14 Search Results for "Mao, Yuchen"

Document
DOI: 10.4230/LIPIcs.STACS.2026.57
Improving Lagarias-Odlyzko Algorithm for Average-Case Subset Sum: Modular Arithmetic Approach

Authors: Antoine Joux and Karol Węgrzycki

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
Lagarias and Odlyzko (J.ACM 1985) proposed a polynomial-time algorithm for solving "almost all" instances of the Subset Sum problem with n integers of size Ω(Γ_LO), where log₂(Γ_LO) > n² log₂(γ) and γ is a parameter of the lattice basis reduction (γ > √{4/3} for LLL). The algorithm of Lagarias and Odlyzko is a cornerstone of cryptography. However, the theoretical guarantee on the density of feasible instances has remained unimproved for almost 40 years. In this paper, we propose an algorithm that solves "almost all" instances of Subset Sum with integers of size Ω(√{Γ_LO}) after a single call to lattice reduction. Additionally, our approach allows solving the Subset Sum problem for multiple targets, whereas the previous method could handle only one target per call to lattice basis reduction. We introduce a modular arithmetic approach to the Subset Sum problem, leveraging lattice reduction to solve a linear system modulo a suitably large prime. By analyzing the lengths of the LLL-reduced basis vectors of both the primal and dual lattices simultaneously, we show that density guarantees can be improved.
Cite as

Antoine Joux and Karol Węgrzycki. Improving Lagarias-Odlyzko Algorithm for Average-Case Subset Sum: Modular Arithmetic Approach. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 57:1-57:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{joux_et_al:LIPIcs.STACS.2026.57,
  author =	{Joux, Antoine and W\k{e}grzycki, Karol},
  title =	{{Improving Lagarias-Odlyzko Algorithm for Average-Case Subset Sum: Modular Arithmetic Approach}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{57:1--57:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.57},
  URN =		{urn:nbn:de:0030-drops-255462},
  doi =		{10.4230/LIPIcs.STACS.2026.57},
  annote =	{Keywords: Average-Case Analysis, Subset Sum, Lattice Reduction, LLL}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.50
On the PTAS Complexity of Multidimensional Knapsack

Authors: Ilan Doron-Arad, Ariel Kulik, and Pasin Manurangsi

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
We study the d-dimensional knapsack problem. We are given a set of items, each with a d-dimensional cost vector and a profit, along with a d-dimensional budget vector. The goal is to select a set of items that do not exceed the budget in all dimensions and maximize the total profit. A polynomial-time approximation scheme (PTAS) with running time n^{Θ(d/{ε})} has long been known for this problem, where {ε} is the error parameter and n is the encoding size. Despite decades of active research, the best running time of a PTAS has remained O(n^{⌈ d/{ε} ⌉ - d}). Unfortunately, existing lower bounds only cover the special case with two dimensions d = 2, and do not answer whether there is a n^{o(d/({ε)})}-time PTAS for larger values of d. In this work, we show that the running times of the best-known PTAS cannot be improved up to a polylogarithmic factor assuming the Exponential Time Hypothesis (ETH). Our techniques are based on a robust reduction from 2-CSP, which embeds 2-CSP constraints into a desired number of dimensions. Then, using a recent result of [Bafna Karthik and Minzer, STOC'25], we succeed in exhibiting tight trade-off between d and {ε} for all regimes of the parameters assuming d is sufficiently large. Informally, our result also shows that under ETH, for any function f there is no f(d/({ε)}) ⋅ n^{õ(d/({ε)})}-time (1-{ε})-approximation for d-dimensional knapsack, where n is the number of items and õ hides polylogarithmic factors in d/({ε)}.
Cite as

Ilan Doron-Arad, Ariel Kulik, and Pasin Manurangsi. On the PTAS Complexity of Multidimensional Knapsack. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 50:1-50:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{doronarad_et_al:LIPIcs.ITCS.2026.50,
  author =	{Doron-Arad, Ilan and Kulik, Ariel and Manurangsi, Pasin},
  title =	{{On the PTAS Complexity of Multidimensional Knapsack}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{50:1--50:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.50},
  URN =		{urn:nbn:de:0030-drops-253377},
  doi =		{10.4230/LIPIcs.ITCS.2026.50},
  annote =	{Keywords: d-dimensional Knapsack, Multidimensional Knapsack, PTAS, CSP}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.51
Near-Optimal Sparsifiers for Stochastic Knapsack and Assignment Problems

