Tree tricks osdc_melbourne_20101124

Tree TricksOSDC Melbourne 2010/11/24Copyright(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




Graph

Directed

Connected

Acyclic

Max(indegree) = 1


What’s a Graph, Really?



Nodes



NodesEdges


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 GraphsCREATE 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 ClosureCREATE TABLE reflexive_closure ( tail INTEGER NOT NULL REFERENCES message, head INTEGER NOT NULL REFERENCES message);

INSERT INTO reflexive_closureSELECT tail, head FROM edge UNIONSELECT tail, tail FROM edge UNIONSELECT head, head FROM edge;


Symmetric Closure

CREATE TABLE symmetric_closure ( tail INTEGER NOT NULL REFERENCES message, head INTEGER NOT NULL REFERENCES message);

INSERT INTO symmetric_closureSELECT tail, head FROM edge UNIONSELECT head, tail FROM edge;


Transitive ClosureCREATE TABLE transitive_closure ( tail INTEGER NOT NULL REFERENCES message, head INTEGER NOT NULL REFERENCES message);



INSERT INTO transitive_closure



INSERT INTO transitive_closureSELECT



INSERT INTO transitive_closureSELECTEr



INSERT INTO transitive_closureSELECTErUm



INSERT INTO transitive_closureSELECTErUmHrm...


Down the Rabbit Hole


Transitive Closure QueryWITH RECURSIVE t(tail, head, chain) AS ( SELECT tail, head, ARRAY[tail, head] FROM edgeUNION 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

?Tuesday, November 23, 2010


Graph

Directed

Connected

Acyclic

Max(indegree) = 1


Max(indegree) = 1

CREATE TABLE edge ( tail INTEGER NOT NULL REFERENCES message, head INTEGER NOT NULL REFERENCES message, PRIMARY KEY(tail, head));

ALTER TABLE edge ADD UNIQUE(head)


No Cycles!


Cycle FinderWITH RECURSIVE t(tail, head, chain) AS ( SELECT tail, head, ARRAY[tail, head] FROM edgeUNION ALL SELECT e.tail, e.head, t.chain || e.head FROM edge e JOIN t ON (t.head = e.tail) WHERE e.tail = ANY(t.chain))SELECT * FROM t


Cycle Finder FunctionCREATE OR REPLACE FUNCTION has_cycle()RETURNS BOOLEANLANGUAGE SQL AS $$SELECT EXISTS ( 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 (t.head = e.tail) WHERE e.tail = ANY(t.chain) ) SELECT * FROM t)


Cyclotomic Trigger FunctionCREATE OR REPLACE FUNCTION decyclifier()RETURNS TRIGGERLANGUAGE plpgsqlAS $$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 ConstraintCREATE OR REPLACE FUNCTION count_only_heads()RETURNS INTEGERLANGUAGE SQLAS $$SELECT count(tail)FROM edge eWHERE NOT EXISTS ( SELECT 1 FROM edge WHERE edge.head = e.tail)$$;


Tree ConstraintCREATE OR REPLACE FUNCTION one_head()RETURNS TRIGGERLANGUAGE plpgsqlAS $$BEGIN IF count_only_heads() <> 1 THEN RAISE EXCEPTION 'This is a tree!'; END IF; RETURN NEW;END;$$;


Tree Constraint

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


Questions?Comments?Brickbats?


Thanks!Copyright(C) 2010 by David Fetter

All Rights Reserved.


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Tree tricks osdc_melbourne_20101124