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Documents authored by Li, Yaqiao

Document
DOI: 10.4230/LIPIcs.SWAT.2024.16
On the Online Weighted Non-Crossing Matching Problem

Authors: Joan Boyar, Shahin Kamali, Kim S. Larsen, Ali Mohammad Lavasani, Yaqiao Li, and Denis Pankratov

Published in: LIPIcs, Volume 294, 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024)

Abstract
We introduce and study the weighted version of an online matching problem in the Euclidean plane with non-crossing constraints: 2n points with non-negative weights arrive online, and an algorithm can match an arriving point to one of the unmatched previously arrived points. In the vanilla model, the decision on how to match (if at all) a newly arriving point is irrevocable. The goal is to maximize the total weight of matched points under the constraint that straight-line segments corresponding to the edges of the matching do not intersect. The unweighted version of the problem was introduced in the offline setting by Atallah in 1985, and this problem became a subject of study in the online setting with and without advice in several recent papers. We observe that deterministic online algorithms cannot guarantee a non-trivial competitive ratio for the weighted problem. We study various regimes of the problem which permit non-trivial online algorithms. In particular, when weights are restricted to the interval [1, U] we give a deterministic algorithm achieving competitive ratio Ω(2^{-2√{log U}}). We also prove that deterministic online algorithms cannot achieve competitive ratio better than O (2^{-√{log U}}). Interestingly, we establish that randomization alone suffices to achieve competitive ratio 1/3 even when there are no restrictions on the weights. Additionally, if one allows an online algorithm to revoke acceptances, then one can achieve a competitive ratio ≈ 0.2862 deterministically for arbitrary weights. We also establish a lower bound on the competitive ratio of randomized algorithms in the unweighted setting, and improve the best-known bound on advice complexity to achieve a perfect matching.
Cite as

Joan Boyar, Shahin Kamali, Kim S. Larsen, Ali Mohammad Lavasani, Yaqiao Li, and Denis Pankratov. On the Online Weighted Non-Crossing Matching Problem. In 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 294, pp. 16:1-16:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{boyar_et_al:LIPIcs.SWAT.2024.16,
  author =	{Boyar, Joan and Kamali, Shahin and Larsen, Kim S. and Lavasani, Ali Mohammad and Li, Yaqiao and Pankratov, Denis},
  title =	{{On the Online Weighted Non-Crossing Matching Problem}},
  booktitle =	{19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024)},
  pages =	{16:1--16:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-318-8},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{294},
  editor =	{Bodlaender, Hans L.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2024.16},
  URN =		{urn:nbn:de:0030-drops-200567},
  doi =		{10.4230/LIPIcs.SWAT.2024.16},
  annote =	{Keywords: Online algorithms, weighted matching problem, Euclidean plane, non-crossing constraints, competitive analysis, randomized online algorithms, online algorithms with advice, online algorithms with revoking}
}
Document
DOI: 10.4230/LIPIcs.CCC.2017.16
Trading Information Complexity for Error

Authors: Yuval Dagan, Yuval Filmus, Hamed Hatami, and Yaqiao Li

Published in: LIPIcs, Volume 79, 32nd Computational Complexity Conference (CCC 2017)

Abstract
We consider the standard two-party communication model. The central problem studied in this article is how much can one save in information complexity by allowing a certain error. * For arbitrary functions, we obtain lower bounds and upper bounds indicating a gain that is of order Omega(h(epsilon)) and O(h(sqrt{epsilon})). Here h denotes the binary entropy function. * We analyze the case of the two-bit AND function in detail to show that for this function the gain is Theta(h(epsilon)). This answers a question of Braverman et al. [Braverman, STOC 2013]. * We obtain sharp bounds for the set disjointness function of order n. For the case of the distributional error, we introduce a new protocol that achieves a gain of Theta(sqrt{h(epsilon)}) provided that n is sufficiently large. We apply these results to answer another of question of Braverman et al. regarding the randomized communication complexity of the set disjointness function. * Answering a question of Braverman [Braverman, STOC 2012], we apply our analysis of the set disjointness function to establish a gap between the two different notions of the prior-free information cost. In light of [Braverman, STOC 2012], this implies that amortized randomized communication complexity is not necessarily equal to the amortized distributional communication complexity with respect to the hardest distribution. As a consequence, we show that the epsilon-error randomized communication complexity of the set disjointness function of order n is n[C_{DISJ} - Theta(h(epsilon))] + o(n), where C_{DISJ} ~ 0.4827$ is the constant found by Braverman et al. [Braverman, STOC 2012].
Cite as

Yuval Dagan, Yuval Filmus, Hamed Hatami, and Yaqiao Li. Trading Information Complexity for Error. In 32nd Computational Complexity Conference (CCC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 79, pp. 16:1-16:59, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{dagan_et_al:LIPIcs.CCC.2017.16,
  author =	{Dagan, Yuval and Filmus, Yuval and Hatami, Hamed and Li, Yaqiao},
  title =	{{Trading Information Complexity for Error}},
  booktitle =	{32nd Computational Complexity Conference (CCC 2017)},
  pages =	{16:1--16:59},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-040-8},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{79},
  editor =	{O'Donnell, Ryan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2017.16},
  URN =		{urn:nbn:de:0030-drops-75179},
  doi =		{10.4230/LIPIcs.CCC.2017.16},
  annote =	{Keywords: communication complexity, information complexity}
}
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