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## graph-dominators

Find immediate dominators in a directed graph.

## Usage

(require-extension graph-dominators)

## Documentation

In a control-flow graph (CFG), block M dominates block N if every path from the entry that reaches block N has to pass through block M. The entry block dominates all blocks.

Block M immediately dominates block N if M dominates N, and there is no intervening block P such that M dominates P and P dominates N. In other words, M is the last dominator on any path from entry to N. Each block has a unique immediate dominator, if it has any at all.

This fast dominator code is based upon Lengauer and Tarjan, A Fast Algorithm for Finding Dominators in a Flowgraph, ACM TOPLAS 1:1, pp. 121--141, July 1979. It runs in time O(|E|\log|V|), where |E|is the number of edges and |V| is the number of vertices. A smaller time bound of O(|E|\alpha(|E|,|V|)), where alpha is the inverse of Ackerman's function, can be achieved with more complex versions of the internal link! and eval! procedures.

### Procedures

[procedure] graph-find-dominators-quickly!:: G -> UNDEFINED

Computes the dominator tree of the given rooted, directed graph. When done, the meta-data field of each node will contain its immediate dominator. It assumes that the meta-data slot for each node contains a list, and modifies the car of that list. Requires that the list initially contain #f as its car value.

[procedure] graph-find-dominators-slowly!:: G -> UNDEFINED

The fast dominator algorithm is difficult to prove correct, so this procedure is provided in order to check its results. The slow algorithm, which runs in time O(|E||V|), is adapted from Aho and Ullman, The Theory of Parsing, Translation, and Compiling, Prentice-Hall, 1973, p. 916.

## Examples

;; example adapted from graph example in the Boost library documentation
(require-extension srfi-1)
(require-extension digraph)
(require-extension graph-dominators)

(define g (make-digraph 'depgraph "dependency graph"))

(define used-by
(list
(cons 'dax_h 'foo_cpp) (cons 'dax_h 'bar_cpp) (cons 'dax_h 'yow_h)
(cons 'yow_h 'bar_cpp) (cons 'yow_h 'zag_cpp) (cons 'boz_h 'bar_cpp)
(cons 'boz_h 'zig_cpp) (cons 'boz_h 'zag_cpp)
(cons 'foo_cpp 'foo_o) (cons 'foo_o 'libfoobar_a)
(cons 'bar_cpp 'bar_o) (cons 'bar_o 'libfoobar_a)
(cons 'libfoobar_a 'libzigzag_a)  (cons 'zig_cpp 'zig_o)
(cons 'zig_o 'libzigzag_a) (cons 'libfoobar_a 'dax_h) (cons 'zag_cpp 'zag_o)
(cons 'zag_o 'libzigzag_a) (cons 'libzigzag_a 'killerapp)))

(define node-list (delete-duplicates
(concatenate (list (map car used-by) (map cdr used-by)))))

(define node-ids (list-tabulate (length node-list) values))

(for-each (lambda (i n) ((g 'add-node!) i (list #f n))) node-ids node-list)
(define node-map (zip node-list node-ids))

(for-each (lambda (e)
(match e ((ni . nj) (let ((i (car (alist-ref ni node-map)))
(j (car (alist-ref nj node-map))))
((g 'add-edge!) (list i j (format "~A->~A" ni nj)))))
(else (error "invalid edge " e))))
used-by)

(graph-find-dominators-quickly! g)



### Author

Richard Kelsey; ported to Chicken by Ivan Raikov

### Version history

1.5
Documentation converted to wiki format
1.4
Added matchable to list of required eggs
1.3
Ported to Chicken 4
1.0
Initial release

Copyright by Richard Kelsey.

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