module Flow

: sig

Algorithms on flows

The following flow algorithms only apply to networks, that are directed graphs together with a source (a 0 in-degree vertex) and a terminal (a 0 out-degree vertex).

Maximum flow algorithms

module type FLOW = sig

Signature for edges' flow.

type t

Type of edges.

type label

Type of labels on edges.

Maximum and minimum capacities for a label on an edge.

val max_capacity : label -> t

val min_capacity : label -> t

Current flow for a label on an edge.

val flow : label -> t

+ and - on flows.

val add : t -> t -> t

val sub : t -> t -> t

Neutral element for add and sub.

val zero : t

A total ordering over flows.

val compare : t -> t -> int

end

Goldberg maximal flow algorithm

module type G_GOLDBERG = sig

Minimal graph signature for Goldberg. Sub-signature of Sig.G.

type t

module V : Sig.COMPARABLE

module E : Sig.EDGE with type vertex = V.t

val nb_vertex : t -> int

val iter_vertex : (V.t -> unit) -> t -> unit

val iter_edges_e : (E.t -> unit) -> t -> unit

val fold_succ_e : (E.t -> 'a -> 'a) -> t -> V.t -> 'a -> 'a

val fold_pred_e : (E.t -> 'a -> 'a) -> t -> V.t -> 'a -> 'a

end

module Goldberg : functor (G : G_GOLDBERG) -> functor (F : FLOW with type label = G.E.label) -> sig

val maxflow : G.t -> G.V.t -> G.V.t -> (G.E.t -> F.t) * F.t

maxflow g v1 v2 searchs the maximal flow from source v1 to terminal v2 using the Goldberg algorithm. It returns the new flows on each edges and the growth of the flow.

end

Ford-Fulkerson maximal flow algorithm

module type G_FORD_FULKERSON = sig

Minimal digraph signature for Ford-Fulkerson. Sub-signature of Sig.G.

type t

module V : Sig.HASHABLE

module E : sig

type t

type label

val src : t -> V.t

val dst : t -> V.t

val label : t -> label

end

val iter_succ_e : (E.t -> unit) -> t -> V.t -> unit

val iter_pred_e : (E.t -> unit) -> t -> V.t -> unit

end

module Ford_Fulkerson : functor (G : G_FORD_FULKERSON) -> functor (F : FLOW with type label = G.E.label) -> sig

val maxflow : G.t -> G.V.t -> G.V.t -> (G.E.t -> F.t) * F.t

maxflow g v1 v2 searchs the maximal flow from source v1 to terminal v2 using the Ford-Fulkerson algorithm. It returns the new flows on each edges and the growth of the flow.

end