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Module type Sig_pack.S

module type S = sig .. end

Signature gathering an imperative graph signature and all algorithms. Vertices and edges are labeled with integers.

Graph structure

type t

abstract type of graphs

module V: sig .. end

Vertices

type vertex = V.t 
module E: sig .. end

Edges

type edge = E.t 
val is_directed : bool

is this an implementation of directed graphs?

Graph constructors and destructors

val create : ?size:int -> unit -> t

Return an empty graph. Optionally, a size can be given, which should be on the order of the expected number of vertices that will be in the graph (for hash tables-based implementations). The graph grows as needed, so size is just an initial guess.

val clear : t -> unit

Remove all vertices and edges from the given graph.

val copy : t -> t

copy g returns a copy of g. Vertices and edges (and eventually marks, see module Mark) are duplicated.

val add_vertex : t -> V.t -> unit

add_vertex g v adds the vertex v from the graph g. Do nothing if v is already in g.

val remove_vertex : t -> V.t -> unit

remove g v removes the vertex v from the graph g (and all the edges going from v in g). Do nothing if v is not in g.

val add_edge : t -> V.t -> V.t -> unit

add_edge g v1 v2 adds an edge from the vertex v1 to the vertex v2 in the graph g. Add also v1 (resp. v2) in g if v1 (resp. v2) is not in g. Do nothing if this edge is already in g.

val add_edge_e : t -> E.t -> unit

add_edge_e g e adds the edge e in the graph g. Add also E.src e (resp. E.dst e) in g if E.src e (resp. E.dst e) is not in g. Do nothing if e is already in g.

val remove_edge : t -> V.t -> V.t -> unit

remove_edge g v1 v2 removes the edge going from v1 to v2 from the graph g. Do nothing if this edge is not in g.

val remove_edge_e : t -> E.t -> unit

remove_edge_e g e removes the edge e from the graph g. Do nothing if e is not in g.

module Mark: sig .. end

Vertices contains integers marks, which can be set or used by some algorithms (see for instance module Marking below)

Size functions

val is_empty : t -> bool
val nb_vertex : t -> int
val nb_edges : t -> int

Degree of a vertex

val out_degree : t -> V.t -> int

out_degree g v returns the out-degree of v in g.

val in_degree : t -> V.t -> int

in_degree g v returns the in-degree of v in g.

Membership functions

val mem_vertex : t -> V.t -> bool
val mem_edge : t -> V.t -> V.t -> bool
val mem_edge_e : t -> E.t -> bool
val find_edge : t -> V.t -> V.t -> E.t
val find_all_edges : t -> V.t -> V.t -> E.t list

Successors and predecessors of a vertex

val succ : t -> V.t -> V.t list

succ g v returns the successors of v in g.

val pred : t -> V.t -> V.t list

pred g v returns the predecessors of v in g.

Labeled edges going from/to a vertex

val succ_e : t -> V.t -> E.t list

succ_e g v returns the edges going from v in g.

val pred_e : t -> V.t -> E.t list

pred_e g v returns the edges going to v in g.

Graph iterators

iter/fold on all vertices/edges of a graph

val iter_vertex : (V.t -> unit) -> t -> unit
val iter_edges : (V.t -> V.t -> unit) -> t -> unit
val fold_vertex : (V.t -> 'a -> 'a) -> t -> 'a -> 'a
val fold_edges : (V.t -> V.t -> 'a -> 'a) -> t -> 'a -> 'a
val map_vertex : (V.t -> V.t) -> t -> t

map iterator on vertex

iter/fold on all labeled edges of a graph

val iter_edges_e : (E.t -> unit) -> t -> unit
val fold_edges_e : (E.t -> 'a -> 'a) -> t -> 'a -> 'a

Vertex iterators

Each iterator iterator f v g iters f to the successors/predecessors of v in the graph g and raises Invalid_argument if v is not in g.

iter/fold on all successors/predecessors of a vertex.

