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Documents authored by Chen, Guangting

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Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2026.60
Near-Tight Approximation Algorithms for Bottleneck Multiple Knapsack Problems

Authors: Lin Chen, Tingwei Hu, Yuchen Mao, Yong Chen, Lili Mei, An Zhang, Guangting Chen, and Guochuan Zhang

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

Abstract
In the bottleneck multiple knapsack problem, we are given a set of items and a set of knapsacks, where each item has a profit and a weight, and each knapsack has a capacity. Our goal is to assign items to knapsacks so as to maximize the minimum profit received by any knapsack subject to the capacity constraint. When all knapsacks have identical capacity, we give a (2/3 - ε)-approximation algorithm for any constant ε > 0. This result almost matches the (2/3 + ε) inapproximability bound for the bottleneck multiple subset sum problem (Caprara et al., 2000). When the knapsacks can have arbitrary capacities, we propose a (1/2 - ε)-approximation algorithm for any constant ε > 0. We also prove a hardness bound of (1/2 + ε) for any constant ε > 0.
Cite as

Lin Chen, Tingwei Hu, Yuchen Mao, Yong Chen, Lili Mei, An Zhang, Guangting Chen, and Guochuan Zhang. Near-Tight Approximation Algorithms for Bottleneck Multiple Knapsack Problems. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 60:1-60:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chen_et_al:LIPIcs.ICALP.2026.60,
  author =	{Chen, Lin and Hu, Tingwei and Mao, Yuchen and Chen, Yong and Mei, Lili and Zhang, An and Chen, Guangting and Zhang, Guochuan},
  title =	{{Near-Tight Approximation Algorithms for Bottleneck Multiple Knapsack Problems}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{60:1--60:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael 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.2026.60},
  URN =		{urn:nbn:de:0030-drops-264495},
  doi =		{10.4230/LIPIcs.ICALP.2026.60},
  annote =	{Keywords: Bottleneck multiple knapsack, approximation algorithms}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.49
Maximizing Social Welfare Among EF1 Allocations at the Presence of Two Types of Agents

Authors: Jiaxuan Ma, Yong Chen, Guangting Chen, Mingyang Gong, Guohui Lin, and An Zhang

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
We study the fair allocation of indivisible items to n agents to maximize the utilitarian social welfare, where the fairness criterion is envy-free up to one item and there are only two different utility functions shared by the agents. We present a 2-approximation algorithm when the two utility functions are normalized, improving the previous best ratio of 16 √n shown for general normalized utility functions; thus this constant ratio approximation algorithm confirms the APX-completeness in this special case previously shown APX-hard. When there are only three agents, i.e., n = 3, the previous best ratio is 3 shown for general utility functions, and we present an improved and tight 5/3-approximation algorithm when the two utility functions are normalized, and a best possible and tight 2-approximation algorithm when the two utility functions are unnormalized.
Cite as

Jiaxuan Ma, Yong Chen, Guangting Chen, Mingyang Gong, Guohui Lin, and An Zhang. Maximizing Social Welfare Among EF1 Allocations at the Presence of Two Types of Agents. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 49:1-49:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ma_et_al:LIPIcs.ISAAC.2025.49,
  author =	{Ma, Jiaxuan and Chen, Yong and Chen, Guangting and Gong, Mingyang and Lin, Guohui and Zhang, An},
  title =	{{Maximizing Social Welfare Among EF1 Allocations at the Presence of Two Types of Agents}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{49:1--49:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.49},
  URN =		{urn:nbn:de:0030-drops-249570},
  doi =		{10.4230/LIPIcs.ISAAC.2025.49},
  annote =	{Keywords: Fair allocation, utilitarian social welfare, envy-free up to one item, envy-cycle elimination, round robin, approximation algorithm}
}
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