(in-package #:metabang.graph)
-;;; ---------------------------------------------------------------------------
;;;
-;;; ---------------------------------------------------------------------------
(defstruct (vertex-datum (:conc-name node-) (:type list))
(color nil)
(depth most-positive-fixnum)
(parent nil))
-;;; ---------------------------------------------------------------------------
(defmethod initialize-vertex-data ((graph basic-graph))
(let ((vertex-data (make-container 'simple-associative-container)))
- (iterate-vertexes graph (lambda (v)
- (setf (item-at vertex-data v)
+ (iterate-vertexes graph (lambda (v)
+ (setf (item-at vertex-data v)
(make-vertex-datum :color :white))))
(values vertex-data)))
-
-;;; ---------------------------------------------------------------------------
+
;;; breadth-first-search by GWK
-;;; ---------------------------------------------------------------------------
(defmethod breadth-first-visitor ((graph basic-graph) (source t) fn)
(breadth-first-visitor graph (find-vertex graph source) fn))
-;;; ---------------------------------------------------------------------------
(defmethod breadth-first-visitor ((graph basic-graph) (source basic-vertex) fn)
;; initialize
(let ((vertex-data (initialize-vertex-data graph))
(queue (make-container 'basic-queue)))
-
+
(let ((source-datum (item-at vertex-data source)))
(setf (node-color source-datum) :grey
(node-depth source-datum) 0)
(enqueue queue source)
-
+
(loop until (empty-p queue) do
(let* ((current-vertex (first-item queue))
(current (item-at vertex-data current-vertex)))
(node-depth child) (1+ (node-depth current))
(node-parent child) current-vertex)
(enqueue queue child-vertex)))))
-
+
(dequeue queue)
(setf (node-color current) :black)
(funcall fn current-vertex)))
-
+
vertex-data)))
-;;; ---------------------------------------------------------------------------
(defmethod breadth-first-search-graph ((graph basic-graph) (source t))
(breadth-first-search-graph graph (find-vertex graph source)))
-;;; ---------------------------------------------------------------------------
(defmethod breadth-first-search-graph ((graph basic-graph) (source basic-vertex))
;; initialize
(let ((vertex-data (initialize-vertex-data graph))
(queue (make-container 'basic-queue)))
-
+
(let ((source-datum (item-at vertex-data source)))
(setf (node-color source-datum) :grey
(node-depth source-datum) 0)
(enqueue queue source)
-
+
(loop until (empty-p queue) do
(let* ((current-vertex (first-item queue))
(current (item-at vertex-data current-vertex)))
(node-depth child) (1+ (node-depth current))
(node-parent child) current-vertex)
(enqueue queue child-vertex)))))
-
+
(dequeue queue)
(setf (node-color current) :black)))
-
+
vertex-data)))
-
-;;; ---------------------------------------------------------------------------
+
;;; single-source-shortest-paths - gwk
-;;; ---------------------------------------------------------------------------
#+NotYet
(defmethod single-source-shortest-paths ((graph basic-graph))
(setf (node-depth source-datum) 0))
))
-;;; ---------------------------------------------------------------------------
;;; connected-components - gwk
-;;; ---------------------------------------------------------------------------
(defmethod connected-components ((graph basic-graph))
(let ((union (make-container 'union-find-container)))
(iterate-vertexes
graph
(lambda (v) (insert-item union v)))
- (iterate-edges
- graph
- (lambda (e)
+ (iterate-edges
+ graph
+ (lambda (e)
(let ((node-1 (representative-node union (vertex-1 e)))
(node-2 (representative-node union (vertex-2 e))))
(unless (eq (find-set node-1) (find-set node-2))
(iterate-elements union 'find-set)
union))
-;;; ---------------------------------------------------------------------------
(defmethod connected-component-count ((graph basic-graph))