val iter_succ : (V.t -> unit) -> t -> V.t -> unit
val iter_pred : (V.t -> unit) -> t -> V.t -> unit
val fold_succ : (V.t -> 'a -> 'a) -> t -> V.t -> 'a -> 'a
val fold_pred : (V.t -> 'a -> 'a) -> t -> V.t -> 'a -> 'a

iter/fold on all edges going from/to a vertex.

val iter_succ_e : (E.t -> unit) -> t -> V.t -> unit
val fold_succ_e : (E.t -> 'a -> 'a) -> t -> V.t -> 'a -> 'a
val iter_pred_e : (E.t -> unit) -> t -> V.t -> unit
val fold_pred_e : (E.t -> 'a -> 'a) -> t -> V.t -> 'a -> 'a

Basic operations

val find_vertex : t -> int -> V.t

vertex g i returns a vertex of label i in g. The behaviour is unspecified if g has several vertices with label i. Note: this function is inefficient (linear in the number of vertices); you should better keep the vertices as long as you create them.

val transitive_closure : ?reflexive:bool -> t -> t

transitive_closure ?reflexive g returns the transitive closure of g (as a new graph). Loops (i.e. edges from a vertex to itself) are added only if reflexive is true (default is false).

val add_transitive_closure : ?reflexive:bool -> t -> t

add_transitive_closure ?reflexive g replaces g by its transitive closure. Meaningless for persistent implementations (then acts as transitive_closure).

val transitive_reduction : ?reflexive:bool -> t -> t

transitive_reduction ?reflexive g returns the transitive reduction of g (as a new graph). Loops (i.e. edges from a vertex to itself) are removed only if reflexive is true (default is false).

val replace_by_transitive_reduction : ?reflexive:bool -> t -> t

replace_by_transitive_reduction ?reflexive g replaces g by its transitive reduction. Meaningless for persistent implementations (then acts as transitive_reduction).

val mirror : t -> t

mirror g returns a new graph which is the mirror image of g: each edge from u to v has been replaced by an edge from v to u. For undirected graphs, it simply returns a copy of g.

val complement : t -> t

complement g builds a new graph which is the complement of g: each edge present in g is not present in the resulting graph and vice-versa. Edges of the returned graph are unlabeled.

val intersect : t -> t -> t

intersect g1 g2 returns a new graph which is the intersection of g1 and g2: each vertex and edge present in g1 *and* g2 is present in the resulting graph.

val union : t -> t -> t

union g1 g2 returns a new graph which is the union of g1 and g2: each vertex and edge present in g1 *or* g2 is present in the resulting graph.

Traversal

module Dfs: sig .. end

Depth-first search

module Bfs: sig .. end

Breadth-first search

module Marking: sig .. end

Graph traversal with marking

Graph generators

module Classic: sig .. end

Classic graphs

module Rand: sig .. end

Random graphs

module Components: sig .. end

Strongly connected components

Classical algorithms

val shortest_path : t -> V.t -> V.t -> E.t list * int

Dijkstra's shortest path algorithm. Weights are the labels.

val ford_fulkerson : t ->
       V.t -> V.t -> (E.t -> int) * int

Ford Fulkerson maximum flow algorithm

val goldberg_tarjan : t ->
       V.t -> V.t -> (E.t -> int) * int

Goldberg-Tarjan maximum flow algorithm

val bellman_ford : t -> V.t -> E.t list

bellman_ford g v finds a negative cycle from v, and returns it, or raises Not_found if there is no such cycle

module PathCheck: sig .. end

Path checking

module Topological: sig .. end

Topological order

val spanningtree : t -> E.t list

Kruskal algorithm

Input / Output

val dot_output : t -> string -> unit

DOT output in a file

val display_with_gv : t -> unit

Displays the given graph using the external tools "dot" and "gv" and returns when gv's window is closed

val parse_gml_file : string -> t
val parse_dot_file : string -> t
val print_gml : Stdlib.Format.formatter -> t -> unit
val print_gml_file : t -> string -> unit