Tree tricks osdc_melbourne_20101124

Tree Tricks
OSDC Melbourne 2010/11/24
Copyright(C) 2010 by David Fetter
All Rights Reserved.
Tuesday, November 23, 2010

What’s a Tree, Really?
Plant
Perennial
Woody
Secondary branches
Off ground
Apical Dominance

What’s a Tree, Really?
Graph
Directed
Connected
Acyclic
Max(indegree) = 1

What’s a Graph, Really?

Nodes

Nodes
Edges

Representing Graphs
CREATE TABLE message (
message_id SERIAL PRIMARY KEY,
parent_message_id INTEGER REFERENCES message,
sender email NOT NULL,
list TEXT NOT NULL,
...
);

FAIL!Tuesday, November 23, 2010

Separate Your Concerns.

Representing Graphs
CREATE TABLE message (
message_id SERIAL PRIMARY KEY,
sender email NOT NULL,
list TEXT NOT NULL,
...
);
CREATE TABLE edge (
tail INTEGER NOT NULL REFERENCES message,
head INTEGER NOT NULL REFERENCES message,
PRIMARY KEY(tail, head)
);

WIN!Tuesday, November 23, 2010

Mathematical Flashback

Binary Relations

Binary Relations
Reﬂexive

Binary Relations
Reﬂexive
Symmetric

Binary Relations
Reﬂexive
Symmetric
Transitive

CLOSURE
(need to get some)

Reﬂexive Closure
CREATE TABLE reflexive_closure (
head INTEGER NOT NULL REFERENCES message
);
INSERT INTO reflexive_closure
SELECT tail, head FROM edge UNION
SELECT tail, tail FROM edge UNION
SELECT head, head FROM edge;

Symmetric Closure
CREATE TABLE symmetric_closure (
);
INSERT INTO symmetric_closure
SELECT tail, head FROM edge UNION
SELECT head, tail FROM edge;

Transitive Closure
CREATE TABLE transitive_closure (
);

Transitive Closure
);
INSERT INTO transitive_closure

Transitive Closure
);
SELECT

Transitive Closure
);
SELECT
Er

Transitive Closure
);
SELECT
Er
Um

Transitive Closure
);
SELECT
Er
Um
Hrm...

Down the Rabbit Hole

Transitive Closure Query
WITH RECURSIVE t(tail, head, chain) AS (
SELECT tail, head, ARRAY[tail, head]
FROM edge
UNION ALL
SELECT e.tail, e.head, t.chain || e.head
FROM edge e JOIN t
ON (e.tail = t.head)
WHERE e.tail <> ANY(t.chain)
)
SELECT tail, head FROM t

Forest Constraints
?

Max(indegree) = 1
CREATE TABLE edge (
head INTEGER NOT NULL REFERENCES message,
PRIMARY KEY(tail, head)
);
ALTER TABLE edge ADD UNIQUE(head)

No Cycles!

Cycle Finder
FROM edge
UNION ALL
FROM edge e JOIN t
ON (t.head = e.tail)
WHERE e.tail = ANY(t.chain)
)
SELECT * FROM t

Cycle Finder Function
CREATE OR REPLACE FUNCTION has_cycle()
RETURNS BOOLEAN
LANGUAGE SQL AS $$
SELECT EXISTS (
FROM edge
UNION ALL
FROM edge e JOIN t
ON (t.head = e.tail)
WHERE e.tail = ANY(t.chain)
)
SELECT * FROM t
)

Cyclotomic Trigger Function
CREATE OR REPLACE FUNCTION decyclifier()
RETURNS TRIGGER
LANGUAGE plpgsql
AS $$
BEGIN
IF (has_cycle()) THEN
RAISE ERROR 'No cycles allowed!';
END IF;
RETURN NEW;
END;

Cyclotomic Trigger
CREATE TRIGGER edge_decyclifier
AFTER INSERT OR UPDATE ON edge
FOR EACH STATEMENT
EXECUTE PROCEDURE decyclifier();

Tree Constraint
Forest Constraint +
Unique Non-head Node

Tree Constraint
CREATE OR REPLACE FUNCTION count_only_heads()
RETURNS INTEGER
LANGUAGE SQL
AS $$
SELECT count(tail)
FROM edge e
WHERE NOT EXISTS (
SELECT 1 FROM edge
WHERE edge.head = e.tail
)
$$;

Tree Constraint
CREATE OR REPLACE FUNCTION one_head()
RETURNS TRIGGER
LANGUAGE plpgsql
AS $$
BEGIN
IF count_only_heads() <> 1 THEN
RAISE EXCEPTION 'This is a tree!';
END IF;
RETURN NEW;
END;
$$;

Tree Constraint
CREATE TRIGGER edge_one_head
AFTER INSERT OR UPDATE OR DELETE
ON edge
EXECUTE PROCEDURE one_head();

Questions?
Comments?
Brickbats?

Tree tricks osdc_melbourne_20101124

More Related Content

Viewers also liked

Similar to Tree tricks osdc_melbourne_20101124

More from David Fetter

Recently uploaded

Tree tricks osdc_melbourne_20101124