Re: Graph coloring with Scheme

[Jan Wedekind]

Forgot to use the ordering actually. It needs to be:

(define (coloring graph nodes) (assign-colors graph (nodes graph) (order graph 
(nodes graph))))

Or one can do the ordering directly within the "assign-colors" function:

(define (assign-colors graph nodes colors)
  (if (null? nodes) '()
    (let* [(target    (argmin (lambda (node) (length (adjacent graph node))) 
nodes))
           (coloring  (assign-colors (remove-node graph target) (delete target 
nodes) colors))
           (blocked   (map (cut assq-ref coloring <>) (adjacent graph target)))
           (available (lset-difference eq? colors blocked))]
      (cons (cons target (car available)) coloring))))
(define (coloring graph colors) (assign-colors graph (nodes graph) colors))

On Fri, 14 Nov 2014, Jan Wedekind wrote:

> Hi,
> Here is an implementation [1] of Chaitin's graph coloring algorithm using GNU 
> Guile and Graphviz. Any feedback and suggestions are welcome. Let me know if 
> you can make the implementation more concise ;)
>
> Regards Jan
>
> (use-modules (srfi srfi-1)
>             (srfi srfi-26))
> (define (dot graph colors)
>  (apply string-append
>         (append (list "graph g {")
>                 (map (lambda (color) (format #f " ~a [style=filled, 
> fillcolor=~a];" (car color) (cdr color))) colors)
>                 (map (lambda (edge) (format #f " ~a -- ~a;" (car edge) (cdr 
> edge))) graph)
>                 (list " }"))))
> (define (graphviz graph colors) (system (format #f "echo '~a' | dot -Tpng | 
> display -" (dot graph colors))))
> (define (nodes graph) (delete-duplicates (append (map car graph) (map cdr 
> graph))))
> (define (has-node? edge node) (or (eq? (car edge) node) (eq? (cdr edge) 
> node)))
> (define (adjacent graph node) (nodes (filter (cut has-node? <> node) graph)))
> (define (remove-node graph node) (filter (lambda (edge) (not (has-node? edge 
> node))) graph))
> (define (argmin fun lst)
>  (let* [(vals   (map fun lst))
>         (minval (apply min vals))]
>    (list-ref lst (- (length lst) (length (member minval vals))))))
> (define (order graph nodes)
>  (if (null? nodes) '()
>    (let [(target (argmin (lambda (node) (length (adjacent graph node))) 
> nodes))]
>      (cons target (order (remove-node graph target) (delete target 
> nodes))))))
> (define (assign-colors graph nodes colors)
>  (if (null? nodes) '()
>    (let* [(target    (car nodes))
>           (coloring  (assign-colors (remove-node graph target) (delete 
> target nodes) colors))
>           (blocked   (map (cut assq-ref coloring <>) (adjacent graph 
> target)))
>           (available (lset-difference eq? colors blocked))]
>      (cons (cons target (car available)) coloring))))
> (define (coloring graph colors) (assign-colors graph (nodes graph) colors))
> (let [(graph '((b . a) (a . c) (d . c)))] (graphviz graph (coloring graph 
> '(red green blue))))
>
> [1] http://wedesoft.de/graph-coloring.html