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data/graph

Provides an implementation of directed graphs.

This provides basic algorithms for working with graphs, support for super-vertices, and other nifty features.

(add-edge! from to)

Defined at lib/data/graph.lisp:66:2

Add an edge FROM one vertex TO another.

(add-vertex! graph value)

Defined at lib/data/graph.lisp:45:2

Create a vertex with the corresponding VALUE and add it to the GRAPH.

(condensation in-graph)

Defined at lib/data/graph.lisp:145:2

Compute the condensation of an input graph, IN-GRAPH, replacing all strongly connected components with a super vertex.

Example:

> (define g (make-graph))
> (let [(a (add-vertex! g :a))
.       (b (add-vertex! g :b))
.       (c (add-vertex! g :c))]
.   (add-edge! a b)
.   (add-edge! b a)
.   (add-edge! a c))
> (condensation g)
out = «graph: "c" ("b" "a")»

(dominators root)

Defined at lib/data/graph.lisp:253:2

Build the dominators from nodes descended from ROOT.

This uses an adaptation of “A Simple, Fast Dominance Algorithm” by Keith D. Cooper, Timothy J. Harvey and Ken Kennedy. It does not compute post order numbers, as this is designed to be generalised for cyclic graphs.

This returns two objects: a lookup of vertex to its immediate dominator, and a DAG with edges from dominators to their immediate children.

Example:

> (define g (make-graph))
> (define doms
.   (let [(a (add-vertex! g :a))
.         (b (add-vertex! g :b))
.         (c (add-vertex! g :c))
.         (d (add-vertex! g :d))]
.     (add-edge! a b)
.     (add-edge! a c)
.     (add-edge! b c)
.     (add-edge! c b)
.     (add-edge! b d)
.
.     (dominators a)))
> (.> doms (get-vertex g :b))
out = «vertex: "a"»
> (.> doms (get-vertex g :c))
out = «vertex: "a"»
> (.> doms (get-vertex g :d))
out = «vertex: "b"»

(get-vertex graph value)

Defined at lib/data/graph.lisp:58:2

Get the corresponding vertex for this VALUE from the given GRAPH.

(graph->dot graph name)

Defined at lib/data/graph.lisp:28:2

Convert GRAPH to a string in the DOT format, suitable for consumption with GraphViz.

make-graph

Defined at lib/data/graph.lisp:9:2

Create a new, empty graph.

(strongly-connected-components graph)

Defined at lib/data/graph.lisp:78:2

Find all strong components from a GRAPH.

This uses Tarjan’s strongly connected components algorithm, which runs in linear time.

Example:

> (define g (make-graph))
> (let [(a (add-vertex! g :a))
.       (b (add-vertex! g :b))
.       (c (add-vertex! g :c))]
.   (add-edge! a b)
.   (add-edge! b a)
.   (add-edge! a c))
> (strongly-connected-components g)
out = ((«vertex: "c"») («vertex: "b"» «vertex: "a"»))

(traverse-postorder root visitor)

Defined at lib/data/graph.lisp:217:2

Visit a graph using postorder traversal starting at ROOT, calling VISITOR for each vertex.

VISITOR should take the form (lambda (vertex visited)), where vertex is the current vertex and visited is a set of already visited nodes.

Whilst the vertices are traversed in order, edges may be traversed in a different order for semantically identical graphs. This is especially prevalent when the graph contains cycles.

Note that each vertex will be visited exactly ONCE.

Example:

> (define g (make-graph))
> (let [(a (add-vertex! g :a))
.       (b (add-vertex! g :b))
.       (c (add-vertex! g :c))]
.   (add-edge! a b)
.   (add-edge! b c)
.   (traverse-postorder a (compose print! pretty)))
«vertex: "c"»
«vertex: "b"»
«vertex: "a"»
out = nil

(traverse-preorder root visitor)

Defined at lib/data/graph.lisp:180:2

Visit a graph using preorder traversal starting at ROOT, calling VISITOR for each vertex.

VISITOR should take the form (lambda (vertex visited)), where vertex is the current vertex and visited is a set of already visited nodes.

Whilst the vertices are traversed in order, edges may be traversed in a different order for semantically identical graphs. This is especially prevalent when the graph contains cycles.

Note that each vertex will be visited exactly ONCE.

Example:

> (define g (make-graph))
> (let [(a (add-vertex! g :a))
.       (b (add-vertex! g :b))
.       (c (add-vertex! g :c))]
.   (add-edge! a b)
.   (add-edge! b c)
.   (traverse-preorder a (compose print! pretty)))
«vertex: "a"»
«vertex: "b"»
«vertex: "c"»
out = nil

Undocumented symbols

  • $graph Defined at lib/data/graph.lisp:9:2
  • $vertex Defined at lib/data/graph.lisp:17:2
  • (graph? graph) Defined at lib/data/graph.lisp:9:2
  • (vertex? vertex) Defined at lib/data/graph.lisp:17:2