In this paper, we study radio resource allocation for
multicasting in OFDMA based high altitude platforms (HAPs).
We formulate and solve an optimization problem that finds the
best allocation of HAP resources such as radio power, subchannels,
and time slots. The problem also finds the best possible
frequency reuse across the cells that constitute the service area
of the HAP. The objective is to maximize the number of user
terminals that receive the requested multicast streams in the HAP
service area in a given OFDMA frame. A bounding subroutine in
a branch and bound algorithm can be obtained by decomposing it
into two easier subproblems, due to its high complexity, and solving
them iteratively. Subproblem1 turns out to be a binary integer
linear program of no explicitly noticeable structure and therefore
Lagrangian relaxation is used to dualize some constraints to get
a structure that is easy to solve. Subproblem 2 turns out to be a
linear program with a continuous knapsack problem structure.
Hence a greedy algorithm is proposed to solve subproblem 2 to
optimality. The subgradient method is used to solve for the dual
variables in the dual problem to get the tightest bounds.