Authors: Shaddin Dughmi, Yusuf Hakan Kalayci, and Xinyu Liu

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
When uncertainty meets costly information gathering, a fundamental question emerges: which data points should we probe to unlock near-optimal solutions? Sparsification of stochastic packing problems addresses this trade-off. The existing notions of sparsification measure the level of sparsity, called degree, as the ratio of queried items to the optimal solution size. While effective for matching and matroid-type problems with uniform structures, this cardinality-based approach fails for knapsack-type constraints where feasible sets exhibit dramatic structural variation. We introduce a polyhedral sparsification framework that measures the degree as the smallest scalar needed to embed the query set within a scaled feasibility polytope, naturally capturing redundancy without relying on cardinality. Our main contribution establishes that knapsack, multiple knapsack, and generalized assignment problems admit (1-ε)-approximate sparsifiers with degree polynomial in 1/p and 1/ε - where p denotes the independent activation probability of each element - remarkably independent of problem dimensions. The key insight involves grouping items with similar weights and deploying a charging argument: when our query set misses an optimal item, we either substitute it directly with a queried item from the same group or leverage that group’s excess contribution to compensate for the loss. This reveals an intriguing complexity-theoretic separation - while the multiple knapsack problem lacks an FPTAS and generalized assignment is APX-hard, their sparsification counterparts admit efficient (1-ε)-approximation algorithms that identify polynomial degree query sets. Finally, we raise an open question: can such sparsification extend to general integer linear programs with degree independent of problem dimensions?
Cite as

Shaddin Dughmi, Yusuf Hakan Kalayci, and Xinyu Liu. Near-Optimal Sparsifiers for Stochastic Knapsack and Assignment Problems. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 51:1-51:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{dughmi_et_al:LIPIcs.ITCS.2026.51,
  author =	{Dughmi, Shaddin and Kalayci, Yusuf Hakan and Liu, Xinyu},
  title =	{{Near-Optimal Sparsifiers for Stochastic Knapsack and Assignment Problems}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{51:1--51:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.51},
  URN =		{urn:nbn:de:0030-drops-253386},
  doi =		{10.4230/LIPIcs.ITCS.2026.51},
  annote =	{Keywords: Packing Problems, Assignment Problems, Stochastic Selection, Sparsification}
}
Document
Research
DOI: 10.4230/TGDK.3.3.4
Mining Inter-Document Argument Structures in Scientific Papers for an Argument Web

Authors: Florian Ruosch, Cristina Sarasua, and Abraham Bernstein

Published in: TGDK, Volume 3, Issue 3 (2025). Transactions on Graph Data and Knowledge, Volume 3, Issue 3

Abstract
In Argument Mining, predicting argumentative relations between texts (or spans) remains one of the most challenging aspects, even more so in the cross-document setting. This paper makes three key contributions to advance research in this domain. We first extend an existing dataset, the Sci-Arg corpus, by annotating it with explicit inter-document argumentative relations, thereby allowing arguments to be distributed over several documents forming an Argument Web; these new annotations are published using Semantic Web technologies (RDF, OWL). Second, we explore and evaluate three automated approaches for predicting these inter-document argumentative relations, establishing critical baselines on the new dataset. We find that a simple classifier based on discourse indicators with access to context outperforms neural methods. Third, we conduct a comparative analysis of these approaches for both intra- and inter-document settings, identifying statistically significant differences in results that indicate the necessity of distinguishing between these two scenarios. Our findings highlight significant challenges in this complex domain and open crucial avenues for future research on the Argument Web of Science, particularly for those interested in leveraging Semantic Web technologies and knowledge graphs to understand scholarly discourse. With this, we provide the first stepping stones in the form of a benchmark dataset, three baseline methods, and an initial analysis for a systematic exploration of this field relevant to the Web of Data and Science.
Cite as

