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669bb81f08
maxflow.c. Also in this checkin, fixes to the OS X and GTK back ends to get ALIGN_VNORMAL right. This is the first time I've used it! :-) [originally from svn r6390]
96 lines
3.6 KiB
C
96 lines
3.6 KiB
C
/*
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* Edmonds-Karp algorithm for finding a maximum flow and minimum
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* cut in a network. Almost identical to the Ford-Fulkerson
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* algorithm, but apparently using breadth-first search to find the
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* _shortest_ augmenting path is a good way to guarantee
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* termination and ensure the time complexity is not dependent on
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* the actual value of the maximum flow. I don't understand why
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* that should be, but it's claimed on the Internet that it's been
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* proved, and that's good enough for me. I prefer BFS to DFS
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* anyway :-)
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*/
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#ifndef MAXFLOW_MAXFLOW_H
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#define MAXFLOW_MAXFLOW_H
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/*
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* The actual algorithm.
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*
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* Inputs:
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*
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* - `scratch' is previously allocated scratch space of a size
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* previously determined by calling `maxflow_scratch_size'.
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*
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* - `nv' is the number of vertices. Vertices are assumed to be
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* numbered from 0 to nv-1.
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*
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* - `source' and `sink' are the distinguished source and sink
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* vertices.
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*
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* - `ne' is the number of edges in the graph.
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*
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* - `edges' is an array of 2*ne integers, giving a (source, dest)
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* pair for each network edge. Edge pairs are expected to be
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* sorted in lexicographic order.
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*
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* - `backedges' is an array of `ne' integers, each a distinct
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* index into `edges'. The edges in `edges', if permuted as
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* specified by this array, should end up sorted in the _other_
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* lexicographic order, i.e. dest taking priority over source.
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*
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* - `capacity' is an array of `ne' integers, giving a maximum
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* flow capacity for each edge. A negative value is taken to
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* indicate unlimited capacity on that edge, but note that there
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* may not be any unlimited-capacity _path_ from source to sink
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* or an assertion will be failed.
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*
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* Output:
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*
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* - `flow' must be non-NULL. It is an array of `ne' integers,
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* each giving the final flow along each edge.
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*
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* - `cut' may be NULL. If non-NULL, it is an array of `nv'
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* integers, which will be set to zero or one on output, in such
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* a way that:
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* + the set of zero vertices includes the source
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* + the set of one vertices includes the sink
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* + the maximum flow capacity between the zero and one vertex
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* sets is achieved (i.e. all edges from a zero vertex to a
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* one vertex are at full capacity, while all edges from a
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* one vertex to a zero vertex have no flow at all).
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*
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* - the returned value from the function is the total flow
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* achieved.
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*/
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int maxflow_with_scratch(void *scratch, int nv, int source, int sink,
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int ne, const int *edges, const int *backedges,
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const int *capacity, int *flow, int *cut);
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/*
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* The above function expects its `scratch' and `backedges'
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* parameters to have already been set up. This allows you to set
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* them up once and use them in multiple invocates of the
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* algorithm. Now I provide functions to actually do the setting
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* up.
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*/
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int maxflow_scratch_size(int nv);
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void maxflow_setup_backedges(int ne, const int *edges, int *backedges);
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/*
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* Simplified version of the above function. All parameters are the
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* same, except that `scratch' and `backedges' are constructed
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* internally. This is the simplest way to call the algorithm as a
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* one-off; however, if you need to call it multiple times on the
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* same network, it is probably better to call the above version
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* directly so that you only construct `scratch' and `backedges'
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* once.
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*
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* Additional return value is now -1, meaning that scratch space
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* could not be allocated.
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*/
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int maxflow(int nv, int source, int sink,
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int ne, const int *edges, const int *capacity,
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int *flow, int *cut);
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#endif /* MAXFLOW_MAXFLOW_H */
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