# AdWords and generalized on-line matching

@article{Mehta2005AdWordsAG, title={AdWords and generalized on-line matching}, author={Aranyak Mehta and Amin Saberi and Umesh V. Vazirani and Vijay V. Vazirani}, journal={46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05)}, year={2005}, pages={264-273} }

How does a search engine company decide what ads to display with each query so as to maximize its revenue? This turns out to be a generalization of the online bipartite matching problem. We introduce the notion of a tradeoff revealing LP and use it to derive two optimal algorithms achieving competitive ratios of 1-1/e for this problem.

## 552 Citations

Randomized Online Algorithms for Adwords

- MathematicsArXiv
- 2021

A randomized online algorithm achieving a competitive ratio of (k-TYPICAL, k ∈ Z+,) is given, which seems a reasonable assumption for a “typical” instance, at least for moderate values of k.

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A tail inequality bound is given, namely that Ranking is (1 − 1 e − α)-competitive with probability at least 1 − e n where n is the size of the maximum matching in the instance.

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We consider the generalizations of two classical problems, online bipartite matching and ski rental, in the field of online algorithms, and establish a novel connection between them.

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This work gives the first approximation factor beating 0.5, namely a 0.505 approximation, by suitably adapting and interpreting the powerful technique of Online Correlated Selection.

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- Computer Science
- 2021

This paper has stated the result for SMALL, namely an optimal, online, budgetoblivious algorithm, as a Conditional Theorem, after assuming the no-surpassing property, and believes that in typical instances, this property fails on very few queries, if any.

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- Computer Science, EconomicsSODA '08
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An online assignment problem, motivated by Adwords Allocation, in which queries are to be assigned to bidders with budget constraints is studied, with a tight analysis of Greedy in this model showing that it has a competitive ratio of 1 - 1/e for maximizing the value of the assignment.

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- Computer Science
- 2017

This paper analyzes a general problem of allocating finite inventories to heterogeneous customers arriving sequentially under the framework of competitive analysis, and develops algorithms which achieve the best-possible weight-dependent competitive ratios, which depend on the sets of feasible prices given in advance.

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- Mathematics, Computer ScienceAlgorithmica
- 2007

The technique of factor-revealing linear programs is used to show that the greedy algorithm for the remote-clique problem actually achieves an approximation ratio of 2, which is tight.

Online Matching in Regular Bipartite Graphs with Randomized Adversary

- MathematicsAdventures Between Lower Bounds and Higher Altitudes
- 2018

The competitive ratio for 2-regular graphs for any number of random decisions made by the adversary is determined and upper and lower bounds for other values of the degree are given.

Algorithms for Online Matching, Assortment, and Pricing with Tight Weight-dependent Competitive Ratios

- Computer ScienceOper. Res.
- 2020

This paper studies a general problem of allocating finite inventories to heterogeneous customers arriving sequentially under the framework of competitive analysis, and develops algorithms which achieve the best-possible weight-dependent competitive ratios, which depend on the sets of feasible prices given in advance.

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