B
BigBaz
If we have a graph G=(N,E), where N is the set of nodes, and E is the
set of edges. If we partition N into k parts (partition 1, 2,3...k).
And this partition is given by an array, with the node number as the
index. For example, C[x]=a means node x is belongs to partition a.
We define the "Quotient graph" with respect to the above partition as:
A simple graph with no multiple edges. With the set of nodes 1 to K,
and the set of edges (i,j) such that for each each edge (u,v) in E
(the original set of edges in G), there is C=i and C[v]=j.
In English, the quotient graph is a graph with all the K partition
numbers as the edges.
How can I give an algorithm to construct a Quotient Graph from G, with
running time O(size(N)+size(E)).
set of edges. If we partition N into k parts (partition 1, 2,3...k).
And this partition is given by an array, with the node number as the
index. For example, C[x]=a means node x is belongs to partition a.
We define the "Quotient graph" with respect to the above partition as:
A simple graph with no multiple edges. With the set of nodes 1 to K,
and the set of edges (i,j) such that for each each edge (u,v) in E
(the original set of edges in G), there is C=i and C[v]=j.
In English, the quotient graph is a graph with all the K partition
numbers as the edges.
How can I give an algorithm to construct a Quotient Graph from G, with
running time O(size(N)+size(E)).