Florian Ruosch, Cristina Sarasua, and Abraham Bernstein. Mining Inter-Document Argument Structures in Scientific Papers for an Argument Web. In Transactions on Graph Data and Knowledge (TGDK), Volume 3, Issue 3, pp. 4:1-4:33, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@Article{ruosch_et_al:TGDK.3.3.4,
  author =	{Ruosch, Florian and Sarasua, Cristina and Bernstein, Abraham},
  title =	{{Mining Inter-Document Argument Structures in Scientific Papers for an Argument Web}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{4:1--4:33},
  ISSN =	{2942-7517},
  year =	{2025},
  volume =	{3},
  number =	{3},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.3.3.4},
  URN =		{urn:nbn:de:0030-drops-252159},
  doi =		{10.4230/TGDK.3.3.4},
  annote =	{Keywords: Argument Mining, Large Language Models, Knowledge Graphs, Link Prediction}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.44
Approximation Schemes for k-Subset Sum Ratio and k-Way Number Partitioning Ratio

Authors: Sotiris Kanellopoulos, Giorgos Mitropoulos, Antonis Antonopoulos, Nikos Leonardos, Aris Pagourtzis, Christos Pergaminelis, Stavros Petsalakis, and Kanellos Tsitouras

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

Abstract
The Subset Sum Ratio problem (SSR) asks, given a multiset A of positive integers, to find two disjoint subsets of A such that the largest-to-smallest ratio of their sums is minimized. In this paper we study the k-version of SSR, namely k-Subset Sum Ratio (k-SSR), which asks to minimize the largest-to-smallest ratio of sums of k disjoint subsets of A. We develop an approximation scheme for k-SSR running in O(n^{2k}/ε^{k-1}) time, where n = |A| and ε is the error parameter. To the best of our knowledge, this is the first FPTAS for k-SSR for fixed k > 2. We also study the k-way Number Partitioning Ratio (k-PART) problem, which differs from k-SSR in that the k subsets must constitute a partition of A; this problem in fact corresponds to the objective of minimizing the largest-to-smallest sum ratio in the family of Multiway Number Partitioning problems. We present a more involved FPTAS for k-PART, also achieving O(n^{2k}/ε^{k-1}) time complexity. Notably, k-PART is also equivalent to the Minimum Envy-Ratio problem with identical valuation functions, which has been studied in the context of fair division of indivisible goods. Thus, for the case of identical valuations, our FPTAS represents a significant improvement over the O(n^{4k²+1}/ε^{2k²}) bound obtained by Nguyen and Rothe’s FPTAS [Trung Thanh Nguyen and Jörg Rothe, 2014] for Minimum Envy-Ratio with general additive valuations. Lastly, we propose a second FPTAS for k-SSR, which employs carefully designed calls to the first one; the new scheme has a time complexity of Õ(n/ε^{3k-1}), thus being much faster when n≫ 1/ ε.
Cite as

Sotiris Kanellopoulos, Giorgos Mitropoulos, Antonis Antonopoulos, Nikos Leonardos, Aris Pagourtzis, Christos Pergaminelis, Stavros Petsalakis, and Kanellos Tsitouras. Approximation Schemes for k-Subset Sum Ratio and k-Way Number Partitioning Ratio. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 44:1-44:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kanellopoulos_et_al:LIPIcs.ISAAC.2025.44,
  author =	{Kanellopoulos, Sotiris and Mitropoulos, Giorgos and Antonopoulos, Antonis and Leonardos, Nikos and Pagourtzis, Aris and Pergaminelis, Christos and Petsalakis, Stavros and Tsitouras, Kanellos},
  title =	{{Approximation Schemes for k-Subset Sum Ratio and k-Way Number Partitioning Ratio}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{44:1--44:22},
  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.2025.44},
  URN =		{urn:nbn:de:0030-drops-249521},
  doi =		{10.4230/LIPIcs.ISAAC.2025.44},
  annote =	{Keywords: Fully polynomial-time approximation schemes, Subset Sum Ratio, Number Partitioning, Fair division, Envy minimization, Pseudo-polynomial time algorithms}
}
Document
Survey
DOI: 10.4230/TGDK.3.2.1
Resilience in Knowledge Graph Embeddings

