Related papers: Online Mixed Packing and Covering
We consider online fractional covering problems with a convex objective, where the covering constraints arrive over time. Formally, we want to solve $\min\,\{f(x) \mid Ax\ge \mathbf{1},\, x\ge 0\},$ where the objective function…
We study the online convex covering problem and online convex packing problem. The (offline) convex covering problem is modeled by the following convex program: $\min_{x \in R_+^n} f(x) \ \text{s.t}\ A x \ge 1$, where $f : R_+^n \mapsto…
This paper presents fast first-order methods for solving linear programs (LPs) approximately. We adapt online linear programming algorithms to offline LPs and obtain algorithms that avoid any matrix multiplication. We also introduce a…
Mixed packing and covering problems are problems that can be formulated as linear programs using only non-negative coefficients. Examples include multicommodity network flow, the Held-Karp lower bound on TSP, fractional relaxations of set…
We consider the problem of solving packing/covering LPs online, when the columns of the constraint matrix are presented in random order. This problem has received much attention and the main focus is to figure out how large the right-hand…
This paper presents an algorithmic study of a class of covering mixed-integer linear programming problems which encompasses classic cover problems, including multidimensional knapsack, facility location and supplier selection problems. We…
We consider set covering problems where the underlying set system satisfies a particular replacement property w.r.t. a given partial order on the elements: Whenever a set is in the set system then a set stemming from it via the replacement…
In this paper, we exploit linear programming duality in the online setting (i.e., where input arrives on the fly) from the unique perspective of designing lower bounds on the competitive ratio. In particular, we provide a general technique…
Positive linear programs (LP), also known as packing and covering linear programs, are an important class of problems that bridges computer science, operations research, and optimization. Despite the consistent efforts on this problem, all…
We give an algorithmic framework for minimizing general convex objectives (that are differentiable and monotone non-decreasing) over a set of covering constraints that arrive online. This substantially extends previous work on online…
Consider the following online version of the submodular maximization problem under a matroid constraint: We are given a set of elements over which a matroid is defined. The goal is to incrementally choose a subset that remains independent…
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…
Online bin stretching is an online packing problem where some of the best known lower and upper bounds were found through computational searches. The limiting factor in obtaining better bounds with such methods is the computational time…
We investigate several online packing problems in which convex polygons arrive one by one and have to be placed irrevocably into a container, while the aim is to minimize the used space. Among other variants, we consider strip packing and…
Though competitive analysis is often a very good tool for the analysis of online algorithms, sometimes it does not give any insight and sometimes it gives counter-intuitive results. Much work has gone into exploring other performance…
Learning-augmented algorithms has been extensively studied recently in the computer-science community, due to the potential of using machine learning predictions in order to improve the performance of algorithms. Predictions are especially…
Semidefinite programming (SDP) is a unifying framework that generalizes both linear programming and quadratically-constrained quadratic programming, while also yielding efficient solvers, both in theory and in practice. However, there exist…
In this paper we consider several related online computation problems. First, we study answering sequences of statistical queries arriving online, and being answered immediately when they arrive with differential privacy. Known matrix…
We give a very general and simple framework to incorporate predictions on requests for online covering problems in a rigorous and black-box manner. Our framework turns any online algorithm with competitive ratio $\rho(k, \cdot)$ depending…
A variant of the well-known Set Covering Problem is studied in this paper, where subsets of a collection have to be selected, and pairwise conflicts among subsets of items exist. The selection of each subset has a cost, and the inclusion of…