Online Competitive Algorithms for Maximizing Weighted Throughput of Unit Jobs

Bartal, Yair; Chin, F.; Chrobák, Marek; Fung, Stanley P. Y.; Jawor, Wojciech; Lavi, Ron; Sgall, Jiřį́; Tichý, Tomáš

doi:10.1007/978-3-540-24749-4_17

Cited by 34 publications

(36 citation statements)

References 6 publications

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“…Using the above characterization, it is possible to prove that the greedy algorithm is monotone [7] (see Section 2.4 for a description). Together with the result of [8], this gives a truthful mechanism that is 1 2 competitive. However, a closer look at this mechanism may make one wonder if it is indeed applicable.…”

Section: The Value-only Model: Is Monotonicity Enough?mentioning

confidence: 90%

“…We show that this is the best possible by proving that no prompt deterministic mechanism can guarantee a competitive ratio better than 1 2 . We also present a randomized mechanism that guarantees a constant competitive ratio.…”

Section: Definition 11 We Say That a Mechanism For The Scheduling Prmentioning

confidence: 95%

“…No truthful randomized mechanism for the scheduling problem in the generalized model can obtain a competitive ratio better than 1 2 .…”

Section: Theoremmentioning

confidence: 99%

“…In the non-strategic setting, this problem and its variants have been widely studied (e.g., [1,8,3]). The best deterministic algorithm to date guarantees a competitive ratio of ≈ 0.547 [4,11], while it is known that no deterministic algorithm can obtain a ratio better than 2 √ 5+1 ≈ 0.618 [2].…”

Section: Introductionmentioning

confidence: 99%

“…The best deterministic algorithm to date guarantees a competitive ratio of ≈ 0.547 [4,11], while it is known that no deterministic algorithm can obtain a ratio better than 2 √ 5+1 ≈ 0.618 [2]. In the randomized setting, a competitive ratio of 1 − 1 e is achieved by [1], and no algorithm can achieve a ratio better than 0.8 [2]. This scheduling problem provides an excellent example of the extra barriers we face when designing online mechanisms.…”

Section: Introductionmentioning

confidence: 99%

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Prompt Mechanisms for Online Auctions

Cole

Dobzinski

Fleischer

2008

Algorithmic Game Theory

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We study the following online problem: at each time unit, one of m identical items is offered for sale. Bidders arrive and depart dynamically, and each bidder is interested in winning one item between his arrival and departure. Our goal is to design truthful mechanisms that maximize the welfare, the sum of the utilities of winning bidders.We first consider this problem under the assumption that the private information for each bidder is his value for getting an item. In this model constant-competitive mechanisms are known, but we observe that these mechanisms suffer from the following disadvantage: a bidder might learn his payment only when he departs. We argue that these mechanism are essentially unusable, because they impose several seemingly undesirable requirements on any implementation of the mechanisms.To crystalize these issues, we define the notions of prompt and tardy mechanisms. We present two prompt truthful mechanisms -one deterministic and the other randomized, that guarantee a constant competitive ratio. We also prove that our deterministic mechanism is optimal for this setting.We then study a model in which both the value and the departure time are private information. While in the deterministic setting only a trivial competitive ratio can be guaranteed, we use randomization to obtain a prompt truthful Θ( 1 log m )-competitive mechanism. Finally, we show that no truthful randomized mechanism can achieve a ratio better than 1 2 in this model.

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Section: The Value-only Model: Is Monotonicity Enough?mentioning

confidence: 90%

Section: Definition 11 We Say That a Mechanism For The Scheduling Prmentioning

confidence: 95%

“…No truthful randomized mechanism for the scheduling problem in the generalized model can obtain a competitive ratio better than 1 2 .…”

Section: Theoremmentioning

confidence: 99%