A Predictive Incremental Hierarchical Level of Detail Optimization Algorithm

We present a new hierarchical level of detail optimization algorithm that is predictive and so may be used for active frame rate control. We base our approach on earlier work demonstrating the equivalence of level of detail optimization to the Multiple Choice Knapsack Problem (MCKP). We show that this equivalence is broken for hierarchical level of detail scene descriptions in which shared representations may be provided for groups of objects, and that the level of detail optimization problem for such descriptions is equivalent to a generalization of the MCKP which we call the Hierarchical MCKP. We present a greedy approximation algorithm for this Hierarchical MCKP whose solution we prove is guaranteed to be at least half-optimal for a useful subproblem in which more expensive selections provide diminishing returns. Furthermore we show that the typical behaviour of the algorithm is much better than half-optimal and that the instances in which it is not are relatively rare. The level of detail optimization algorithm we present is an incremental version of this greedy algorithm designed to exploit frame-to-frame coherence by basing its initial solution on the solution found for the previous frame. We prove the equivalence of the two algorithms by considering their state spaces and showing that both reach the same solution state.