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| Data.Graph | | Portability | non-portable (requires non-portable module ST) | | Stability | experimental | | Maintainer | libraries@haskell.org |
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| Contents |
- External interface
- Graphs
- Building graphs
- Graph properties
- Algorithms
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| Description |
A version of the graph algorithms described in: Lazy Depth-First Search and Linear Graph Algorithms in Haskell,
by David King and John Launchbury.
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| Synopsis |
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| stronglyConnComp :: (Ord key) => [(node, key, [key])] -> [SCC node] | | | stronglyConnCompR :: (Ord key) => [(node, key, [key])] -> [SCC (node, key, [key])] | | | | | flattenSCC :: SCC vertex -> [vertex] | | | flattenSCCs :: [SCC a] -> [a] | | | type Graph = Table [Vertex] | | | type Table a = Array Vertex a | | | type Bounds = (Vertex, Vertex) | | | type Edge = (Vertex, Vertex) | | | type Vertex = Int | | | graphFromEdges :: (Ord key) => [(node, key, [key])] -> (Graph, Vertex -> (node, key, [key])) | | | buildG :: Bounds -> [Edge] -> Graph | | | transposeG :: Graph -> Graph | | | vertices :: Graph -> [Vertex] | | | edges :: Graph -> [Edge] | | | outdegree :: Graph -> Table Int | | | indegree :: Graph -> Table Int | | | dfs :: Graph -> [Vertex] -> Forest Vertex | | | dff :: Graph -> Forest Vertex | | | topSort :: Graph -> [Vertex] | | | components :: Graph -> Forest Vertex | | | scc :: Graph -> Forest Vertex | | | bcc :: Graph -> Forest [Vertex] | | | reachable :: Graph -> Vertex -> [Vertex] | | | path :: Graph -> Vertex -> Vertex -> Bool | | | module Data.Tree |
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| External interface |
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| stronglyConnComp |
| :: (Ord key) | | | => [(node, key, [key])] | The graph: a list of nodes uniquely identified by keys,
with a list of keys of nodes this node has edges to.
The out-list may contain keys that don't correspond to
nodes of the graph; such edges are ignored. | | -> [SCC node] | | | The strongly connected components of a directed graph, topologically
sorted. |
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| stronglyConnCompR |
| :: (Ord key) | | | => [(node, key, [key])] | The graph: a list of nodes uniquely identified by keys,
with a list of keys of nodes this node has edges to.
The out-list may contain keys that don't correspond to
nodes of the graph; such edges are ignored. | | -> [SCC (node, key, [key])] | Topologically sorted | | The strongly connected components of a directed graph, topologically
sorted. The function is the same as stronglyConnComp, except that
all the information about each node retained.
This interface is used when you expect to apply SCC to
(some of) the result of SCC, so you don't want to lose the
dependency information. |
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| data SCC vertex |
| Strongly connected component. | | Constructors | | AcyclicSCC vertex | A single vertex that is not
in any cycle. | | CyclicSCC [vertex] | A maximal set of mutually
reachable vertices. |
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| flattenSCC :: SCC vertex -> [vertex] |
| The vertices of a strongly connected component. |
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| flattenSCCs :: [SCC a] -> [a] |
| The vertices of a list of strongly connected components. |
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| Graphs |
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| type Graph = Table [Vertex] |
| Adjacency list representation of a graph, mapping each vertex to its
list of successors. |
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| type Table a = Array Vertex a |
| Table indexed by a contiguous set of vertices. |
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| type Bounds = (Vertex, Vertex) |
| The bounds of a Table. |
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| type Edge = (Vertex, Vertex) |
| An edge from the first vertex to the second. |
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| type Vertex = Int |
| Abstract representation of vertices. |
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| Building graphs |
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| graphFromEdges :: (Ord key) => [(node, key, [key])] -> (Graph, Vertex -> (node, key, [key])) |
| Build a graph from a list of nodes uniquely identified by keys,
with a list of keys of nodes this node should have edges to.
The out-list may contain keys that don't correspond to
nodes of the graph; they are ignored. |
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| buildG :: Bounds -> [Edge] -> Graph |
| Build a graph from a list of edges. |
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| transposeG :: Graph -> Graph |
| The graph obtained by reversing all edges. |
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| Graph properties |
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| vertices :: Graph -> [Vertex] |
| All vertices of a graph. |
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| edges :: Graph -> [Edge] |
| All edges of a graph. |
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| outdegree :: Graph -> Table Int |
| A table of the count of edges from each node. |
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| indegree :: Graph -> Table Int |
| A table of the count of edges into each node. |
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| Algorithms |
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| dfs :: Graph -> [Vertex] -> Forest Vertex |
| A spanning forest of the part of the graph reachable from the listed
vertices, obtained from a depth-first search of the graph starting at
each of the listed vertices in order. |
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| dff :: Graph -> Forest Vertex |
| A spanning forest of the graph, obtained from a depth-first search of
the graph starting from each vertex in an unspecified order. |
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| topSort :: Graph -> [Vertex] |
| A topological sort of the graph.
The order is partially specified by the condition that a vertex i
precedes j whenever j is reachable from i but not vice versa. |
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| components :: Graph -> Forest Vertex |
| The connected components of a graph.
Two vertices are connected if there is a path between them, traversing
edges in either direction. |
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| scc :: Graph -> Forest Vertex |
| The strongly connected components of a graph. |
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| bcc :: Graph -> Forest [Vertex] |
| The biconnected components of a graph.
An undirected graph is biconnected if the deletion of any vertex
leaves it connected. |
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| reachable :: Graph -> Vertex -> [Vertex] |
| A list of vertices reachable from a given vertex. |
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| path :: Graph -> Vertex -> Vertex -> Bool |
| Is the second vertex reachable from the first? |
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| module Data.Tree |
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| Produced by Haddock version 0.4 |