;;?? Gary King 2005-11-28: Super ugh
- (size
+ (size
(remove-duplicates
- (collect-elements
+ (collect-elements
(connected-components graph)
:transform #'parent)))
-
+
#+Fails
;;?? Gary King 2005-11-28: fails on big graphs? iterator design
;;?? Gary King 2005-11-28: ideally we don't want to cons up the list at all
- (size
+ (size
(collect-elements
(make-iterator (connected-components graph) :unique t :transform #'parent))))
-;;; ---------------------------------------------------------------------------
-
(defmethod find-connected-components ((graph basic-graph))
(collect-elements
(make-iterator (connected-components graph) :unique t :transform #'parent)
- :transform
+ :transform
(lambda (component)
- (subgraph-containing graph (element component)
- most-positive-fixnum))))
+ (subgraph-containing graph (element component)
+ :depth most-positive-fixnum))))
#+Alternate
(defmethod find-connected-components ((graph basic-graph))
(let ((element (element (parent component))))
(unless (item-at found-elements element)
(setf (item-at found-elements element) t)
-
- (push (subgraph-containing graph (element component)
+ (push (subgraph-containing graph (element component)
most-positive-fixnum)
result)))))
-
+
result))
-
-;;; ---------------------------------------------------------------------------
+
;;; minimum-spanning-tree based on kruskal's algorithm detailed in clrs2 -jjm
-;;; ---------------------------------------------------------------------------
(defmethod mst-find-set ((vertex basic-vertex))
#+ignore
(setf (previous-node vertex) (mst-find-set (previous-node vertex))))
(previous-node vertex))
-;;; ---------------------------------------------------------------------------
(defmethod mst-make-set ((vertex basic-vertex))
(setf (previous-node vertex) vertex
(rank vertex) 0))
-;;; ---------------------------------------------------------------------------
(defmethod mst-tree-union ((v1 basic-vertex) (v2 basic-vertex))
(mst-link (mst-find-set v1) (mst-find-set v2)))
-;;; ---------------------------------------------------------------------------
(defmethod mst-link ((v1 basic-vertex) (v2 basic-vertex))
(cond ((> (rank v1) (rank v2))
(when (= (rank v1) (rank v2))
(incf (rank v2))))))
-;;; ---------------------------------------------------------------------------
;;; jjm's implementation of mst depends on this
;;; todo - figure out some what to add and edge we create to a graph rather
;;; than always using add-edge-between-vertexes interface
-;;; ---------------------------------------------------------------------------
-(defmethod add-edges-to-graph ((graph basic-graph) (edges list)
+(defmethod add-edges-to-graph ((graph basic-graph) (edges list)
&key (if-duplicate-do :ignore))
(iterate-elements
edges
(lambda (edge)
- (bind ((v1 (element (source-vertex edge)))
- (v2 (element (target-vertex edge))))
+ (let ((v1 (element (source-vertex edge)))
+ (v2 (element (target-vertex edge))))
(add-edge-between-vertexes
graph v1 v2 :edge-class (type-of edge)
:edge-type (if (directed-edge-p edge)
:if-duplicate-do if-duplicate-do))))
graph)
-;;; ---------------------------------------------------------------------------
-;;; for completeness
-;;; ---------------------------------------------------------------------------
-
-(defmethod make-graph-from-vertexes ((vertex-list list))
- (bind ((edges-to-keep nil)
- (g (copy-template (graph (first vertex-list)))))
-
- (iterate-elements
- vertex-list
- (lambda (v)
- (add-vertex g (element v))
- (iterate-elements
- (edges v)
- (lambda (e)
- (when (and (member (vertex-1 e) vertex-list)
- (member (vertex-2 e) vertex-list))
- (pushnew e edges-to-keep :test #'eq))))))
-
- (iterate-elements
- edges-to-keep
- (lambda (e)
- (bind ((v1 (source-vertex e))
- (v2 (target-vertex e)))
- ;;?? can we use copy here...
