Template class implementing a Union-Find algorithm with path compression for maintaining the connected components of a graph.
See Cormen et al. 2nd Edition. MIT Press, 2001. ISBN 0-262-03293-7. Chapter 21: Data structures for Disjoint Sets, pp. 498-524. and Tarjan (1975). Efficiency of a Good But Not Linear Set Union Algorithm. Journal of the ACM 22(2):215-225 It is implemented as a template so that the size of NodeIndex can be chosen depending on the size of the graphs considered. The main interest is that arcs do not need to be kept. Thus the memory complexity is O(n) where n is the number of nodes in the graph. The complexity of this algorithm is O(n . alpha(n)) where alpha(n) is the inverse Ackermann function. alpha(n) <= log(log(log(..log(log(n))..) In practice alpha(n) <= 5. See Tarjan and van Leeuwen (1984). Worst-case analysis of set union algorithms. Journal of the ACM 31(2):245-281.
Usage example: ConnectedComponents<int, int> components; components.Init(num_nodes); for (int arc = 0; arc < num_arcs; ++arc) { components.AddArc(tail[arc], head[arc]); } int num_connected_components = components.GetNumberOfConnectedComponents(); if (num_connected_components == 1) { ///< Graph is completely connected. } ///< Group the nodes in the same connected component together. ///< group[class_number][i] contains the i-th node in group class_number. hash_map<int, std::vector<int> > group(num_connected_components); for (int node = 0; node < num_nodes; ++node) { group[components.GetClassRepresentative(node)].push_back(node); }
Keywords: graph, connected components.
Definition at line 67 of file connectivity.h.
Public Member Functions | |
| ConnectedComponents () | |
| void | Init (NodeIndex num_nodes) |
| Reserves memory for num_nodes and resets the data structures. More... | |
| void | AddArc (NodeIndex tail, NodeIndex head) |
| Adds the information that NodeIndex tail and NodeIndex head are connected. More... | |
| template<typename Graph > | |
| void | AddGraph (const Graph &graph) |
| Adds a complete StarGraph to the object. More... | |
| NodeIndex | CompressPath (NodeIndex node) |
| Compresses the path for node. More... | |
| NodeIndex | GetClassRepresentative (NodeIndex node) |
| Returns the equivalence class representative for node. More... | |
| NodeIndex | GetNumberOfConnectedComponents () |
| Returns the number of connected components. More... | |
| void | MergeClasses (NodeIndex node1, NodeIndex node2) |
| Merges the equivalence classes of node1 and node2. More... | |
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Definition at line 69 of file connectivity.h.
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Adds the information that NodeIndex tail and NodeIndex head are connected.
Definition at line 83 of file connectivity.h.
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Adds a complete StarGraph to the object.
Note that Depth-First Search is a better algorithm for finding connected components on graphs.
Definition at line 95 of file connectivity.h.
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Compresses the path for node.
Definition at line 106 of file connectivity.h.
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Returns the equivalence class representative for node.
Definition at line 123 of file connectivity.h.
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Returns the number of connected components.
Allocates num_nodes_ bits for the computation.
Definition at line 129 of file connectivity.h.
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Reserves memory for num_nodes and resets the data structures.
Definition at line 72 of file connectivity.h.
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Merges the equivalence classes of node1 and node2.
It's faster (~10%) to swap the two values and have a single piece of code for merging the classes.
Definition at line 138 of file connectivity.h.