Authors: Arnab Sharma, N'Dah Jean Kouagou, and Axel-Cyrille Ngonga Ngomo

Published in: TGDK, Volume 3, Issue 2 (2025). Transactions on Graph Data and Knowledge, Volume 3, Issue 2

Abstract
In recent years, knowledge graphs have gained interest and witnessed widespread applications in various domains, such as information retrieval, question-answering, recommendation systems, amongst others. Large-scale knowledge graphs to this end have demonstrated their utility in effectively representing structured knowledge. To further facilitate the application of machine learning techniques, knowledge graph embedding models have been developed. Such models can transform entities and relationships within knowledge graphs into vectors. However, these embedding models often face challenges related to noise, missing information, distribution shift, adversarial attacks, etc. This can lead to sub-optimal embeddings and incorrect inferences, thereby negatively impacting downstream applications. While the existing literature has focused so far on adversarial attacks on KGE models, the challenges related to the other critical aspects remain unexplored. In this paper, we, first of all, give a unified definition of resilience, encompassing several factors such as generalisation, in-distribution generalization, distribution adaption, and robustness. After formalizing these concepts for machine learning in general, we define them in the context of knowledge graphs. To find the gap in the existing works on resilience in the context of knowledge graphs, we perform a systematic survey, taking into account all these aspects mentioned previously. Our survey results show that most of the existing works focus on a specific aspect of resilience, namely robustness. After categorizing such works based on their respective aspects of resilience, we discuss the challenges and future research directions.
Cite as

Arnab Sharma, N'Dah Jean Kouagou, and Axel-Cyrille Ngonga Ngomo. Resilience in Knowledge Graph Embeddings. In Transactions on Graph Data and Knowledge (TGDK), Volume 3, Issue 2, pp. 1:1-1:38, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@Article{sharma_et_al:TGDK.3.2.1,
  author =	{Sharma, Arnab and Kouagou, N'Dah Jean and Ngomo, Axel-Cyrille Ngonga},
  title =	{{Resilience in Knowledge Graph Embeddings}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{1:1--1:38},
  ISSN =	{2942-7517},
  year =	{2025},
  volume =	{3},
  number =	{2},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.3.2.1},
  URN =		{urn:nbn:de:0030-drops-248117},
  doi =		{10.4230/TGDK.3.2.1},
  annote =	{Keywords: Knowledge graphs, Resilience, Robustness}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.86
New Algorithms for Pigeonhole Equal Subset Sum

Authors: Ce Jin, Ryan Williams, and Stan Zhang

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
We study the Pigeonhole Equal Subset Sum problem, which is a total-search variant of the Subset Sum problem introduced by Papadimitriou (1994): we are given a set of n positive integers {w₁,…,w_n} with the additional restriction that ∑_{i=1}^n w_i < 2ⁿ - 1, and want to find two different subsets A,B ⊆ [n] such that ∑_{i∈A} w_i = ∑_{i∈B} w_i. Very recently, Jin and Wu (ICALP 2024) gave a randomized algorithm solving Pigeonhole Equal Subset Sum in O^*(2^{0.4n}) time, beating the classical meet-in-the-middle algorithm with O^*(2^{n/2}) runtime. In this paper, we refine Jin and Wu’s techniques to improve the runtime even further to O^*(2^{n/3}).
Cite as

Ce Jin, Ryan Williams, and Stan Zhang. New Algorithms for Pigeonhole Equal Subset Sum. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 86:1-86:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jin_et_al:LIPIcs.ESA.2025.86,
  author =	{Jin, Ce and Williams, Ryan and Zhang, Stan},
  title =	{{New Algorithms for Pigeonhole Equal Subset Sum}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{86:1--86:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.86},
  URN =		{urn:nbn:de:0030-drops-245541},
  doi =		{10.4230/LIPIcs.ESA.2025.86},
  annote =	{Keywords: pigeonhole principle, subset sums}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.30
Convolution and Knapsack in Higher Dimensions

