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Documents authored by Mao, Yuchen

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.51
Weakly Approximating Knapsack in Subquadratic Time

Authors: Lin Chen, Jiayi Lian, Yuchen Mao, and Guochuan Zhang

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We consider the classic Knapsack problem. Let t and OPT be the capacity and the optimal value, respectively. If one seeks a solution with total profit at least OPT/(1 + ε) and total weight at most t, then Knapsack can be solved in Õ(n + (1/(ε))²) time [Chen, Lian, Mao, and Zhang '24][Mao '24]. This running time is the best possible (up to a logarithmic factor), assuming that (min,+)-convolution cannot be solved in truly subquadratic time [Künnemann, Paturi, and Schneider '17][Cygan, Mucha, Węgrzycki, and Włodarczyk '19]. The same upper and lower bounds hold if one seeks a solution with total profit at least OPT and total weight at most (1 + ε)t. Therefore, it is natural to ask the following question. If one seeks a solution with total profit at least OPT/(1+ε) and total weight at most (1 + ε)t, can Knsapck be solved in Õ(n + (1/(ε))^{2-δ}) time for some constant δ > 0? We answer this open question affirmatively by proposing an Õ(n + (1/(ε))^{7/4})-time algorithm.
Cite as

Lin Chen, Jiayi Lian, Yuchen Mao, and Guochuan Zhang. Weakly Approximating Knapsack in Subquadratic Time. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 51:1-51:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chen_et_al:LIPIcs.ICALP.2025.51,
  author =	{Chen, Lin and Lian, Jiayi and Mao, Yuchen and Zhang, Guochuan},
  title =	{{Weakly Approximating Knapsack in Subquadratic Time}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{51:1--51:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.51},
  URN =		{urn:nbn:de:0030-drops-234286},
  doi =		{10.4230/LIPIcs.ICALP.2025.51},
  annote =	{Keywords: Knapsack, FPTAS}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2019.38
Restricted Max-Min Allocation: Approximation and Integrality Gap

Authors: Siu-Wing Cheng and Yuchen Mao

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
Asadpour, Feige, and Saberi proved that the integrality gap of the configuration LP for the restricted max-min allocation problem is at most 4. However, their proof does not give a polynomial-time approximation algorithm. A lot of efforts have been devoted to designing an efficient algorithm whose approximation ratio can match this upper bound for the integrality gap. In ICALP 2018, we present a (6 + delta)-approximation algorithm where delta can be any positive constant, and there is still a gap of roughly 2. In this paper, we narrow the gap significantly by proposing a (4+delta)-approximation algorithm where delta can be any positive constant. The approximation ratio is with respect to the optimal value of the configuration LP, and the running time is poly(m,n)* n^{poly(1/(delta))} where n is the number of players and m is the number of resources. We also improve the upper bound for the integrality gap of the configuration LP to 3 + 21/26 =~ 3.808.
Cite as

Siu-Wing Cheng and Yuchen Mao. Restricted Max-Min Allocation: Approximation and Integrality Gap. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 38:1-38:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{cheng_et_al:LIPIcs.ICALP.2019.38,
  author =	{Cheng, Siu-Wing and Mao, Yuchen},
  title =	{{Restricted Max-Min Allocation: Approximation and Integrality Gap}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{38:1--38:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.38},
  URN =		{urn:nbn:de:0030-drops-106143},
  doi =		{10.4230/LIPIcs.ICALP.2019.38},
  annote =	{Keywords: fair allocation, configuration LP, approximation, integrality gap}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.37
Restricted Max-Min Fair Allocation

Authors: Siu-Wing Cheng and Yuchen Mao

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
The restricted max-min fair allocation problem seeks an allocation of resources to players that maximizes the minimum total value obtained by any player. It is NP-hard to approximate the problem to a ratio less than 2. Comparing the current best algorithm for estimating the optimal value with the current best for constructing an allocation, there is quite a gap between the ratios that can be achieved in polynomial time: 4+delta for estimation and 6 + 2 sqrt{10} + delta ~~ 12.325 + delta for construction, where delta is an arbitrarily small constant greater than 0. We propose an algorithm that constructs an allocation with value within a factor 6 + delta from the optimum for any constant delta > 0. The running time is polynomial in the input size for any constant delta chosen.
Cite as

Siu-Wing Cheng and Yuchen Mao. Restricted Max-Min Fair Allocation. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 37:1-37:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{cheng_et_al:LIPIcs.ICALP.2018.37,
  author =	{Cheng, Siu-Wing and Mao, Yuchen},
  title =	{{Restricted Max-Min Fair Allocation}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{37:1--37:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.37},
  URN =		{urn:nbn:de:0030-drops-90418},
  doi =		{10.4230/LIPIcs.ICALP.2018.37},
  annote =	{Keywords: Fair allocation, approximation, local search}
}
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