• Corpus ID: 14137115

Online Covering with Convex Objectives and Applications

  title={Online Covering with Convex Objectives and Applications},
  author={Yossi Azar and Ilan Reuven Cohen and Debmalya Panigrahi},
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 covering for linear objectives (Alon {\em et al.}, STOC 2003) and online covering with offline packing constraints (Azar {\em et al.}, SODA 2013). To the best of our knowledge, this is the first result in online optimization for generic non-linear objectives… 

Covering with Sum of l q-Norm Objectives

Improved online algorithms for non-uniform buy-at-bulk network design and the first online algorithm for throughput maximization under lp-norm edge capacities are obtained.

Worst Case Competitive Analysis of Online Algorithms for Conic Optimization

This work derives a sufficient condition on the objective function that guarantees a constant worst case competitive ratio (greater than or equal to $\frac{1}{2}$) for monotone objective functions, and hence design effective smoothing customized for a given cost function.

Designing smoothing functions for improved worst-case competitive ratio in online optimization

The worst case competitive ratio of two primal-dual algorithms for a class of online convex (conic) optimization problems is analyzed and it is shown that the optimal smoothing can be derived by solving a convex optimization problem.

Online Convex Covering and Packing Problems

For any convex polynomial cost functions with non-negative coefficients and maximum degree $\tau$, an O(\tau \log n)^\tau$-competitive online convex covering algorithm, and an O(tau)-competitiveOnline convex packing algorithm are introduced, matching the known $\Omega(\Tau)$ and $Omega(n)$ lower bounds respectively.

Online Packing and Covering Framework with Convex Objectives

Using this fractional solver with problem-dependent randomized rounding procedures, competitive algorithms are obtained for the following problems: online covering LPs minimizing $\ell_p$-norms of arbitrary packing constraints, set cover with multiple cost functions, capacity constrained facility location, capacitated multicast problem, setCover with set requests, and profit maximization with non-separable production costs.

Online Algorithms for Covering and Packing Problems with Convex Objectives

A primal-dual approach is used to give online algorithms for covering and packing problems with (non-linear) convex objectives, and these algorithms are used to simplify, unify, and improve upon previous results for several applications.

D S ] 1 4 A pr 2 01 5 Online Convex Covering and Packing Problems

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∈Rn+ f(~x) s.t. A~x ≥ ~1 where

Online and Random-order Load Balancing Simultaneously

This paper provides algorithms with simultaneous guarantees for the worst-case model as well as for the random-order model, where an arbitrary set of jobs comes in random order, and proposes algorithm SimultaneousLB, a new algorithm with improved regret for Online Linear Optimization over the non-negative vectors in the lq ball.

Online covering with $$\ell _q$$ℓq-norm objectives and applications to network design

An improved online algorithm for non-uniform buy-at-bulk network design and a poly-logarithmic competitive ratio for throughput maximization under ℓp-norm capacities are obtained.

Online Covering with Sum of $\ell_q$-Norm Objectives

Improved online algorithms for non-uniform buy-at-bulk network design and the first online algorithm for throughput maximization under $\ell_p$-norm edge capacities are obtained.



Online Mixed Packing and Covering

This work demonstrates that the classical framework of solving optimization problems by obtaining a fractional solution to a linear program and rounding it to an integer solution can be extended to the online setting using primal-dual techniques and obtains the first algorithm that obtains a polylogarithmic competitive ratio for solving mixed LPs online.

Online Primal-Dual Algorithms for Covering and Packing

This work provides general deterministic primal-dual algorithms for online fractional covering and packing problems and also provides deterministic algorithms for several integral online covering andpacking problems.

Approximation algorithms for scheduling on multiple machines

We develop a single rounding algorithm for scheduling on unrelated parallel machines; this algorithm works well with the known linear programming, quadratic programming, and convex

Convex programming for scheduling unrelated parallel machines

This work considers the classical problem of scheduling parallel unrelated machines and provides a 2-approximation algorithm for any fixed lp norm (p>1) and gives the first time that general convex programming techniques are used in the area of scheduling.

Better bounds for online load balancing on unrelated machines

The first randomized online algorithms which outperform deterministic ones under any (integral) Lp norm for p = 2,…,137 are presented, providing a positive answer to the question whether randomization helps online load balancing under Lp norms on unrelated machines.

Online Node-Weighted Steiner Forest and Extensions via Disk Paintings

The central idea in this technique is to amortize the cost of primal updates to a set of carefully selected mutually disjoint fixed-radius dual disks centered at a subset of terminals to form a new framework for online network design problems that is called disk paintings.

Online Primal-Dual for Non-linear Optimization with Applications to Speed Scaling

This analysis shows that competitive algorithms exist for problems that had resisted analysis using the dominant potential function approach in the speed-scaling literature, and provides alternate cleaner analysis for other known results.

Towards the randomized k-server conjecture: a primal-dual approach

Recently, Coté et al. [10] proposed an approach for solving the k-server problem on Hierchically Separated Trees (HSTs). In particular, they define a problem on a uniform metric, and show that if an

The competitiveness of on-line assignments

It is concluded that for the on-line problem where a number of servers are ready to provide service to a set of customers, randomized algorithms differ from deterministic ones by precisely a constant factor.

Generalized machine activation problems

A greedy algorithm is developed that yields a fractional assignment of jobs, such that at least n − ε jobs are assigned fractionally and the total cost is at most 1 + ln(n/ε) times the optimum, which gives an affirmative answer to the open question posed in earlier work on universal facility location.