Online knapsack of unknown capacity

Apart for the interest in a new version of the fundamental knapsack problem, the motivations that lead to define this new variant come from energy consumption constraints in smartphones communications. We provide lower and upper bounds to the problem for various cases. In general, we design an optimal algorithm admitting a 12-competitive ratio. When all items admit uniform ratio of profit over size, our algorithm provides a 4986=.569… competitive ratio that leaves some gap with the provided bound of 1φ=.618…, the inverse of the golden number. We then conduct experimental analysis for the competitive ratio guaranteed algorithms compared to the optimum and to various heuristics.