Diagnosis of S.aureus mastitis can be done by direct milk culture for detection of bacteria as well as some indirect test like MCMT
, gram staining for detection of gram positive staphylococcus colony and leukococytosis in hematological examination (Boerlin et al., 2003; Tenhagen et al., 2009).
Multi Constraint Multicast Tree Problem (MCMT): The Multi Constraint Multicast Tree Problem is given below:- The graph G = <[??], [??]> represents a mesh network with the above described Delay, Cost and Congestion Optimization goal.
An optimal MCMT is a tree originated at s that covers the destinations set S and the total delays along the route between the source s and every destination v [member of] S is restricted and is not exceeded by D and sum total of the cost over the links in the tree spanning the destinations is minimum and such that each edge used must satisfies the congestion constraint described above.
The above MCMT is NP-complete but here we have written heuristic algorithm to construct a solution which is approximately optimal and is built on approximation algorithm of Steiner tree by Berman, Kou, and Markowsy.
The above KMB algorithm does not essentially yield a MCMT. But, we have added constraints at every step which guarantee that it produces an MCMT.
Prior to the description of the MCMT algorithm shortest constrained path (SCP) between two nodes need to be defined.
Below we have describe MCMT algorithm and applied on the identical graph as in figure-1.
To determine the average case performance of MCMT algorithm is ran on a number of graphs generated randomly.
where [X.sub.j] = cost of MCMT in jth run and [O.sub.j] = cost of Optimal Tree in jth run