Related papers: Near-Tight Approximation Algorithms for Bottleneck…
We study the problem of maximizing a monotone submodular function subject to a Multiple Knapsack constraint. The input is a set $I$ of items, each has a non-negative weight, and a set of bins of arbitrary capacities. Also, we are given a…
A multiple knapsack constraint over a set of items is defined by a set of bins of arbitrary capacities, and a weight for each of the items. An assignment for the constraint is an allocation of subsets of items to the bins which adheres to…
The stochastic knapsack problem is the stochastic variant of the classical knapsack problem in which the algorithm designer is given a a knapsack with a given capacity and a collection of items where each item is associated with a profit…
In the knapsack interdiction problem, there are $n$ items, each with a non-negative profit, interdiction cost, and packing weight. There is also an interdiction budget and a capacity. The objective is to select a set of items to interdict…
We propose a method for finding approximate solutions to multiple-choice knapsack problems. To this aim we transform the multiple-choice knapsack problem into a bi-objective optimization problem whose solution set contains solutions of the…
We study the uniform $2$-dimensional vector multiple knapsack (2VMK) problem, a natural variant of multiple knapsack arising in real-world applications such as virtual machine placement. The input for 2VMK is a set of items, each associated…
In this paper, we study the problem of maximizing $k$-submodular functions subject to a knapsack constraint. For monotone objective functions, we present a $\frac{1}{2}(1-e^{-2})\approx 0.432$ greedy approximation algorithm. For the…
In the incremental knapsack problem ($\IK$), we are given a knapsack whose capacity grows weakly as a function of time. There is a time horizon of $T$ periods and the capacity of the knapsack is $B_t$ in period $t$ for $t = 1, \ldots, T$.…
The multiple knapsack problem with grouped items aims to maximize rewards by assigning groups of items among multiple knapsacks, considering knapsack capacities. Either all items in a group are assigned or none at all. We propose algorithms…
In this work, we study the classic submodular maximization problem under knapsack constraints and beyond. We first present an $(7/16-\varepsilon)$-approximate algorithm for single knapsack constraint, which requires…
We study the non-uniform capacitated multi-item lot-sizing (\lotsizing) problem. In this problem, there is a set of demands over a planning horizon of $T$ time periods and all demands must be satisfied on time. We can place an order at the…
We study the knapsack problem with group fairness constraints. The input of the problem consists of a knapsack of bounded capacity and a set of items, each item belongs to a particular category and has and associated weight and value. The…
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…
Obtaining strong linear relaxations of capacitated covering problems constitute a major technical challenge even for simple settings. For one of the most basic cases, the Knapsack-Cover (Min-Knapsack) problem, the relaxation based on…
We study the three-dimensional Knapsack (3DK) problem, in which we are given a set of axis-aligned cuboids with associated profits and an axis-aligned cube knapsack. The objective is to find a non-overlapping axis-aligned packing (by…
We study the proximity of the optimal value of the m-dimensional knapsack problem to the optimal value of that problem with the additional restriction that only one type of items is allowed to include in the solution. We derive exact and…
We consider the problem of maximizing a monotone submodular function subject to a knapsack constraint. Our main contribution is an algorithm that achieves a nearly-optimal, $1 - 1/e - \epsilon$ approximation, using…
Knapsack is one of the most fundamental problems in theoretical computer science. In the $(1 - \epsilon)$-approximation setting, although there is a fine-grained lower bound of $(n + 1 / \epsilon) ^ {2 - o(1)}$ based on the $(\min,…
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…
The problem of non-monotone $k$-submodular maximization under a knapsack constraint ($\kSMK$) over the ground set size $n$ has been raised in many applications in machine learning, such as data summarization, information propagation, etc.…