Up

# modulePath

: sig

Paths

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module type G = sig

Minimal graph signature for Dijkstra's algorithm. Sub-signature of Sig.G.

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type t
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module V : Sig.COMPARABLE
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module E : sig
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type t
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type label
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val label : t -> label
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val src : t -> V.t
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val dst : t -> V.t
end
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val iter_vertex : (V.t -> unit) -> t -> unit
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val iter_succ : (V.t -> unit) -> t -> V.t -> unit
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val iter_succ_e : (E.t -> unit) -> t -> V.t -> unit
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val fold_edges_e : (E.t -> 'a -> 'a) -> t -> 'a -> 'a
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val nb_vertex : t -> int
end
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module type WEIGHT = sig

Signature for edges' weights.

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type label

Type for labels of graph edges.

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type t

Type of edges' weights.

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val weight : label -> t

Get the weight of an edge.

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val compare : t -> t -> int

Weights must be ordered.

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val add : t -> t -> t

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val zero : t

end
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module Dijkstra : functor (G : G) -> functor (W : WEIGHT with type label = G.E.label) -> sig
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val shortest_path : G.t -> G.V.t -> G.V.t -> G.E.t list * W.t

`shortest_path g v1 v2` computes the shortest path from vertex `v1` to vertex `v2` in graph `g`. The path is returned as the list of followed edges, together with the total length of the path. raise `Not_found` if the path from `v1` to `v2` does not exist.

Complexity: at most O((V+E)log(V))

end
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module BellmanFord : functor (G : G) -> functor (W : WEIGHT with type label = G.E.label) -> sig
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module H : Hashtbl.S with type key = G.V.t
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exception NegativeCycle of G.E.t list
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val all_shortest_paths : G.t -> G.V.t -> W.t H.t

`shortest_path g vs` computes the distances of shortest paths from vertex `vs` to all other vertices in graph `g`. They are returned as a hash table mapping each vertex reachable from `vs` to its distance from `vs`. If `g` contains a negative-length cycle reachable from `vs`, raises `NegativeCycle l` where `l` is such a cycle.

Complexity: at most O(VE)

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val find_negative_cycle_from : G.t -> G.V.t -> G.E.t list

`find_negative_cycle_from g vs` looks for a negative-length cycle in graph `g` that is reachable from vertex `vs` and returns it as a list of edges. If no such a cycle exists, raises `Not_found`.

Complexity: at most O(VE).

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val find_negative_cycle : G.t -> G.E.t list

`find_negative_cycle g` looks for a negative-length cycle in graph `g` and returns it. If the graph `g` is free from such a cycle, raises `Not_found`.

Complexity: O(V^2E)

end
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module Check : functor (G : sig
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type t
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module V : Sig.COMPARABLE
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val iter_succ : (V.t -> unit) -> t -> V.t -> unit
end
) -> sig

Check for a path.

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type path_checker

the abstract data type of a path checker; this is a mutable data structure

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val create : G.t -> path_checker

`create g` builds a new path checker for the graph `g`; if the graph is mutable, it must not be mutated while this path checker is in use (through the function `check_path` below).

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val check_path : path_checker -> G.V.t -> G.V.t -> bool

`check_path pc v1 v2` checks whether there is a path from `v1` to `v2` in the graph associated to the path checker `pc`.

Complexity: The path checker contains a cache of all results computed so far. This cache is implemented with a hash table so access in this cache is usually O(1). When the result is not in the cache, Dijkstra's algorithm is run to check for the path, and all intermediate results are cached.

Note: if checks are to be done for almost all pairs of vertices, it may be more efficient to compute the transitive closure of the graph (see module `Oper`).

end
end