2 Search Results for "Zhang, Jie"

Document
DOI: 10.4230/LIPIcs.MFCS.2018.24
Hardness Results for Consensus-Halving

Authors: Aris Filos-Ratsikas, Søren Kristoffer Stiil Frederiksen, Paul W. Goldberg, and Jie Zhang

Published in: LIPIcs, Volume 117, 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)

Abstract
The Consensus-halving problem is the problem of dividing an object into two portions, such that each of n agents has equal valuation for the two portions. We study the epsilon-approximate version, which allows each agent to have an epsilon discrepancy on the values of the portions. It was recently proven in [Filos-Ratsikas and Goldberg, 2018] that the problem of computing an epsilon-approximate Consensus-halving solution (for n agents and n cuts) is PPA-complete when epsilon is inverse-exponential. In this paper, we prove that when epsilon is constant, the problem is PPAD-hard and the problem remains PPAD-hard when we allow a constant number of additional cuts. Additionally, we prove that deciding whether a solution with n-1 cuts exists for the problem is NP-hard.
Cite as

Aris Filos-Ratsikas, Søren Kristoffer Stiil Frederiksen, Paul W. Goldberg, and Jie Zhang. Hardness Results for Consensus-Halving. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 24:1-24:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{filosratsikas_et_al:LIPIcs.MFCS.2018.24,
  author =	{Filos-Ratsikas, Aris and Frederiksen, S{\o}ren Kristoffer Stiil and Goldberg, Paul W. and Zhang, Jie},
  title =	{{Hardness Results for Consensus-Halving}},
  booktitle =	{43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
  pages =	{24:1--24:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Potapov, Igor and Spirakis, Paul and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.24},
  URN =		{urn:nbn:de:0030-drops-96069},
  doi =		{10.4230/LIPIcs.MFCS.2018.24},
  annote =	{Keywords: PPAD, PPA, consensus halving, generalized-circuit, reduction}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2017.16
Smoothed and Average-Case Approximation Ratios of Mechanisms: Beyond the Worst-Case Analysis

Authors: Xiaotie Deng, Yansong Gao, and Jie Zhang

Published in: LIPIcs, Volume 83, 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)

Abstract
The approximation ratio has become one of the dominant measures in mechanism design problems. In light of analysis of algorithms, we define the smoothed approximation ratio to compare the performance of the optimal mechanism and a truthful mechanism when the inputs are subject to random perturbations of the worst-case inputs, and define the average-case approximation ratio to compare the performance of these two mechanisms when the inputs follow a distribution. For the one-sided matching problem, Filos-Ratsikas et al. [2014] show that, amongst all truthful mechanisms, random priority achieves the tight approximation ratio bound of Theta(sqrt{n}). We prove that, despite of this worst-case bound, random priority has a constant smoothed approximation ratio. This is, to our limited knowledge, the first work that asymptotically differentiates the smoothed approximation ratio from the worst-case approximation ratio for mechanism design problems. For the average-case, we show that our approximation ratio can be improved to 1+e. These results partially explain why random priority has been successfully used in practice, although in the worst case the optimal social welfare is Theta(sqrt{n}) times of what random priority achieves. These results also pave the way for further studies of smoothed and average-case analysis for approximate mechanism design problems, beyond the worst-case analysis.
Cite as

Xiaotie Deng, Yansong Gao, and Jie Zhang. Smoothed and Average-Case Approximation Ratios of Mechanisms: Beyond the Worst-Case Analysis. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 16:1-16:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

Copy BibTex To Clipboard

@InProceedings{deng_et_al:LIPIcs.MFCS.2017.16,
  author =	{Deng, Xiaotie and Gao, Yansong and Zhang, Jie},
  title =	{{Smoothed and Average-Case Approximation Ratios of Mechanisms: Beyond the Worst-Case Analysis}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{16:1--16:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-046-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{83},
  editor =	{Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean-Francois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.16},
  URN =		{urn:nbn:de:0030-drops-80936},
  doi =		{10.4230/LIPIcs.MFCS.2017.16},
  annote =	{Keywords: mechanism design, approximation ratio, smoothed analysis, average-case analysis}
}
  • Refine by Author
  • 2 Zhang, Jie
  • 1 Deng, Xiaotie
  • 1 Filos-Ratsikas, Aris
  • 1 Frederiksen, Søren Kristoffer Stiil
  • 1 Gao, Yansong
  • Show More...

  • Refine by Classification
  • 1 Theory of computation → Problems, reductions and completeness

  • Refine by Keyword
  • 1 PPA
  • 1 PPAD
  • 1 approximation ratio
  • 1 average-case analysis
  • 1 consensus halving
  • Show More...

  • Refine by Type
  • 2 document

  • Refine by Publication Year
  • 1 2017
  • 1 2018

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact