Solving the Knapsack Problem for Adaptive Multimedia Systems

The Multiple-Choice Multi-Dimension Knapsack Problem (MMKP) is a variant of the 0-1 knapsack problem, an NP-Hard problem. Due to its high computational complexity, algorithms for exact solution of the MMKPs are not suitable for most real-time decision-making applications, such as quality adaptation and admission control for interactive multimedia systems, or service level agreement (SLA) management in telecommunication networks. This paper presents a heuristic for finding near-optimal solutions of the MMKP, with reduced computational complexity, and is suitable for real-time applications. Based on Toyoda’s concept of aggregate resource, the heuristic employs an iterative improvement procedure using savings in aggregate resource and value per unit of extra aggregate resource. Experimental results suggest that this heuristic finds solutions which are close to the optimal (within 6% of the optimal value), and that it out-performs Moser’s heuristic for the MMKP in both solution quality and execution time.