Related papers: Integrality Gaps of Integer Knapsack Problems
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…
Combinatorial optimization has wide applications from industry to natural science. Ising machines bring an emerging computing paradigm for efficiently solving a combinatorial optimization problem by searching a ground state of a given Ising…
The "0-1 knapsack problem" stands as a classical combinatorial optimization conundrum, necessitating the selection of a subset of items from a given set. Each item possesses inherent values and weights, and the primary objective is to…
We address the question of whether it may be worthwhile to convert certain, now classical, NP-complete problems to one of a smaller number of kernel NP-complete problems. In particular, we show that Karp's classical set of 21 NP-complete…
We introduce and study a novel generalization of the classical Knapsack Problem (KP), called the Colored Knapsack Problem (CKP). In this problem, the items are partitioned into classes of colors and the packed items need to be ordered such…
The article focuses on the problems of prime gaps and zero spacings. Possible solutions of several related problems such as the greatest lower bound, the least upper bound of the zero spacings, and the least upper bound of the prime gaps…
We consider the problem of maximizing a fractionally subadditive function under a knapsack constraint that grows over time. An incremental solution to this problem is given by an order in which to include the elements of the ground set, and…
In the bottleneck multiple knapsack problem, we are given a set of items and a set of knapsacks, where each item has a profit and a weight, and each knapsack has a capacity. Our goal is to assign items to knapsacks so as to maximize the…
The Bin Packing Problem is one of the most important problems in discrete optimization, as it captures the requirements of many real-world problems. Because of its importance, it has been approached with the main theoretical and practical…
Iterative rounding has enjoyed tremendous success in elegantly resolving open questions regarding the approximability of problems dominated by covering constraints. Although iterative rounding methods have been applied to packing problems,…
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…
Multi-armed bandit problems are the predominant theoretical model of exploration-exploitation tradeoffs in learning, and they have countless applications ranging from medical trials, to communication networks, to Web search and advertising.…
We show that in a knapsack feasibility problem an integral vector $p$, which is short, and near parallel to the constraint vector gives a branching direction with small integer width. We use this result to analyze two computationally…
In contrast to finite arithmetic configurations, relatively little is known about which infinite patterns can be found in every set of natural numbers with positive density. Building on recent advances showing infinite sumsets can be found,…
An overview of the results of new exhaustive computations of gaps between primes in arithmetic progressions is presented. We also give new numerical results for exceptionally large least primes in arithmetic progressions.
We consider random discrepancy under weighted importance sampling of a class of stratified input. We give the expected $L_p-$discrepancy($2\leq p<\infty$) upper bound in weighted form under a class of stratified sampling. This result…
We consider binary integer programming problems with the min-max regret objective function under interval objective coefficients. We propose a new heuristic framework, which we call the iterated dual substitution (iDS) algorithm. The iDS…
Rollout algorithms have demonstrated excellent performance on a variety of dynamic and discrete optimization problems. Interpreted as an approximate dynamic programming algorithm, a rollout algorithm estimates the value-to-go at each…
This paper studies the extreme gaps between eigenvalues of random matrices. We give the joint limiting law of the smallest gaps for Haar-distributed unitary matrices and matrices from the Gaussian unitary ensemble. In particular, the kth…
This paper considers pairs of optimization problems that are defined from a single input and for which it is desired to find a good approximation to either one of the problems. In many instances, it is possible to efficiently find an…