Related papers: Online Class Cover Problem
Partial set cover problem and set multi-cover problem are two generalizations of set cover problem. In this paper, we consider the partial set multi-cover problem which is a combination of them: given an element set $E$, a collection of…
Online bidding is a classical problem in online decision-making, with applications in resource allocation, hierarchical clustering, and the analysis of approximation algorithms. We study its randomized learning-augmented variant, where an…
This open problem asks whether there exists an online learning algorithm for binary classification that guarantees, for all target concepts, to make a sublinear number of mistakes, under only the assumption that the (possibly random)…
The online bipartite matching problem, extensively studied in the literature, deals with the allocation of online arriving vertices (items) to a predetermined set of offline vertices (agents). However, little attention has been given to the…
In this paper, we investigate the online allocation problem of maximizing the overall revenue subject to both lower and upper bound constraints. Compared to the extensively studied online problems with only resource upper bounds, the…
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…
Bereg et al. (2012) introduced the Boxes Class Cover problem, which has its roots in classification and clustering applications: Given a set of n points in the plane, each colored red or blue, find the smallest cardinality set of…
We study the online multi-class selection problem with group fairness guarantees, where limited resources must be allocated to sequentially arriving agents. Our work addresses two key limitations in the existing literature. First, we…
We study various discrete nonlinear combinatorial optimization problems in an online learning framework. In the first part, we address the question of whether there are negative results showing that getting a vanishing (or even vanishing…
Coloring is a notoriously hard problem, and even more so in the online setting, where each arriving vertex has to be colored immediately and irrevocably. Already on trees, which are trivially two-colorable, it is impossible to achieve…
This paper studies the online vector bin packing (OVBP) problem and the related problem of online hypergraph coloring (OHC). Firstly, we use a double counting argument to prove an upper bound of the competitive ratio of $FirstFit$ for OVBP.…
We consider the classical online scheduling problem P||C_{max} in which jobs are released over list and provide a nearly optimal online algorithm. More precisely, an online algorithm whose competitive ratio is at most (1+\epsilon) times…
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 consider the problem of online multiclass classification with partial feedback, where an algorithm predicts a class for a new instance in each round and only receives its correctness. Although several methods have been developed for this…
We consider the problem of assigning items to platforms in the presence of group fairness constraints. In the input, each item belongs to certain categories, called classes in this paper. Each platform specifies the group fairness…
We analyze the problem of packing squares in an online fashion: Given a semi-infinite strip of width 1 and an unknown sequence of squares of side length in [0,1] that arrive from above, one at a time. The objective is to pack these items as…
We study the relationship between the competitive ratio and the tail distribution of randomized online minimization problems. To this end, we define a broad class of online problems that includes some of the well-studied problems like…
We consider the online bin packing problem under the advice complexity model where the 'online constraint' is relaxed and an algorithm receives partial information about the future requests. We provide tight upper and lower bounds for the…
For numerous online bipartite matching problems, such as edge-weighted matching and matching under two-sided vertex arrivals, the state-of-the-art fractional algorithms outperform their randomized integral counterparts. This gap is…
We investigate deterministic non-preemptive online scheduling with delayed commitment for total completion time minimization on parallel identical machines. In this problem, jobs arrive one-by-one and their processing times are revealed…