- (add-edge-between-vertexes
- g (element v1) (element v2)
- :edge-type (if (directed-edge-p e)
- :directed
- :undirected)
- :if-duplicate-do :force
- :edge-class (type-of e)
- :value (value e)
- :edge-id (edge-id e)
- :element (element e)
- :tag (tag e)
- :graph g
- :color (color e)))))
- g))
-
-;;; ---------------------------------------------------------------------------
(defmethod edge-lessp-by-weight ((e1 basic-edge) (e2 basic-edge))
(< (weight e1) (weight e2)))
-;;; ---------------------------------------------------------------------------
;;; minumum spanning tree
-;;; ---------------------------------------------------------------------------
-(defmethod minimum-spanning-tree ((graph basic-graph)
+(defmethod minimum-spanning-tree ((graph basic-graph)
&key
(edge-sorter #'edge-lessp-by-weight))
- (bind ((result nil))
- (iterate-vertexes
+ (let ((result nil))
+ (iterate-vertexes
graph
(lambda (v)
(mst-make-set v)))
-
+
(loop for edge in (sort (edges graph) edge-sorter) do
- (bind ((v1 (source-vertex edge))
+ (let ((v1 (source-vertex edge))
(v2 (target-vertex edge)))
-
+
(unless (eq (mst-find-set v1)
(mst-find-set v2))
(push edge result)
(values t result))
(t (values nil result)))))))
-;;; ---------------------------------------------------------------------------
-#+ignore ;;; shit
-(defmethod minimum-spanning-tree ((vertex-list list)
+#+ignore ;;; shoot
+(defmethod minimum-spanning-tree ((vertex-list list)
&key
(edge-sorter #'edge-lessp-by-weight))
- (bind ((result nil)
- (v-edges (remove-duplicates
+ (let ((result nil)
+ (v-edges (remove-duplicates
(flatten (mapcar #'edges vertex-list)) :test #'eq)))
-
+
(iterate-container
vertex-list
(lambda (v)
(mst-make-set v)))
-
-
-
+
(loop for edge in (sort v-edges edge-sorter) do
- (bind ((v1 (source-vertex edge))
- (v2 (target-vertex edge))
- (v1-set (mst-find-set v1))
- (v2-set (mst-find-set v2)))
+ (let ((v1 (source-vertex edge))
+ (v2 (target-vertex edge))
+ (v1-set (mst-find-set v1))
+ (v2-set (mst-find-set v2)))
(when (or (not v1-set)
(not v2-set))
(return-from minimum-spanning-tree nil))
-
-
+
+
(unless (eq (mst-find-set v1)
(mst-find-set v2))
(push edge result)
(values t result))
(t (values nil result)))))))
-;;; ---------------------------------------------------------------------------
;;; uses mst to determine if the graph is connected
-;;; ---------------------------------------------------------------------------
-(defmethod connected-graph-p ((graph basic-graph) &key
+(defmethod connected-graph-p ((graph basic-graph) &key
(edge-sorter 'edge-lessp-by-weight))
(minimum-spanning-tree graph :edge-sorter edge-sorter))
-
-;;; ---------------------------------------------------------------------------
+
#+test
-(bind ((g (make-container 'graph-container)))
+(let ((g (make-container 'graph-container)))
(add-edge-between-vertexes g :v :y :edge-type :directed)
(add-edge-between-vertexes g :u :x :edge-type :directed)
(add-edge-between-vertexes g :x :v :edge-type :directed)
:if-duplicate-do :force)
(minimum-spanning-tree g))
-;;; ---------------------------------------------------------------------------
-;;; GWK's implementation of kruskal's - slightly faster, but it doesn't return
+;;; GWK's implementation of kruskal's - slightly faster, but it doesn't return
;;; a tree (still faster even if it does). Will decide later if which to use
;;; ignoring for now -jjm
-;;; ---------------------------------------------------------------------------
#+not-yet
(defmethod minimum-spanning-tree ((graph basic-graph) &key (weight 'weight))
(let ((a nil)
(union (make-container 'union-find-container))
(edges (sort (edges graph) #'< :key weight)))
- (iterate-vertexes
+ (iterate-vertexes
graph (lambda (v) (insert-item union v)))
