Optimization problems due to noisy data are usually solved using stochastic programming or robust optimization approaches. Both requiring the explicit characterization of an uncertainty set that models the nature of the noise. Such approaches tightly depend on the modeling of the uncertainty set. In this paper, we introduce a framework that implicitly models the uncertain data. We define the ge...

Many combinatorial optimization problems are known to be NP-complete. A common point of view is that finding fast algorithms for such problems using polynomial number of processors is unlikely. However facts of this kind usually are established for "worst" case situations and in practice many instances of NP-complete problems are successfully solved in polynomial time by such traditional combin...

We consider so-called “incremental” dynamic programming algorithms, and are interested in the number of subproblems produced by them. The standard dynamic programming algorithm for the n-dimensional Knapsack problem is incremental, produces nK subproblems and nK relations (wires) between the subproblems, where K is the capacity of the knapsack. We show that any incremental algorithm for this pr...

New variants of greedy algorithms, called advanced greedy algorithms, are identified for knapsack and covering problems with linear and quadratic objective functions. Beginning with single-constraint problems, we provide extensions for multiple knapsack and covering problems, in which objects must be allocated to different knapsacks and covers, and also for multi-constraint (multi-dimensional) ...

We explain how the Knapsack problem and interactive rendering are related. We also discuss several additional concerns regarding interactive rendering and how these affect the solution to the original Knapsack problem. Lastly, we present two approximate algorithms and compare how they meet the needs of interactive rendering. 1 Background Knapsack Problem We are given a set of n items, S = x1, x...