Related papers: Online Class Cover Problem
We study the Generalized Red-Blue Annulus Cover problem for two sets of points, red ($R$) and blue ($B$), where each point $p \in R\cup B$ is associated with a positive penalty ${\cal P}(p)$. The red points have non-covering penalties, and…
We consider the following fundamental routing problem. An adversary inputs packets arbitrarily at sources, each packet with an arbitrary destination. Traffic is constrained by link capacities and buffer sizes, and packets may be dropped at…
The online bin covering problem is: given an input sequence of items find a placement of the items in the maximum number of bins such that the sum of the items' sizes in each bin is at least~1. Boyar~{\em et~al}.\@~\cite{boyar2021} present…
We consider the Ordered Open End Bin Packing problem. Items of sizes in $(0,1]$ are presented one by one, to be assigned to bins in this order. An item can be assigned to any bin for which the current total size strictly below $1$. 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,…
Huang et al.~(STOC 2018) introduced the fully online matching problem, a generalization of the classic online bipartite matching problem in that it allows all vertices to arrive online and considers general graphs. They showed that the…
We study online competitive algorithms for the \emph{line chasing problem} in Euclidean spaces $\reals^d$, where the input consists of an initial point $P_0$ and a sequence of lines $X_1,X_2,...,X_m$, revealed one at a time. At each step…
Covering problems are fundamental classical problems in optimization, computer science and complexity theory. Typically an input to these problems is a family of sets over a finite universe and the goal is to cover the elements of the…
Clique clustering is the problem of partitioning the vertices of a graph into disjoint clusters, where each cluster forms a clique in the graph, while optimizing some objective function. In online clustering, the input graph is given one…
We consider the set multi-cover problem in geometric settings. Given a set of points P and a collection of geometric shapes (or sets) F, we wish to find a minimum cardinality subset of F such that each point p in P is covered by (contained…
We revisit the classic online bin packing problem. In this problem, items of positive sizes no larger than 1 are presented one by one to be packed into subsets called "bins" of total sizes no larger than 1, such that every item is assigned…
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…
We study the online traveling repairperson problem on a line within the recently proposed learning-augmented framework, which provides predictions on the requests to be served via machine learning. In the original model (with no…
We consider online packing problems where we get a stream of axis-parallel rectangles. The rectangles have to be placed in the plane without overlapping, and each rectangle must be placed without knowing the subsequent rectangles. The goal…
The online bisection problem is a natural dynamic variant of the classic optimization problem, where one has to dynamically maintain a partition of $n$ elements into two clusters of cardinality $n/2$. During runtime, an online algorithm is…
This paper studies online optimization under inventory (budget) constraints. While online optimization is a well-studied topic, versions with inventory constraints have proven difficult. We consider a formulation of inventory-constrained…
We study a version of online edge coloring, where the goal is to color as many edges as possible using only a given number, $k$, of available colors. All of our results are with regard to competitive analysis. Previous attempts to identify…
We study the online minimum cost bipartite perfect matching with delays problem. In this problem, $m$ servers and $m$ requests arrive over time, and an online algorithm can delay the matching between servers and requests by paying the delay…
We study the problem of conformal prediction in a novel online framework that directly optimizes efficiency. In our problem, we are given a target miscoverage rate $\alpha > 0$, and a time horizon $T$. On each day $t \le T$ an algorithm…
Given a universe $\mathcal{U}=R \cup B$ of a finite set of red elements $R$, and a finite set of blue elements $B$ and a family $\mathcal{F}$ of subsets of $\mathcal{U}$, the \RBSC problem is to find a subset $\mathcal{F}'$ of $\mathcal{F}$…