Related papers: Online Knapsack Problems with Estimates
In the online general knapsack problem, an algorithm is presented with an item $x=(s,v)$ of size $s$ and value $v$ and must irrevocably choose to pack such an item into the knapsack or reject it before the next item appears. The goal is to…
In the online simple knapsack problem items are presented in an iterative fashion and an algorithm has to decide for each item whether to reject or permanently include it into the knapsack without any knowledge about the rest of the…
The online knapsack problem is a classic online resource allocation problem in networking and operations research. Its basic version studies how to pack online arriving items of different sizes and values into a capacity-limited knapsack.…
In the knapsack problem, we are given a knapsack of some capacity and a set of items, each with a size and a value. The goal is to pack a selection of these items fitting the knapsack that maximizes the total value. The online version of…
Online knapsack problem is considered, where items arrive in a sequential fashion that have two attributes; value and weight. Each arriving item has to be accepted or rejected on its arrival irrevocably. The objective is to maximize the sum…
We prove new lower bounds for suitable competitive ratio measures of two relaxed online packing problems: online removable multiple knapsack, and a recently introduced online minimum peak appointment scheduling problem. The high level…
In this paper, we introduce online knapsack problems with a resource buffer. In the problems, we are given a knapsack with capacity $1$, a buffer with capacity $R\ge 1$, and items that arrive one by one. Each arriving item has to be taken…
A variant of the online knapsack problem is considered in the settings of trusted and untrusted predictions. In Unit Profit Knapsack, the items have unit profit, and it is easy to find an optimal solution offline: Pack as many of the…
We introduce the Online Unbounded Knapsack Problem with Removal, a variation of the well-known Online Knapsack Problem. Items, each with a weight and value, arrive online and an algorithm must decide on whether or not to pack them into a…
The fractional knapsack problem is one of the classical problems in combinatorial optimization, which is well understood in the offline setting. However, the corresponding online setting has been handled only briefly in the theoretical…
In the knapsack problem under explorable uncertainty, we are given a knapsack instance with uncertain item profits. Instead of having access to the precise profits, we are only given uncertainty intervals that are guaranteed to contain the…
The online knapsack problem is a classic problem in the field of online algorithms. Its canonical version asks how to pack items of different values and weights arriving online into a capacity-limited knapsack so as to maximize the total…
We study the dynamic pricing problem with knapsack, addressing the challenge of balancing exploration and exploitation under resource constraints. We introduce three algorithms tailored to different informational settings: a Boundary…
The knapsack problem is one of the classical problems in combinatorial optimization: Given a set of items, each specified by its size and profit, the goal is to find a maximum profit packing into a knapsack of bounded capacity. In the…
We consider the problem of online resource allocation with average budget constraints. At each time point the decision maker makes an irrevocable decision of whether to accept or reject a request before the next request arrives with the…
Imagine yourself moving to another place, and therefore, you need to pack all of your belongings into moving boxes with some capacity. In the classical bin packing model, you would try to minimize the number of boxes, knowing the exact size…
Two related online problems: knapsack and truthful bipartite matching are considered. For these two problems, the common theme is how to `match' an arriving left vertex in an online fashion with any of the available right vertices, if at…
We analyze the competitive ratio and the advice complexity of the online unbounded knapsack problem. An instance is given as a sequence of n items with a size and a value each, and an algorithm has to decide how often to pack each item into…
Promotions and discounts are essential components of modern e-commerce platforms, where they are often used to incentivize customers towards purchase completion. Promotions also affect revenue and may incur a monetary loss that is often…
We study different online optimization problems in the random-order model. There is a finite set of bins with known capacity and a finite set of items arriving in a random order. Upon arrival of an item, its size and its value for each of…