## graph-separators

Determine the separation vertices of a graph.

## Documentation

A graph is said to have a separation vertex `v` (sometimes called an articulation point) if there exist vertices `a` and `b`, where `a != b` and `b != v`, and all paths connecting `a` and `b` pass through `v`. A graph which has a separation vertex is called separable, and one which has none is called non-separable.

### Procedures

*[procedure]*

`graph-separation-vertices:: G -> SEPARATORS * COMPONENTS`

Computes the separation vertices of the given graph. Returns a list of separation vertices and a list of graph components that contain a separation vertex.

## Examples

(import scheme (chicken base)srfi-1 digraph graph-separators) (define g (make-digraph 'depgraph "dependency graph")) (define used-by (list (cons 'dax_h 'foo_cpp) (cons 'def_h 'foo_cpp) (cons 'xyz_h 'foo_cpp) (cons 'foo_cpp 'libfoobar_a ) (cons 'foo_cpp 'libzigzag_a) (cons 'libfoobar_a 'app) (cons 'libzigzag_a 'app) )) (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) (add-node! g 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)))) (add-edge! g (list i j (format "~A->~A" ni nj))))) (else (error "invalid edge " e)))) used-by) (graph-separation-vertices g)

## About this egg

### Author

Richard Kelsey; ported to Chicken by Ivan Raikov

### Version history

- 2.0
- Ported to Chicken 5
- 1.4
- Documentation converted to wiki format
- 1.3
- Ported to Chicken 4
- 1.0
- Initial release

### License

Copyright by Richard Kelsey. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: - Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. - Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. - Neither name of the copyright holders nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND THE CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDERS OR THE CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.