (other than the fundamental), even if conceivably the parent's could be copied.

The various Set::Relation::V1 operators know about and look for certain special cases of inputs which allow them to short-circuit the operation. In some cases they may return certain constant values, or they may just return one of their input objects directly. They may also use a cheaper operation than you requested which for example doesn't involve creating or using indexes. For example, if you use `join`

on 2 input relations that have all the same attributes, it will short circuit to `intersection`

. Or for example if you do `union`

and one input relation has zero tuples, it will simply return the other input object.

Now in the general relational model where relations are immutable, that makes no semantical difference, but it is important to know if you plan to mutate the result object of a relational operation, as you might then be mutating an argument too. So take appropriate precautions and do appropriate tests where necessary so that you don't have undesired side-effects in your program.

Note that due to an aspect of its design, using the Set::Relation-defined parameter `$allow_dup_tuples`

on any applicable method of `Set::Relation::V1`

will have no effect since uniqueness comparisons for tuples are always done eagerly on storage and there is no mechanism to have even partial multiset semantics for performance.

*Note from 2016 May 3: While the hashing-based algorithm Set::Relation::V1 (and V2) uses internally to make relational operations perform in O(N)/O(1) rather than O(N*M) was invented by its author in 2009 for this purpose, in retrospect it turns out that the algorithm had prior art and an industry standard name, that being "hash join".*

# INTERFACE

Set::Relation::V1 composes the Set::Relation::Mutable role declared in the Set::Relation file, which in turn composes the Set::Relation role.

# DIAGNOSTICS

*This documentation is pending.*

# CONFIGURATION AND ENVIRONMENT

*This documentation is pending.*

# DEPENDENCIES

This file requires any version of Perl 5.x.y that is at least 5.8.0.

It also requires these Perl packages that are available both bundled with Perl 5.8.0+ and on CPAN: Carp-ver(1.01..*).

It also requires these Perl packages that are available both bundled with Perl 5.8.1+ and on CPAN: Scalar::Util-ver(1.13..*).

It also requires these Perl packages that are available both bundled with Perl 5.26.0+ and on CPAN: List::Util-ver(1.4602..*).

# INCOMPATIBILITIES

None reported.

# SEE ALSO

Go to Set::Relation for the majority of both distribution-internal and external references.

# BUGS AND LIMITATIONS

*This documentation is pending.*

# AUTHOR

Darren Duncan (`darren@DarrenDuncan.net`

)

# LICENSE AND COPYRIGHT

Set::Relation is Copyright © 2006-2023, Muldis Data Systems, Inc.

See the LICENSE AND COPYRIGHT of Set::Relation for details.

# ACKNOWLEDGEMENTS

The ACKNOWLEDGEMENTS in Set::Relation apply to this file too.