(dolist (edge edges)
(let ((node-1 (representative-node union (vertex-1 edge)))
(unless (eq (find-set node-1) (find-set node-2))
(graft-nodes node-1 node-2)
(push edge a))))
-
+
(values a)))
-;;; ---------------------------------------------------------------------------
#+test
(loop for f in '(mst-kruskal minimum-spanning-tree-kruskal) do
(fluid-bind (((random-seed *random-generator*) 1))
(bind ((g (generate-undirected-graph-via-vertex-probabilities
- *random-generator* (make-instance 'graph-container :default-edge-type :directed)
+ *random-generator* (make-instance 'graph-container :default-edge-type :directed)
100
- #(0.8 0.2)
+ #(0.8 0.2)
#2A((0.2 0.1) (nil 0.2))
- (lambda (kind count)
+ (lambda (kind count)
(form-keyword "H" (format nil "~2,'0D~4,'0D" kind count))))
))
(timeit (:report :values)
(declare (ignore a b))
0)))))))
-;;; ---------------------------------------------------------------------------
;;; end minimum spanning tree
-;;; ---------------------------------------------------------------------------
-
-;;; ---------------------------------------------------------------------------
+
;;; depth-first-search - clrs2
;;; todo - figure out how to name this depth-first-search, which is already
;;; defined in search.lisp
-;;; ---------------------------------------------------------------------------
-;;; ---------------------------------------------------------------------------
;;; should probably make this special
-;;; ---------------------------------------------------------------------------
(defparameter *depth-first-search-timer* -1)
-;;; ---------------------------------------------------------------------------
;;; undirected edges are less than edges that are directed
-;;; ---------------------------------------------------------------------------
#+ignore ;;; incorrect, methinks - jjm
(defmethod edge-lessp-by-direction ((e1 basic-edge) (e2 basic-edge))
(defmethod edge-lessp-by-direction ((e1 basic-edge) (e2 basic-edge))
(and (undirected-edge-p e1) (directed-edge-p e2)))
-;;; ---------------------------------------------------------------------------
(defmethod out-edge-for-vertex-p ((edge basic-edge) (vertex basic-vertex))
(cond ((and (directed-edge-p edge)
t)
(t nil)))
-;;; ---------------------------------------------------------------------------
;;; depth-first-search
-;;; ---------------------------------------------------------------------------
-
-(defmethod dfs ((graph basic-graph) (root t) fn &key
+
+(defmethod dfs ((graph basic-graph) (root t) fn &key
(out-edge-sorter #'edge-lessp-by-direction))
(dfs graph (find-vertex graph root) fn :out-edge-sorter out-edge-sorter))
-;;; ---------------------------------------------------------------------------
(defmethod dfs ((graph basic-graph) (root basic-vertex) fn &key
(out-edge-sorter #'edge-lessp-by-direction))
(setf *depth-first-search-timer* -1)
-
- (iterate-vertexes
+
+ (iterate-vertexes
graph
(lambda (v)
(setf (color v) :white
(previous-node v) nil
(discovery-time v) -1
(finish-time v) -1)))
-
+
(iterate-edges
graph
(lambda (e)
(setf (color e) nil)))
-
- (loop with vl = (remove root (vertexes graph) :test #'eql)
- for v in (push root vl) do
- (when (eql (color v) :white)
- (dfs-visit graph v fn out-edge-sorter)))
-
+
+ (loop for v in (cons root (remove root (vertexes graph) :test #'eql))
+ when (eql (color v) :white)
+ do (dfs-visit graph v fn out-edge-sorter))
+
(values
(sort (copy-list (vertexes graph)) #'< :key #'finish-time)
graph))
-;;; ---------------------------------------------------------------------------
+(defgeneric rooted-dfs (graph root fn &key out-edge-sorter)
+ (:documentation "A variant of DFS that does not visit nodes that are
+unreachable from the ROOT.")