Authors: Kilian Grage, Klaus Jansen, and Björn Schumacher

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
In the Knapsack problem, one is given the task of packing a knapsack of a given size with items in order to gain a packing with a high profit value. As one of the most classical problems in computer science, research for this problem has gone a long way. One important connection to the (max,+)-convolution problem has been established, where knapsack solutions can be combined by building the convolution of two sequences. This observation has been used in recent years to give conditional lower bounds but also parameterized algorithms. In this paper we carry these results into higher dimensions. We consider Knapsack where items are characterized by multiple properties - given through a vector - and a knapsack that has a capacity vector. The packing must not exceed any of the given capacity constraints. In order to show a similar sub-quadratic lower bound we consider a multidimensional version of (max, +)-convolution. We then consider variants of this problem introduced by Cygan et al. and prove that they are all equivalent in terms of algorithms that allow for a running time sub-quadratic in the number of entries of the array. We further develop a parameterized algorithm to solve higher dimensional Knapsack. The techniques we apply are inspired by an algorithm introduced by Axiotis and Tzamos. We will show that even for higher dimensional Knapsack, we can reduce the problem to convolution on one-dimensional, concave sequences, leading to an 𝒪(dn + dD ⋅ max{(Π_{i=1}^d t_i), t_max log t_max}) algorithm, where D is the number of different weight vectors, t the capacity vector and d is the dimension of the problem. Then, we use the techniques to improve the approach of Eisenbrand and Weismantel to obtain an algorithm for Integer Linear Programming with upper bounds with running time 𝒪(dn) + D ⋅ 𝒪(d Δ)^{d(d+1)} + T_LP. Finally, we give an divide-and-conquer algorithm for ILP with running time n^{d+1} ⋅ O(Δ)^d ⋅ log(|u - 𝓁|_∞).
Cite as

Kilian Grage, Klaus Jansen, and Björn Schumacher. Convolution and Knapsack in Higher Dimensions. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 30:1-30:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{grage_et_al:LIPIcs.WADS.2025.30,
  author =	{Grage, Kilian and Jansen, Klaus and Schumacher, Bj\"{o}rn},
  title =	{{Convolution and Knapsack in Higher Dimensions}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{30:1--30:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.30},
  URN =		{urn:nbn:de:0030-drops-242618},
  doi =		{10.4230/LIPIcs.WADS.2025.30},
  annote =	{Keywords: Knapsack, Convolution, Integer Linear Programming}
}
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.2025.126
ETH-Tight FPT Algorithm for Makespan Minimization on Uniform Machines

Authors: Lars Rohwedder

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

Abstract
Given n jobs with processing times p₁,...,p_n ∈ ℕ and m ≤ n machines with speeds s₁,...,s_m ∈ ℕ our goal is to allocate the jobs to machines minimizing the makespan. We present an algorithm that solves the problem in time p_{max}^{O(d)} ⋅ n, where p_{max} is the maximum processing time and d ≤ p_{max} is the number of distinct processing times. This is essentially the best possible due to a lower bound based on the exponential time hypothesis (ETH). Our result improves over prior works that had a quadratic term in d in the exponent and answers an open question by Koutecký and Zink. The algorithm is based on integer programming techniques combined with novel ideas from modular arithmetic. It can also be implemented efficiently for the more compact high-multiplicity instance encoding.
Cite as

Lars Rohwedder. ETH-Tight FPT Algorithm for Makespan Minimization on Uniform Machines. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 126:1-126:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{rohwedder:LIPIcs.ICALP.2025.126,
  author =	{Rohwedder, Lars},
  title =	{{ETH-Tight FPT Algorithm for Makespan Minimization on Uniform Machines}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{126:1--126:13},
  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.2025.126},
  URN =		{urn:nbn:de:0030-drops-235037},
  doi =		{10.4230/LIPIcs.ICALP.2025.126},
  annote =	{Keywords: Scheduling, Integer Programming}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2025.35
Chain of Grounded Objectives: Concise Goal-Oriented Prompting for Code Generation

