Primal beats dual on online packing LPs in the random-order model

Keßelheim, Thomas; Tönnis, Andreas; Radke, Klaus; Vöcking, Berthold

doi:10.1145/2591796.2591810

Cited by 85 publications

(119 citation statements)

References 16 publications

Supporting

Mentioning

116

Contrasting

Order By: Relevance

“…Over the last years the framework has received quite some research interest and many further problems have been studied. These include generalized secretary problems [2,3,13,28,29], the knapsack problem [2,28], bin packing [26], facility location [31], matching problems [17,22,30], packing LPs [27] and convex optimization [20].…”

Section: Introductionmentioning

confidence: 99%

Scheduling in the Random-Order Model

Albers

Janke

2021

Algorithmica

View full text Add to dashboard Cite

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 1960s, Graham showed that Greedy is $$(2-1/m)$$ ( 2 - 1 / m ) -competitive. The best deterministic online algorithm currently known achieves a competitive ratio of 1.9201. No deterministic online strategy can obtain a competitiveness smaller than 1.88. In this paper, we study online makespan minimization in the popular random-order model, where the jobs of a given input arrive as a random permutation. It is known that Greedy does not attain a competitive factor asymptotically smaller than 2 in this setting. We present the first improved performance guarantees. Specifically, we develop a deterministic online algorithm that achieves a competitive ratio of 1.8478. The result relies on a new analysis approach. We identify a set of properties that a random permutation of the input jobs satisfies with high probability. Then we conduct a worst-case analysis of our algorithm, for the respective class of permutations. The analysis implies that the stated competitiveness holds not only in expectation but with high probability. Moreover, it provides mathematical evidence that job sequences leading to higher performance ratios are extremely rare, pathological inputs. We complement the results by lower bounds, for the random-order model. We show that no deterministic online algorithm can achieve a competitive ratio smaller than 4/3. Moreover, no deterministic online algorithm can attain a competitiveness smaller than 3/2 with high probability.

show abstract

Section: Introductionmentioning

confidence: 99%

Scheduling in the Random-Order Model

Albers

Janke

2021

Algorithmica

View full text Add to dashboard Cite

show abstract

“…Random Order Model: There has been a line of work in analyzing online algorithms in the random order model for matching problems and more general packing integer linear programs [10,12,26,1,11,20,14]. These algorithms are usually based off of some sort of primaldual approach.…”

Section: Related Workmentioning

confidence: 99%

Using Predicted Weights for Ad Delivery

Lavastida¹,

Moseley²,

Ravi³

et al. 2021

SIAM Conference on Applied and Computational Discrete Algorithms (ACDA21)

View full text Add to dashboard Cite

We study the performance of a proportional weights algorithm for online capacitated bipartite matching modeling the delivery of impression ads. The algorithm uses predictions on the advertiser nodes to match arriving impression nodes fractionally in proportion to the weights of its neighbors. This paper gives a thorough empirical study of the performance of the algorithm on a data-set of ad impressions from Yahoo! and shows its superior performance compared to natural baselines such as a greedy water-filling algorithm and the ranking algorithm.The proportional weights algorithm has recently received interest in the theoretical literature where it was shown to have strong guarantees beyond the worst-case model of algorithms augmented with predictions. We extend these results to the case where the advertisers' capacities are no longer stationary over time. Additionally, we show the algorithm has near optimal performance in the random-order arrival model when the number of impressions and the optimal matching are sufficiently large.

show abstract

“…Our construction borrows techniques used in designing online algorithms for stochastic online convex programming problems (Agrawal and Devanur, 2015;Chen and Wang, 2013), and stochastic online packing problems (Agrawal et al, 2009;Devanur et al, 2011;Badanidiyuru et al, 2013;Kesselheim et al, 2014). Our online algorithm (Algorithm 4, below) considers the replicas in order, updates the dual variables using multiplicative weight updates based on the current allocation, and allocates to each agent by sampling from the exponential weights distribution as given by Lemma 5.3.…”

Section: Online Entropy Regularized Matchingmentioning

confidence: 99%

Bernoulli factories and black-box reductions in mechanism design

Dughmi

Hartline

Kleinberg

et al. 2017

Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing

View full text Add to dashboard Cite

We provide a polynomial time reduction from Bayesian incentive compatible mechanism design to Bayesian algorithm design for welfare maximization problems. Unlike prior results, our reduction achieves exact incentive compatibility for problems with multi-dimensional and continuous type spaces.The key technical barrier preventing exact incentive compatibility in prior black-box reductions is that repairing violations of incentive constraints requires understanding the distribution of the mechanism's output, which is typically #P-hard to compute. Reductions that instead estimate the output distribution by sampling inevitably suffer from sampling error, which typically precludes exact incentive compatibility.We overcome this barrier by employing and generalizing the computational model in the literature on Bernoulli Factories. In a Bernoulli factory problem, one is given a function mapping the bias of an "input coin" to that of an "output coin", and the challenge is to efficiently simulate the output coin given only sample access to the input coin. Consider a generalization which we call the expectations from samples computational model, in which a problem instance is specified by a function mapping the expected values of a set of input distributions to a distribution over outcomes. The challenge is to give a polynomial time algorithm that exactly samples from the distribution over outcomes given only sample access to the input distributions.In this model, we give a polynomial time algorithm for the function given by exponential weights: expected values of the input distributions correspond to the weights of alternatives and we wish to select an alternative with probability proportional to an exponential function of its weight. This algorithm is the key ingredient in designing an incentive compatible mechanism for bipartite matching, which can be used to make the approximately incentive compatible reduction of exactly incentive compatible.

show abstract

Primal beats dual on online packing LPs in the random-order model

Cited by 85 publications

References 16 publications

Scheduling in the Random-Order Model

Scheduling in the Random-Order Model

Using Predicted Weights for Ad Delivery

Bernoulli factories and black-box reductions in mechanism design

Contact Info

Product

Resources

About