Budget constrained bidding in keyword auctions and online knapsack problems

Zhou, Yunhong; Chakrabarty, Deeparnab; Lukose, Rajan M.

doi:10.1145/1367497.1367747

Cited by 120 publications

(153 citation statements)

References 4 publications

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“…3.2.1. Nevertheless, our proof of optimality is di erent from that given by Zhou et al [31], and leads to an intuitive interpretation on the choice of exponential pricing functions. More importantly, the total weight of items is assumed to be unbounded in the previous work, which is hardly the case for any real-world applications.…”

Section: Related Workmentioning

confidence: 60%

“…Under these assumptions, Buchbinder and Naor [6,7] design an algorithm achieving a competitive ratio of O (log (U /L)), as well as an Ω (log (U /L)) lower bound on the competitive ratio of any algorithm. In the context of advertising auctions, Zhou et al [31] design a (log (U /L) + 1)-competitive algorithm for an online knapsack problem under the above assumptions. Interestingly, their …”

Section: Related Workmentioning

confidence: 99%

“…For example, if a high-valued bid demanding almost all the resource from a cloud provider is rejected, because a small fraction of the resource is occupied by other users, then the worst-case competitive ratio can be in nitely large. In addition, such an assumption is standard in the literature of online resource allocation [29,30] and online knapsack problems [6,7,11,31]. Nonetheless, it is also possible to relax Assumption 2 to specifying an upper bound on d i instead, without signi cantly a ecting our theoretical result.…”

Section: E Basic Resource Allocation Problemmentioning

confidence: 99%

See 2 more Smart Citations

Optimal Posted Prices for Online Cloud Resource Allocation

ZhangZijun

LiZongpeng

WuChuan³

2017

SIGMETRICS Perform. Eval. Rev.

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We study online resource allocation in a cloud computing platform, through a posted pricing mechanism: e cloud provider publishes a unit price for each resource type, which may vary over time; upon arrival at the cloud system, a cloud user either takes the current prices, renting resources to execute its job, or refuses the prices without running its job there. We design pricing functions based on the current resource utilization ratios, in a wide array of demandsupply relationships and resource occupation durations, and prove worst-case competitive ratios of the pricing functions in terms of social welfare. In the basic case of a single-type, non-recycled resource (i.e., allocated resources are not later released for reuse), we prove that our pricing function design is optimal, in that any other pricing function can only lead to a worse competitive ratio. Insights obtained from the basic cases are then used to generalize the pricing functions to more realistic cloud systems with multiple types of resources, where a job occupies allocated resources for a number of time slots till completion, upon which time the resources are returned back to the cloud resource pool.

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Section: Related Workmentioning

confidence: 60%

Section: Related Workmentioning

confidence: 99%

Section: E Basic Resource Allocation Problemmentioning

confidence: 99%

See 1 more Smart Citation

Optimal Posted Prices for Online Cloud Resource Allocation

ZhangZijun

LiZongpeng

WuChuan³

2017

SIGMETRICS Perform. Eval. Rev.

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show abstract

“…While there has been extensive research into various aspects of the sponsored search market during the past few years (see, for example, [7,16,10,1,11,3,17,9,14,12]), the topic of broad matching has remained largely unexplored. The only papers we are aware of that study broad match from an economic and optimization perspective are [8,15].…”

Section: Related Workmentioning

confidence: 99%

Clustering-Based Bidding Languages for Sponsored Search

Mahdian

Wang

2009

Lecture Notes in Computer Science

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Sponsored search auctions provide a marketplace where advertisers can bid for millions of advertising opportunities to promote their products. The main difficulty facing the advertisers in this market is the complexity of picking and evaluating keywords and phrases to bid on. This is due to the sheer number of possible keywords that the advertisers can bid on, and leads to inefficiencies in the market such as lack of coverage for "rare" keywords. Approaches such as broad matching have been proposed to alleviate this problem. However, as we will observe in this paper, broad matching has undesirable economic properties (such as the non-existence of equilibria) that can make it hard for an advertiser to determine how much to bid for a broad-matched keyword.The main contribution of this paper is to introduce a bidding language for sponsored search auctions based on broad-matching keywords to non-overlapping clusters that greatly simplifies the bidding problem for the advertisers. We investigate the algorithmic problem of computing the optimal clustering given a set of estimated values and give an approximation algorithm for this problem. Furthermore, we present experimental results using real advertisers' data that show that it is possible to extract close to the optimal social welfare with a number of clusters considerably smaller than the number of keywords. This demonstrates the applicability of the clustering scheme and our algorithm in practice.

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“…It is easy to see that no deterministic online algorithm can achieve any bounded competitive ratio [28]. Thus, the existing literature on the online knapsack problem mainly considers restricted variants of the problem [14,20,34] or an average-case analysis of randomized algorithms [28].…”

Section: Introductionmentioning

confidence: 99%

The online knapsack problem: Advice and randomization

Böckenhauer

Komm

Královič

et al. 2014

Theoretical Computer Science

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We study the advice complexity and the random bit complexity of the online knapsack problem. Given a knapsack of unit capacity, and n items that arrive in successive time steps, an online algorithm has to decide for every item whether it gets packed into the knapsack or not. The goal is to maximize the value of the items in the knapsack without exceeding its capacity. In the model of advice complexity of online problems, one asks how many bits of advice about the unknown parts of the input are both necessary and sufficient to achieve a specific competitive ratio. It is well-known that even the unweighted online knapsack problem does not admit any competitive deterministic online algorithm.For this problem, we show that a single bit of advice helps a deterministic online algorithm to become 2-competitive, but that Ω(log n) advice bits are necessary to further improve the deterministic competitive ratio. This is the first time that such a phase transition for the number of advice bits has been observed for any problem. Additionally, we show that, surprisingly, instead of an advice bit, a single random bit allows for a competitive ratio of 2, and any further amount of randomness does not improve this. Moreover, we prove that, in a resource augmentation model, i. e., when allowing the online algorithm to overpack the knapsack by some small amount, a constant number of advice bits suffices to achieve a near-optimal competitive ratio.We also study the weighted version of the problem proving that, with O(log n) bits of advice, we can get arbitrarily close to an optimal solution and, using asymptotically fewer bits, we are not competitive. Furthermore, we show that an arbitrary number of random bits does not permit a constant competitive ratio.

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Budget constrained bidding in keyword auctions and online knapsack problems

Cited by 120 publications

References 4 publications

Optimal Posted Prices for Online Cloud Resource Allocation

Optimal Posted Prices for Online Cloud Resource Allocation

Clustering-Based Bidding Languages for Sponsored Search

The online knapsack problem: Advice and randomization

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