Related papers: Online Unit Profit Knapsack with Untrusted Predict…
Makespan minimization on identical machines is a fundamental problem in online scheduling. The goal is to assign a sequence of jobs to $m$ identical parallel machines so as to minimize the maximum completion time of any job. Already in the…
Ranking and Balance are arguably the two most important algorithms in the online matching literature. They achieve the same optimal competitive ratio of $1-1/e$ for the integral version and fractional version of online bipartite matching by…
The online unit clustering problem was proposed by Chan and Zarrabi-Zadeh (WAOA2007 and Theory of Computing Systems 45(3), 2009), which is defined as follows: "Points" are given online in the $d$-dimensional Euclidean space one by one. An…
We study an online version of the max-min fair allocation problem for indivisible items. In this problem, items arrive one by one, and each item must be allocated irrevocably on arrival to one of $n$ agents, who have additive valuations for…
The effectiveness of advertising in e-commerce largely depends on the ability of merchants to bid on and win impressions for their targeted users. The bidding procedure is highly complex due to various factors such as market competition,…
Online bipartite matching is a fundamental problem in online optimization, extensively studied both in its integral and fractional forms due to its theoretical significance and practical applications, such as online advertising and resource…
We study the online bipartite matching problem, introduced by Karp, Vazirani and Vazirani [1990]. For bipartite graphs with matchings of size $n$, it is known that the Ranking randomized algorithm matches at least $(1 - \frac{1}{e})n$ edges…
Aiming to overcome some of the limitations of worst-case analysis, the recently proposed framework of "algorithms with predictions" allows algorithms to be augmented with a (possibly erroneous) machine-learned prediction that they can use…
We contribute the first randomized algorithm that is an integration of arbitrarily many deterministic algorithms for the fully online multiprocessor scheduling with testing problem. When there are two machines, we show that with two…
Benchmark instances for the unbounded knapsack problem are typically generated according to specific criteria within a given constant range $R$, and these instances can be referred to as the unbounded knapsack problem with bounded…
This work presents an empirical analysis of exact algorithms for the unbounded knapsack problem, which includes seven algorithms from the literature, two commercial solvers, and more than ten thousand instances. The terminating step-off, a…
We study generalizations of online bipartite matching in which each arriving vertex (customer) views a ranked list of offline vertices (products) and matches to (purchases) the first one they deem acceptable. The number of products that the…
The burgeoning field of algorithms with predictions studies the problem of using possibly imperfect machine learning predictions to improve online algorithm performance. While nearly all existing algorithms in this framework make no…
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…
Online algorithms with predictions is a popular and elegant framework for bypassing pessimistic lower bounds in competitive analysis. In this model, online algorithms are supplied with future predictions, and the goal is for the competitive…
Online caching is among the most fundamental and well-studied problems in the area of online algorithms. Innovative algorithmic ideas and analysis -- including potential functions and primal-dual techniques -- give insight into this…
The advice complexity of an online problem is a measure of how much knowledge of the future an online algorithm needs in order to achieve a certain competitive ratio. Using advice complexity, we define the first online complexity class,…
Online decision-making in the presence of uncertain future information is abundant in many problem domains. In the critical problem of energy generation scheduling for microgrids, one needs to decide when to switch energy supply between a…
In this paper, we obtain a number of new simple pseudo-polynomial time algorithms on the well-known knapsack problem, focusing on the running time dependency on the number of items $n$, the maximum item weight $w_\mathrm{max}$, and the…
In the d-dimensional online bin packing problem, d-dimensional cubes of positive sizes no larger than 1 are presented one by one to be assigned to positions in d-dimensional unit cube bins. In this work, we provide improved upper bounds on…