Group multicasting is a generalization of multicasting whereby every member of a group is allowed to multicast messages to other members that belongs to the same group. The group multicast routing problem (GMRP) is that of finding a set of multicast trees with bandwidth requirements, each rooted at a member of the group, for multicasting messages to other members of the group. An optimal solution to GMRP is a set of trees, one for each member of the group, that incurs the least overall cost. This problem is known to be NP-complete and hence heuristic algorithms are likely to be the only viable approach for computing near optimal solutions in practice. In this paper, we derive a lower bound on the cost of an optimal solution to GMRP by using Lagrangean Relaxation and Subgradient Optimization. This lower bound is used to evaluate the two existing heuristic algorithms in terms of their ability to find close-to-optimal solutions.

In this paper we addresses the problem of finding feasible solutions for the Group Multicast Routing Problem (GMRP). This problem is a generalization of the multicast routing problem whereby every member of the group is allowed to multicast messages to other members from the same group. The routing problem involves the construction of a set of low cost multicast trees with bandwidth requirements for all the group members in the network. We first prove that the problem of finding feasible solutions to GMRP is NP-complete. Following that we propose a new heuristic algorithm for constructing feasible solutions for GMRP. Simulation results show that our proposed algorithm is able to achieve good performance in terms of its ability of finding feasible solutions whenever one exist.

Multicasting is an efficient communication tool for use in multi-point applications such as conferencing and information distribution. In ad hoc networks, node mobility causes frequent changes of network topology, and re-construction of the multicast tree in an efficient and effective manner becomes a critical issues. In case of link breakage, most of the multicast tree construction protocols available presently require either a total re-build of the tree or to reconnect a disjoined node back to the multicast tree via the shortest path which may disrupt the optimising factors, such as energy consumption, delay or cost, used in the building of the original tree. In this paper, we introduce a computationally efficient recovery algorithm which will also minimise the power consumption on the tree.