Randomized algorithms for online knapsack problems

Online Knapsack Problems

Since no competitive online algorithms exist for general knapsack problems, we consider online variants of knapsack problems with two assumptions: (i) the weight of each item is very small compared to the knapsack capacity; (ii) the value-to-weight ratio of each item is lower and upper bounded by two positive constants L and U . We design a deterministic threshold-based algorithm for the online...

Approximation Algorithms for Constrained Knapsack Problems

We study constrained versions of the knapsack problem in which dependencies between items are given by a graph. In one version, an item can be selected only if one of its neighbours is also selected. In the other version, an item can be selected only when all its neighbours are also selected. These problems generalize and unify several problems including the prize collecting and budgeted maximu...

Randomized Online Algorithms for Dynamic Multi-Period Routing Problems

The Dynamic Multi-Period Routing Problem (Dmprp) introduced by Angelelli et al. [1] gives a model for a two-stage online-offline routing problem. At the beginning of each time period a set of customers becomes known. The customers need to be served either in the current time period or in the following. Postponed customers have to be served in the next time period. The decision whether to postpo...

Online Knapsack Problems with Limited Cuts

The (offline) maximization (resp., minimization) knapsack problem is given a set of items with weights and sizes, and the capacity of a knapsack, to maximize (resp., minimize) the total weight of selected items under the constraint that the total size of the selected items is at most (resp., at least) the capacity of the knapsack. In this paper, we study online maximization and minimization kna...

Online algorithms for clustering problems