Authors: Sangyeop Yeo, Seung-Won Hwang, and Yu-Seung Ma

Published in: LIPIcs, Volume 333, 39th European Conference on Object-Oriented Programming (ECOOP 2025)

Abstract
The use of Large Language Models (LLMs) for code generation has gained significant attention in recent years. Existing methods often aim to improve the quality of generated code by incorporating additional contextual information or guidance into input prompts. Many of these approaches adopt process-oriented reasoning strategies, mimicking human-like step-by-step thinking; however, they may not always align with the structured nature of programming languages. This paper introduces Chain of Grounded Objectives (CGO), a concise goal-oriented prompting approach that embeds functional objectives into prompts to enhance code generation. By focusing on precisely defined objectives rather than explicit procedural steps, CGO aligns more naturally with programming tasks while retaining flexibility. Empirical evaluations on HumanEval, MBPP, their extended versions, and LiveCodeBench show that CGO achieves accuracy comparable to or better than existing methods while using fewer tokens, making it a more efficient approach to LLM-based code generation.
Cite as

Sangyeop Yeo, Seung-Won Hwang, and Yu-Seung Ma. Chain of Grounded Objectives: Concise Goal-Oriented Prompting for Code Generation. In 39th European Conference on Object-Oriented Programming (ECOOP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 333, pp. 35:1-35:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{yeo_et_al:LIPIcs.ECOOP.2025.35,
  author =	{Yeo, Sangyeop and Hwang, Seung-Won and Ma, Yu-Seung},
  title =	{{Chain of Grounded Objectives: Concise Goal-Oriented Prompting for Code Generation}},
  booktitle =	{39th European Conference on Object-Oriented Programming (ECOOP 2025)},
  pages =	{35:1--35:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-373-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{333},
  editor =	{Aldrich, Jonathan and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2025.35},
  URN =		{urn:nbn:de:0030-drops-233271},
  doi =		{10.4230/LIPIcs.ECOOP.2025.35},
  annote =	{Keywords: Artificial Intelligence, Natural Language Processing, Prompt Design, Large Language Models, Code Generation}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.83
Fine-Grained Equivalence for Problems Related to Integer Linear Programming

Authors: Lars Rohwedder and Karol Węgrzycki

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
Integer Linear Programming with n binary variables and m many 0/1-constraints can be solved in time 2^Õ(m²) poly(n) and it is open whether the dependence on m is optimal. Several seemingly unrelated problems, which include variants of Closest String, Discrepancy Minimization, Set Cover, and Set Packing, can be modelled as Integer Linear Programming with 0/1 constraints to obtain algorithms with the same running time for a natural parameter m in each of the problems. Our main result establishes through fine-grained reductions that these problems are equivalent, meaning that a 2^O(m^{2-ε}) poly(n) algorithm with ε > 0 for one of them implies such an algorithm for all of them. In the setting above, one can alternatively obtain an n^O(m) time algorithm for Integer Linear Programming using a straightforward dynamic programming approach, which can be more efficient if n is relatively small (e.g., subexponential in m). We show that this can be improved to {n'}^O(m) + O(nm), where n' is the number of distinct (i.e., non-symmetric) variables. This dominates both of the aforementioned running times.
Cite as

Lars Rohwedder and Karol Węgrzycki. Fine-Grained Equivalence for Problems Related to Integer Linear Programming. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 83:1-83:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{rohwedder_et_al:LIPIcs.ITCS.2025.83,
  author =	{Rohwedder, Lars and W\k{e}grzycki, Karol},
  title =	{{Fine-Grained Equivalence for Problems Related to Integer Linear Programming}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{83:1--83:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.83},
  URN =		{urn:nbn:de:0030-drops-227114},
  doi =		{10.4230/LIPIcs.ITCS.2025.83},
  annote =	{Keywords: Integer Programming, Fine-Grained Complexity, Fixed-Parameter Tractable Algorithms}
}
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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