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Installation

This package uses ASDF. The easiest way to use this is via Quicklisp.

To use, clone this repository and link it from your local ~/quicklisp/local-projects/, for example:

$ cd ~/quicklisp/local-projects/
$ git clone https://github.com/fcbr/graph-algorithms.git
[...]
$ sbcl
* (ql:quickload "graph-algorithms")
To load "graph-algorithms":
  Load 1 ASDF system:
    graph-algorithms
; Loading "graph-algorithms"

("graph-algorithms")
*

See the unit tests for sample usage of each of the defined methods.

Testing

This package uses FiveAM for unit tests.

You can use the package graph-algorithms/tests for unit tests. Sample usage:

$ sbcl
* (require :graph-algorithms/tests)
* (graph-algorithms/tests::test-graph-algorithms)

Running test suite ALL-TESTS
 Running test BFS .
 Running test DEGREES .....
 Running test DIJKSTRA ...
 Running test MAXIMAL-CLIQUES .
 Running test STRONGLY-CONNECTED-COMPONENTS .
 Running test CONNECTED-COMPONENTS .
 Did 12 checks.
    Pass: 12 (100%)
    Skip: 0 ( 0%)
    Fail: 0 ( 0%)

Documentation

Degrees of vertices

(degrees vertices neighbors-fn)

Given a list of VERTICES and a NEIGHBOR-FN function, returns two functions: one that gives the in degree of a vertex and another that gives the out degree of a vertex.

Breadth first search

(breadth-first-search source neighbors-fn visitor-fn)

Performs a breadth-first-search on the graph. SOURCE is the vertex used as the start of the search. NEIGHBORS-FN should return a list of immediate neighbor vertices of a given vertex. VISITOR-FN is called on each new vertex found by the search.

Connected components

(connected-components vertices neighbors-fn visitor-fn)

VERTICES is the list of vertices of the graph. NEIGHBORS-FN should return a list of immediate neighbor vertices of a given vertex. VISITOR-FN is called once for each representative vertex of found components.

Shortest paths

(shortest-paths source vertices neighbors-fn)

Dijkstra's shortest patha algorithm. All reachable vertices from SOURCE are computed. Returns DIST and PREV hash tables. As in the other methods, NEIGHBORS-FN is a function that receives a vertex and returns its neighbors as a list of vertices. Note that this implementation does not consider weighted edges yet.

(reconstruct-path prev target)

Given the PREV hash table returned by DIJKSTRA, reconstruct the path from the original source vertex to TARGET.

Strongly connected components

(strongly-connected-components vertices neighbors-fn visitor-fn)

Tarjan's strongly connected components algorithm. VERTICES is the list of vertices of the graph. NEIGHBORS-FN should return a list of immediate neighbor vertices of a given vertex. VISITOR-FN is called once for each SCC found.

Maximal cliques

(maximal-cliques vertices neighbors-fn visitor-fn)

Implementation of the Bron–Kerbosch algorithm for finding maximal cliques in an undirected graph, without pivoting.

Sample usage

Your graph can be in any format or data structure as you want, as long as you provide a function to access the neighbors of a vertex. For convenience sake, this sample uses property lists as the data structure, where each vertex has an associated list of neighbours. This way, we can use Common Lisp's GETF accessor as the neighbor function.

(defun sample-bfs ()
  (let ((graph
          '(:a (:b :c)
            :b (:d)
            :c (:f))))
    (bfs :a
         (lambda (n) (getf graph n))
         (lambda (n) (print n)))))

Sample call with output for the following graph:

graph

* (sample-bfs)

:A
:B
:C
:D
:F