**3.3 Complexity analysis**

78 Grid Computing – Technology and Applications, Widespread Coverage and New Horizons

to each other will be large and in storing or converting them into their equivalent decimal, a

The solution would be that for storing 0 and 1s, we suppose a threshold number. When a node takes information from its children nodes, including the bitmap, the node first takes the contents of this bitmap then converts the contents of the path position to its equivalent binary number (in the length of counter) and attaches the weight of edge. If the resulted binary number is larger than threshold, this node instead of storing this large number, supposes that the node which this a large number comes from there, is a target node, namely this resource exists in this node, and so stores just the related weight of the edge in the counter, and in fact, the counter in the bitmap starts again. Then this information is sent

Now, when the request reaches one of the nodes and is directed to the target node, a comparison should be made in the target node to identify if the stored number in the target node is 0 and 1, which means the resource is available in this node, otherwise the existing number moves forward of the target node and the above operation again will be performed. Fig. 6, shows this method with threshold = 2 bit, that when the length of bits becomes large in node B from 2 bits, so node B supposes that node C is a target node and stores the address

very large number will result (maybe incomputable).

to the father node and the above operation again will be performed.

of node C in its bitmap, and in fact from node B the counter will start again.

Fig. 6. An example of resource discovery tree with threshold = 2.

Another problem is the large number of the participating nodes and heterogeneity of their available resources. A user may need several resources which may send them in the form of Here, the time and space complexities for our method will be investigated. We suppose that there are n nodes and r resources in the grid environment. Every resource has a attributes and the length of the bitmap would be b bits (Chang & Hu, 2010). Also assume the maximum number of children for a node would be m.