+ (:method ((graph basic-graph) (root t) fn &key
+ (out-edge-sorter #'edge-lessp-by-direction))
+ (rooted-dfs graph (find-vertex graph root) fn :out-edge-sorter out-edge-sorter))
+ (:method ((graph basic-graph) (root basic-vertex) fn &key
+ (out-edge-sorter #'edge-lessp-by-direction))
+ (setf *depth-first-search-timer* -1)
+
+ (iterate-vertexes
+ graph
+ (lambda (v)
+ (setf (color v) :white
+ (previous-node v) nil
+ (discovery-time v) -1
+ (finish-time v) -1)))
+
+ (iterate-edges
+ graph
+ (lambda (e)
+ (setf (color e) nil)))
+
+ (dfs-visit graph root fn out-edge-sorter)
+
+ (values
+ (sort (remove-if #'(lambda (v) (eq (color v) :white))
+ (vertexes graph))
+ #'< :key #'finish-time)
+ graph)))
+
(defmethod dfs-visit ((graph graph-container) (u basic-vertex)
fn sorter)
-
-
+
+
(incf *depth-first-search-timer*)
+ ;; the following should be removed later for efficiency [2011/03/10:rpg]
+ (unless (eq (color u) :white)
+ (error "precondition for DFS-VISIT violated."))
(setf (color u) :gray
(discovery-time u) *depth-first-search-timer*)
-
-
+ ;; moved the funcall up here, fixing a boundary condition where the
+ ;; function was never called on root nodes. [2011/03/10:rpg]
+ (funcall fn u)
+
(loop for edge in (sort (collect-elements
(edges u)
:filter (lambda (e)
- (out-edge-for-vertex-p e u))) sorter) do
- (bind ((v (other-vertex edge u)))
-
- (unless (color edge)
- (setf (color edge) (color v)))
-
- (when (eql (color v) :white)
+ (out-edge-for-vertex-p e u))) sorter)
+ as v = (other-vertex edge u)
+ unless (color edge)
+ do (setf (color edge) (color v))
+ when (eql (color v) :white)
+ do
(setf (previous-node v) u)
- (funcall fn v)
- (dfs-visit graph v fn sorter))))
-
+ (dfs-visit graph v fn sorter))
+
(incf *depth-first-search-timer*)
-
+
(setf (color u) :black
(finish-time u) *depth-first-search-timer*))
-;;; ---------------------------------------------------------------------------
;;; from clrs2
-;;; ---------------------------------------------------------------------------
#+test
-(bind ((g (make-container 'graph-container)))
+(let ((g (make-container 'graph-container)))
(add-edge-between-vertexes g :v :y :edge-type :directed)
(add-edge-between-vertexes g :u :x :edge-type :directed)
(add-edge-between-vertexes g :x :v :edge-type :directed)
(assert (equal '(:X :Y :V :U :Z :W)
(mapcar #'element (dfs g :u #'identity)))))
-;;; ---------------------------------------------------------------------------
(defmethod dfs-tree-edge-p ((edge graph-container-edge))
(eql (color edge) :white))
-;;; ---------------------------------------------------------------------------
(defmethod dfs-back-edge-p ((edge graph-container-edge))
(eql (color edge) :gray))
-;;; ---------------------------------------------------------------------------
;;; not correct - has to look at combination of discovery-time and finish-time
-;;; ---------------------------------------------------------------------------
(defmethod dfs-forward-edge-p ((edge graph-container-edge))
(warn "implementation is not correct.")
(< (discovery-time (source-vertex edge))
(discovery-time (target-vertex edge)))))
-;;; ---------------------------------------------------------------------------
;;; not correct - has to look at combination of discovery-time and finish-time
-;;; ---------------------------------------------------------------------------
(defmethod dfs-cross-edge-p ((edge graph-container-edge))
(warn "implementation is not correct.")
