Multicasting is a technique of communication that allows transmit information to multiple destination hosts at the same time. With the development of the high-performance network technology, such as video on demand, teleconferencing, online education and the increasingly widespread use of many other real-time multimedia applications, multicast technology is becoming the key to support these technologies. While the multicast routing algorithm is one of the key technologies to achieve multicast communication, to build a good performance multicast tree often become the best choice for multicast routing algorithm. Good multicast routing algorithms are often able to minimize network cost in a short time and meet certain QoS constraints so that we can make use of network resources efficiently. Because real-time multimedia applications’ demand for delay is growing higher, so the research on multicast routing algorithm that not only can meet the end to end delay constraint, but also can optimize the network resources is very important, and it is also a hot research topic [1].

From global point of view, optimize network resources can be seen as optimize a multicast routing tree’s total cost, finding a minimum cost multicast routing tree can be formalized as Steiner tree problem. As Steiner tree problem is NP-hard problem [2], so that many scholars have proposed heuristic algorithm to compute standardSteiner tree, the most typical is the MPH algorithm [3]. Besides, the KPP algorithm in literature [4] and BSMA algorithm in literature [5] are able to produce a high performance multicast tree, however, due to the excessive calculation, it is difficult to be applied in practice. Although the calculation of CDKS algorithm proposed by literature [6] is much lower than the previous two algorithms, the cost of the spanning tree is too high. So the literature [7] proposed a algorithm named ESAMPH, this algorithm is based on the basic idea of MPH algorithm to construct a multicast tree, compared with other similar algorithms, it takes full advantage of the shared edges to reduce the cost of the spanning tree, it can get a better balance among consideration, delay and computational complexity, it has a better comprehensive performance. However, the algorithm may chose those who do not satisfy the limit but less costly path add to the spanning tree when selects the next destination node which to be added. So, this paper combines the advantages of MPH multicast in generate multicast tree and the performance of CDKS algorithm on compute time, based on the algorithm of ESAMPH, proposed an improved multicast routing algorithm, named ESAMPH_D.

Generally, we formalized the network as an empowerment undirected graph, in which is the set of nodes of the graph, each node represents a host or a router. is the set of edges in graph and represents the number of edges (or links) of the set. represents the number of nodes in graph and. is the source node, represents the set of destination nodes. Suppose that is the set of trees that rooted with s and ended with, represents the path that from the source node to node in tree.

We defines two functions on each edge, cost function and delay function (represents a positive real number set in these functions). Here, the cost can be seen as the price of use the link or the measure of some resources on network, the delay is the total delay when a packet get through the link, including queuing delay, sending delay and transmission delay.

In the real transmission problems, it often demand to minimum the cost while meet the certain requirements of the delay constraint at the same time. So, we can get the model of the problem like this:

Here, is a positive real number, it presents the end to end delay constraint.

In this simulation experiment part, we use the random graphs to verification the effectiveness and correctness of the improved algorithm, and the random graphs used in the simulation are constructed using the method proposed by Waxman [8,9]. The nodes of a graph are randomly placed on a Cartesian coordinate grid with unit spacing, considering all possible pairs of node, edges are placed with probability like:

where is the Manhattan distance between nodes and, L is the maximum possible distance between two nodes, and are in the range and can be selected to obtain desired characteristics in the graph. Here, we choose and.

Figure 1 shows the relationship between the multicast tree cost and the number of network nodes: make the number of the destination nodes maintaining 20, then change the number of network nodes from 40 to 100, the increments is 10 each time. We can see that the cost of the multicast tree is lower when using the ESAMPH_D algorithm.

Figure 2 shows the relationship between the multicast tree cost and the number of destination nodes: make the number of the network nodes maintaining 160, then change the number of destination nodes from 20 to 80, the increments is 10 each time. We can see that using ESAMPH_D is better than ESAMPH algorithm in generating the multicast tree.

Figure 3 shows the relationship between the multicast

tree cost and the delay constraint: make the other conditions remaining, change the delay constraint from 5 to 30, the increments is 5 each time. We can see that the cost of the multicast tree is lower when using the ESAMPH_D algorithm at the same delay constraint condition.

This paper proposed the ESAMPH_D algorithm based on the weak point of ESAMPH algorithm, the improved algorithm did not add any extra cost in space or time when generating the low-cost multicast tree, so it ensuring the availability of the algorithm in practical application.