Graph coloring with Scheme

[Jan Wedekind <jan@wedesoft.de>]

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