To make a better utilization of the connectivity between virtual nodes, the BFS algorithm is introduced to sort virtual nodes in [14, 19], which is testified to help decrease the path length in link embedding stage.
To deal with the resource fragmentation in substrate network during VN embedding, Qi et al.
In this section, the network model and evaluation indications of VN embedding problem are formulated and elaborated.
Virtual Network Embedding the VN embedding is defined as an embedding action M from [G.sub.v] to a subset of [G.sub.s], which can be denoted as M : [G.sub.v] [right arrow] ([N.sup.sub.sub.s], [L.sup.sub.sub.s], [R.sub.n], [R.sub.L]), where [N.sup.sub.sub.s] [member of] [n.sub.s], [L.sup.sub.sub.s] [member of] [L.sub.s], [R.sub.N] and [R.sub.L] denote the CPU and bandwidth resource of SN that allocated to the VN request.
For two-stage embedding algorithm: the node embedding stage is denoted as [M.sup.N] :([N.sub.v], [A.sup.N.sub.v]) [right arrow] ([N.sup.sub.sub.s], [R.sub.N]); the link embedding stage is denoted as [M.sup.L] :([L.sub.v], [A.sup.L.sub.v]) [right arrow] ([L.sup.sub.sub.s], [R.sub.L]).
Note that every vertex of T, distinct from the root, is incident to at most one convex hull edge in the embedding. Since the first child of the root is not a leaf, no convex hull edge is used to embed this child.
The leaf adjacent to the root can no longer be a convex hull edge and the embedding uses less than n/2 convex hull edges.
Proof: Let [f.sub.0] be an embedding given by Lemma 2.2, of T into G.
Lemma 3.2 If G is a convex geometric graph, then forbidding three consecutive convex hull edges of G forbids the embedding of [T.sub.n].
Note that by Lemma 3.1, in any embedding of [T.sub.n] into G, an edge incident to a leaf of [T.sub.n], must be embedded into a convex hull edge.
At last we conduct watermark embedding for the front pixel blocks according to the information amount to be embedded.
In order to improve the visual quality of the image without reducing the embedding capacity, the difference expansion algorithm is improved in this paper.
In this way, the process of the watermark embedding of a sub-block is accomplished.
In addition, the maximum embedding capacity of this method in a 4 x 4 sub-block is 16-digit watermark, which can embed one-digit more watermark information than the generalized differential expansion watermark algorithm.
That is to say the watermark embedding operation of the image block is completed.