New Bounds for Truthful Scheduling on Two Unrelated Selfish Machines

Kuryatnikova, Olga; Vera, Juan C.

doi:10.1007/s00224-019-09927-x

Cited by 4 publications

(2 citation statements)

References 30 publications

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“…In particular, when the valuations are submodular (and not just additive), Christodoulou, Kotsoupias, and Kovacs obtain a lower bound of Ω( √ n) [5]. Many papers also considered randomized and fractional versions of the problem [3,4,[13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Improved Lower Bounds for Truthful Scheduling

Dobzinski¹,

Shaulker²

2023

Preprint

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The problem of scheduling unrelated machines by a truthful mechanism to minimize the makespan was introduced in the seminal "Algorithmic Mechanism Design" paper by Nisan and Ronen. Nisan and Ronen showed that there is a truthful mechanism that provides an approximation ratio of min(m, n), where n is the number of machines and m is the number of jobs. They also proved that no truthful mechanism can provide an approximation ratio better than 2. Since then, the lower bound was improved to 1 + √2 ≈ 2.41 by Christodoulou, Kotsoupias, and Vidali, and then to 1 + Φ ≈ 2.618 by Kotsoupias and Vidali. The lower bound was improved to 2.755 by Giannakopoulos, Hammerl, and Pocas. In this paper we further improve the bound to 3-δ, for every constant δ > 0. Note that a gap between the upper bound and the lower bounds exists even when the number of machines and jobs is very small. In particular, the known 1 + √2 lower bound requires at least 3 machines and 5 jobs. In contrast, we show a lower bound of 2.2055 that uses only 3 machines and 3 jobs and a lower bound of 1 + √2 that uses only 3 machines and 4 jobs. For the case of two machines and two jobs we show a lower bound of 2. Similar bounds for two machines and two jobs were known before but only via complex proofs that characterized all truthful mechanisms that provide a finite approximation ratio in this setting, whereas our new proof uses a simple and direct approach.

show abstract

Section: Introductionmentioning

confidence: 99%

Improved Lower Bounds for Truthful Scheduling

Dobzinski¹,

Shaulker²

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Many papers also considered randomized and fractional versions of the problem [16,15,17,14,13,12,3,11,4].…”

Section: Introductionmentioning

confidence: 99%

Improved Lower Bounds for Truthful Scheduling

Dobzinski¹,

Shaulker²

2020

Preprint

View full text Add to dashboard Cite

The problem of scheduling unrelated machines by a truthful mechanism to minimize the makespan was introduced in the seminal "Algorithmic Mechanism Design" paper by Nisan and Ronen. Nisan and Ronen showed that there is a truthful mechanism that provides an approximation ratio of min(m, n), where n is the number of machines and m is the number of jobs. They also proved that no truthful mechanism can provide an approximation ratio better than 2. Since then, the lower bound was improved to 1 + √ 2 ≈ 2.41 by Christodoulou, Kotsoupias, and Vidali, and then to 1 + φ ≈ 2.618 by Kotsoupias and Vidali. Very recently, the lower bound was improved to 2.755 by Giannakopoulos, Hammerl, and Pocas. In this paper we further improve the bound to 2.8019.Note that a gap between the upper bound and the lower bounds exists even when the number of machines and jobs is very small. In particular, the known 1 + √ 2 lower bound requires at least 3 machines and 5 jobs. In contrast, we show a lower bound of 2.2055 that uses only 3 machines and 3 jobs and a lower bound of 1 + √ 2 that uses only 3 machines and 4 jobs. For the case of two machines and two jobs we show a lower bound of 2. Similar bounds for two machines and two jobs were known before but only via complex proofs that characterized all truthful mechanisms that provide a finite approximation ratio in this setting, whereas our new proof uses a simple and direct approach.

show abstract