(> (discovery-time (source-vertex edge))
(discovery-time (target-vertex edge)))))
-;;; ---------------------------------------------------------------------------
(defmethod dfs-edge-type ((edge graph-container-edge))
(cond ((dfs-tree-edge-p edge)
:cross)
(t nil)))
-;;; ---------------------------------------------------------------------------
;;; end dfs
-;;; ---------------------------------------------------------------------------
-;;; ---------------------------------------------------------------------------
;;; mapping functions
-;;; ---------------------------------------------------------------------------
-;;; ---------------------------------------------------------------------------
;;; over vertexes
-;;; ---------------------------------------------------------------------------
(defmethod map-over-all-combinations-of-k-vertexes ((graph basic-graph) k fn)
- (bind ((vertex-count (size graph))
+ (let* ((vertex-count (size graph))
(symbols (make-list k :initial-element vertex-count))
- (vertexes (vertexes graph)))
- (iterate-over-indexes
+ (vertexes (vertexes graph)))
+ (iterate-over-indexes
symbols
(lambda (vertex-indexes)
(when (apply #'< vertex-indexes)
(nth-element vertexes vertex-index))
vertex-indexes)))))))
-;;; ---------------------------------------------------------------------------
#+test
-(bind ((result nil)
+(let ((result nil)
(g (make-container 'graph-container)))
(add-edge-between-vertexes g :u :v :edge-type :directed)
(add-edge-between-vertexes g :u :x :edge-type :directed)
(add-edge-between-vertexes g :y :x :edge-type :directed)
(add-edge-between-vertexes g :w :y :edge-type :directed)
(add-edge-between-vertexes g :w :z :edge-type :directed)
-
- (map-over-all-combinations-of-k-vertexes
+
+ (map-over-all-combinations-of-k-vertexes
g
4
(lambda (vertex-list)
- (bind ((graph-from-vertexes (make-graph-from-vertexes vertex-list)))
+ (let ((graph-from-vertexes (make-graph-from-vertexes vertex-list)))
(when (mst-kruskal graph-from-vertexes #'identity-sorter)
(push graph-from-vertexes result)))))
result)
-;;; ---------------------------------------------------------------------------
-;;; over edges
+;;; over edges
;;; todo: merge these two defs
-;;; ---------------------------------------------------------------------------
(defmethod map-over-all-combinations-of-k-edges ((graph basic-graph) k fn)
- (bind ((edge-count (edge-count graph))
+ (let* ((edge-count (edge-count graph))
(symbols (make-list k :initial-element edge-count))
- (edges (edges graph)))
+ (edges (edges graph)))
(print symbols)
- (iterate-over-indexes
+ (iterate-over-indexes
symbols
(lambda (edge-indexes)
(when (apply #'< edge-indexes)
(nth-element edges edge-index))
edge-indexes)))))))
-;;; ---------------------------------------------------------------------------
(defmethod map-over-all-combinations-of-k-edges ((vertex basic-vertex) k fn)
- (bind ((edge-count (edge-count vertex))
+ (let* ((edge-count (edge-count vertex))
(symbols (make-list k :initial-element edge-count))
- (edges (edges vertex)))
- (print symbols)
- (iterate-over-indexes
+ (edges (edges vertex)))
+ ;(print symbols)
+ (iterate-over-indexes
symbols
(lambda (edge-indexes)
(when (apply #'< edge-indexes)
(funcall fn (mapcar (lambda (edge-index)
(nth-element edges edge-index))
edge-indexes)))))))
-;;; ---------------------------------------------------------------------------
#+test
-(map-over-all-combinations-of-k-edges
+(map-over-all-combinations-of-k-edges
(generate-undirected-graph-via-verex-probabilities
- *random-generator* 'graph-container
+ *random-generator* 'graph-container
10
- #(0.8 0.2)
+ #(0.8 0.2)
#2A((0.2 0.1) (nil 0.2))
- (lambda (kind count)
+ (lambda (kind count)
(form-keyword "H" (format nil "~2,'0D~4,'0D" kind count))))
- 2
+ 2
(lambda (es)
(format t "~%")
(mapc (lambda (e)
projects / cl-graph.git / blobdiff