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connection is requested and then the working tree for the request is established. Working tree
can be divided into some un-overlapped working segments and the backup segments are
allocated to working segments. Costs of links are computed and then wavelength capacity is
allocated/reserved for requested multicast connection. When a link fails in the network, the
newly re-provisioned working segment and backup segment should be provided for working
segments and for their corresponding backup segments that the failed link passes through
them. For this purpose, the traffic of the primary working segments and backup segments
should be restored and then their wavelength resources are released. Link-cost of each
primary backup segment is computed and then a newly re-provisioned working segment with
the minimum cost is computed. After allocating a wavelength to these segments, traffic is
reverted from the primary backup segments to the newly re-provisioned working segment.
For each failed primary backup segment, the least cost of the newly re-provisioned working
segment is computed under link-disjoint constraint and then a new wavelength capacity is
reserved for the newly re-provisioned backup segment. Finally, network state is updated.
Note that both the MPH and the Dijkstra's algorithms are used in the SSPR algorithm in order
to find minimum cost and shortest path parameters. The simulation results in  show that
the blocking probability of SSPR is lower than the link shared protection and the path-pair
4.6. Sparse Splitting Constrained Multicast Protection (SSMP) 
The wavelength channels can be shared with the primary tree in sparse splitting by SSMP
algorithm and then the wavelength resources utilized by the multicast session are minimized.
In this approach there are some definitions as follows:
Physical layer : is used to map the network state and topology .
Physical edges : each undirected link ( x,y ) in the physical network corresponding to
physical edges( x p ,y p ) and ( y p , x p ) in the physical layer of an auxiliary graph ( AG )
Sharing layer : is used to represent the primary wavelength channels that can be
shared by backup paths .
Sharing edge : It can be further divided into forward sharing ( FS ) edges and reversed
sharing ( RS ) edges. For each edge ( x,y ) in a light tree, there is a FS edge from x s to y s
in the sharing layer of AG . For each MC node (or leaf node) u on the light tree, there
is an RS edge from node u s to node v s , where v s is the parent MC node of node u on
the light tree. The parent MC node of node u is defined as the nearest upstream MC
node to u on the light tree .
Adding and dropping edges : for each node x in the physical network, there is an
adding edge from node x p to x s in auxiliary graph. For each MC node u on the light
tree, there is a dropping edge from node u s to u p in the auxiliary graph .
The SSMP is applied to find the backup paths for each light forest, where a light forest is
formed from multiple light trees with the sparse splitting and wavelength continuity
constraints . The SSMP algorithm is run in two phases: