34 Search Results for "Jin, Ce"

Document
DOI: 10.4230/LIPIcs.ESA.2025.51
Quantum Approximate k-Minimum Finding

Authors: Minbo Gao, Zhengfeng Ji, and Qisheng Wang

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

Abstract
Quantum k-minimum finding is a fundamental subroutine with numerous applications in combinatorial problems and machine learning. Previous approaches typically assume oracle access to exact function values, making it challenging to integrate this subroutine with other quantum algorithms. In this paper, we propose an (almost) optimal quantum k-minimum finding algorithm that works with approximate values for all k ≥ 1, extending a result of van Apeldoorn, Gilyén, Gribling, and de Wolf (FOCS 2017) for k = 1. As practical applications, we present efficient quantum algorithms for identifying the k smallest expectation values among multiple observables and for determining the k lowest ground state energies of a Hamiltonian with a known eigenbasis.
Cite as

Minbo Gao, Zhengfeng Ji, and Qisheng Wang. Quantum Approximate k-Minimum Finding. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 51:1-51:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gao_et_al:LIPIcs.ESA.2025.51,
  author =	{Gao, Minbo and Ji, Zhengfeng and Wang, Qisheng},
  title =	{{Quantum Approximate k-Minimum Finding}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{51:1--51:15},
  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.2025.51},
  URN =		{urn:nbn:de:0030-drops-245192},
  doi =		{10.4230/LIPIcs.ESA.2025.51},
  annote =	{Keywords: Quantum Computing, Quantum Algorithms, Quantum Minimum Finding}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.94
Faster Algorithm for Bounded Tree Edit Distance in the Low-Distance Regime

Authors: Tomasz Kociumaka and Ali Shahali

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

Abstract
The tree edit distance is a natural dissimilarity measure between rooted ordered trees whose nodes are labeled over an alphabet Σ. It is defined as the minimum number of node edits - insertions, deletions, and relabelings - required to transform one tree into the other. The weighted variant assigns costs ≥ 1 to edits (based on node labels), minimizing total cost rather than edit count. The unweighted tree edit distance between two trees of total size n can be computed in 𝒪(n^{2.6857}) time; in contrast, determining the weighted tree edit distance is fine-grained equivalent to the All-Pairs Shortest Paths (APSP) problem and requires n³/2^Ω(√{log n}) time [Nogler, Polak, Saha, Vassilevska Williams, Xu, Ye; STOC'25]. These impractical super-quadratic times for large, similar trees motivate the bounded version, parameterizing runtime by the distance k to enable faster algorithms for k ≪ n. Prior algorithms for bounded unweighted edit distance achieve 𝒪(nk²log n) [Akmal & Jin; ICALP’21] and 𝒪(n + k⁷log k) [Das, Gilbert, Hajiaghayi, Kociumaka, Saha; STOC'23]. For weighted, only 𝒪(n + k^{15}) is known [Das, Gilbert, Hajiaghayi, Kociumaka, Saha; STOC'23]. We present an 𝒪(n + k⁶ log k)-time algorithm for bounded tree edit distance in both weighted/unweighted settings. First, we devise a simpler weighted 𝒪(nk² log n)-time algorithm. Next, we exploit periodic structures in input trees via an optimized universal kernel: modifying prior 𝒪(n)-time 𝒪(k⁵)-size kernels to generate such structured instances, enabling efficient analysis.
Cite as

Tomasz Kociumaka and Ali Shahali. Faster Algorithm for Bounded Tree Edit Distance in the Low-Distance Regime. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 94:1-94:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kociumaka_et_al:LIPIcs.ESA.2025.94,
  author =	{Kociumaka, Tomasz and Shahali, Ali},
  title =	{{Faster Algorithm for Bounded Tree Edit Distance in the Low-Distance Regime}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{94:1--94:16},
  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.2025.94},
  URN =		{urn:nbn:de:0030-drops-245634},
  doi =		{10.4230/LIPIcs.ESA.2025.94},
  annote =	{Keywords: tree edit distance, edit distance, kernelization, dynamic programming}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.90
Separating Two Points with Obstacles in the Plane: Improved Upper and Lower Bounds

Authors: Jack Spalding-Jamieson and Anurag Murty Naredla

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

Abstract
Given two points in the plane, and a set of "obstacles" given as curves through the plane with assigned weights, we consider the point-separation problem, which asks for a minimum-weight subset of the obstacles separating the two points. A few computational models for this problem have been previously studied. We give a unified approach to this problem in all models via a reduction to a particular shortest-path problem, and obtain improved running times in essentially all cases. In addition, we also give fine-grained lower bounds for many cases.
Cite as

Jack Spalding-Jamieson and Anurag Murty Naredla. Separating Two Points with Obstacles in the Plane: Improved Upper and Lower Bounds. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 90:1-90:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{spaldingjamieson_et_al:LIPIcs.ESA.2025.90,
  author =	{Spalding-Jamieson, Jack and Naredla, Anurag Murty},
  title =	{{Separating Two Points with Obstacles in the Plane: Improved Upper and Lower Bounds}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{90:1--90:18},
  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.2025.90},
  URN =		{urn:nbn:de:0030-drops-245598},
  doi =		{10.4230/LIPIcs.ESA.2025.90},
  annote =	{Keywords: obstacle separation, point separation, geometric intersection graph, Z₂-homology, fine-grained lower bounds}
}
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/OASIcs.SpaceCHI.2025.6
Toward an Earth-Independent System for EVA Mission Planning: Integrating Physical Models, Domain Knowledge, and Agentic RAG to Provide Explainable LLM-Based Decision Support

Authors: Kaisheng Li and Richard S. Whittle

Published in: OASIcs, Volume 130, Advancing Human-Computer Interaction for Space Exploration (SpaceCHI 2025)

Abstract
We propose a unified framework for an Earth‑independent AI system that provides explainable, context‑aware decision support for EVA mission planning by integrating six core components: a fine‑tuned EVA domain LLM, a retrieval‑augmented knowledge base, a short-term memory store, physical simulation models, an agentic orchestration layer, and a multimodal user interface. To ground our design, we analyze the current roles and substitution potential of the Mission Control Center - identifying which procedural and analytical functions can be automated onboard while preserving human oversight for experiential and strategic tasks. Building on this framework, we introduce RASAGE (Retrieval & Simulation Augmented Guidance Agent for Exploration), a proof‑of‑concept toolset that combines Microsoft Phi‑4‑mini‑instruct with a FAISS (Facebook AI Similarity Search)‑powered EVA knowledge base and custom A* path planning and hypogravity metabolic models to generate grounded, traceable EVA plans. We outline a staged validation strategy to evaluate improvements in route efficiency, metabolic prediction accuracy, anomaly response effectiveness, and crew trust under realistic communication delays. Our findings demonstrate the feasibility of replicating key Mission Control functions onboard, enhancing crew autonomy, reducing cognitive load, and improving safety for deep‑space exploration missions.
Cite as

Kaisheng Li and Richard S. Whittle. Toward an Earth-Independent System for EVA Mission Planning: Integrating Physical Models, Domain Knowledge, and Agentic RAG to Provide Explainable LLM-Based Decision Support. In Advancing Human-Computer Interaction for Space Exploration (SpaceCHI 2025). Open Access Series in Informatics (OASIcs), Volume 130, pp. 6:1-6:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{li_et_al:OASIcs.SpaceCHI.2025.6,
  author =	{Li, Kaisheng and Whittle, Richard S.},
  title =	{{Toward an Earth-Independent System for EVA Mission Planning: Integrating Physical Models, Domain Knowledge, and Agentic RAG to Provide Explainable LLM-Based Decision Support}},
  booktitle =	{Advancing Human-Computer Interaction for Space Exploration (SpaceCHI 2025)},
  pages =	{6:1--6:17},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-384-3},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{130},
  editor =	{Bensch, Leonie and Nilsson, Tommy and Nisser, Martin and Pataranutaporn, Pat and Schmidt, Albrecht and Sumini, Valentina},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.SpaceCHI.2025.6},
  URN =		{urn:nbn:de:0030-drops-239967},
  doi =		{10.4230/OASIcs.SpaceCHI.2025.6},
  annote =	{Keywords: Human-AI Interaction for Space Exploration, Extravehicular Activities, Cognitive load and Human Performance Issues, Human Systems Exploration, Lunar Exploration, LLM}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.42
On the Spectral Expansion of Monotone Subsets of the Hypercube

Authors: Yumou Fei and Renato Ferreira Pinto Jr.

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
We study the spectral gap of subgraphs of the hypercube induced by monotone subsets of vertices. For a monotone subset A ⊆ {0,1}ⁿ of density μ(A), the previous best lower bound on the spectral gap, due to Cohen [Cohen, 2016], was γ ≳ μ(A)/n², improving upon the earlier bound γ ≳ μ(A)²/n² established by Ding and Mossel [Ding and Mossel, 2014]. In this paper, we prove the optimal lower bound γ ≳ μ(A)/n. As a corollary, we improve the mixing time upper bound of the random walk on constant-density monotone sets from O(n³), as shown by Ding and Mossel, to O(n²). Along the way, we develop two new inequalities that may be of independent interest: (1) a directed L²-Poincaré inequality on the hypercube, and (2) an "approximate" FKG inequality for monotone sets.
Cite as

Yumou Fei and Renato Ferreira Pinto Jr.. On the Spectral Expansion of Monotone Subsets of the Hypercube. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 42:1-42:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fei_et_al:LIPIcs.APPROX/RANDOM.2025.42,
  author =	{Fei, Yumou and Ferreira Pinto Jr., Renato},
  title =	{{On the Spectral Expansion of Monotone Subsets of the Hypercube}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{42:1--42:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.42},
  URN =		{urn:nbn:de:0030-drops-244081},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.42},
  annote =	{Keywords: Random walks, mixing time, FKG inequality, Poincar\'{e} inequality, directed isoperimetry}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.4
Streaming Algorithms for Network Design

Authors: Chandra Chekuri, Rhea Jain, Sepideh Mahabadi, and Ali Vakilian

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
We consider the Survivable Network Design problem (SNDP) in the single-pass insertion-only streaming model. The input to SNDP is an edge-weighted graph G = (V, E) and an integer connectivity requirement r(uv) for each u, v ∈ V. The objective is to find a minimum-weight subgraph H ⊆ G such that, for every pair of vertices u, v ∈ V, u and v are r(uv)-edge/vertex-connected. Recent work by [Ce Jin et al., 2024] obtained approximation algorithms for edge-connectivity augmentation, and via that, also derived algorithms for edge-connectivity SNDP (EC-SNDP). In this work we consider vertex-connectivity setting (VC-SNDP) and obtain several results for it as well as improved results for EC-SNDP. - We provide a general framework for solving connectivity problems including SNDP and others in streaming; this is based on a connection to fault-tolerant spanners. For VC-SNDP we provide an O(tk)-approximation in Õ(k^{1-1/t}n^{1 + 1/t}) space, where k is the maximum connectivity requirement, assuming an exact algorithm at the end of the stream. Using a refined LP-based analysis, we provide an O(β t)-approximation where β is the integrality gap of the natural cut-based LP relaxation. These are the first approximation algorithms in the streaming model for VC-SNDP. When applied to the EC-SNDP, our framework provides an O(t)-approximation in Õ(k^{1/2-1/(2t)}n^{1 + 1/t} + kn) space, improving the O(t log k)-approximation of [Ce Jin et al., 2024] using Õ(kn^{1+1/t}) space; this also extends to element-connectivity SNDP. - We consider vertex connectivity-augmentation in the link-arrival model. The input is a k-vertex-connected spanning subgraph G, and additional weighted links L arrive in the stream; the goal is to store the min-weight set of links such that G ∪ L is (k+1)-vertex-connected. We obtain constant-factor approximations in near-linear space for k = 1, 2. Our result for k = 2 is based on using the SPQR tree, a novel application for this well-known representation of 2-connected graphs.
Cite as

Chandra Chekuri, Rhea Jain, Sepideh Mahabadi, and Ali Vakilian. Streaming Algorithms for Network Design. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 4:1-4:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chekuri_et_al:LIPIcs.APPROX/RANDOM.2025.4,
  author =	{Chekuri, Chandra and Jain, Rhea and Mahabadi, Sepideh and Vakilian, Ali},
  title =	{{Streaming Algorithms for Network Design}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{4:1--4:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.4},
  URN =		{urn:nbn:de:0030-drops-243709},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.4},
  annote =	{Keywords: Streaming Algorithms, Survivable Network Design, Fault-Tolerant Spanners}
}
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.2025.110
An Optimal 3-Fault-Tolerant Connectivity Oracle

Authors: Evangelos Kosinas

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

Abstract
We present an optimal oracle for answering connectivity queries in undirected graphs in the presence of at most three vertex failures. Specifically, we show that we can process a graph G in O(n+m) time, in order to build a data structure that occupies O(n) space, which can be used in order to answer queries of the form "given a set F of at most three vertices, and two vertices x and y not in F, are x and y connected in G⧵ F?" in constant time, where n and m denote the number of vertices and edges, respectively, of G. The idea is to rely on the DFS-based framework introduced by Kosinas [ESA'23], for handling connectivity queries in the presence of multiple vertex failures. Our technical contribution is to show how to appropriately extend the toolkit of the DFS-based parameters, in order to optimally handle up to three vertex failures. Our approach has the interesting property that it does not rely on a compact representation of vertex cuts, and has the potential to provide optimal solutions for more vertex failures. Furthermore, we show that the DFS-based framework can be easily extended in order to answer vertex-cut queries, and the number of connected components in the presence of multiple vertex failures. In the case of three vertex failures, we can answer such queries in O(log n) time.
Cite as

Evangelos Kosinas. An Optimal 3-Fault-Tolerant Connectivity Oracle. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 110:1-110:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kosinas:LIPIcs.ICALP.2025.110,
  author =	{Kosinas, Evangelos},
  title =	{{An Optimal 3-Fault-Tolerant Connectivity Oracle}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{110:1--110:20},
  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.2025.110},
  URN =		{urn:nbn:de:0030-drops-234879},
  doi =		{10.4230/LIPIcs.ICALP.2025.110},
  annote =	{Keywords: Graphs, Connectivity, Fault-Tolerant, Oracles}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.64
Fully Scalable MPC Algorithms for Euclidean k-Center

Authors: Artur Czumaj, Guichen Gao, Mohsen Ghaffari, and Shaofeng H.-C. Jiang

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

Abstract
The k-center problem is a fundamental optimization problem with numerous applications in machine learning, data analysis, data mining, and communication networks. The k-center problem has been extensively studied in the classical sequential setting for several decades, and more recently there have been some efforts in understanding the problem in parallel computing, on the Massively Parallel Computation (MPC) model. For now, we have a good understanding of k-center in the case where each local MPC machine has sufficient local memory to store some representatives from each cluster, that is, when one has Ω(k) local memory per machine. While this setting covers the case of small values of k, for a large number of clusters these algorithms require undesirably large local memory, making them poorly scalable. The case of large k has been considered only recently for the fully scalable low-local-memory MPC model for the Euclidean instances of the k-center problem. However, the earlier works have been considering only the constant dimensional Euclidean space, required a super-constant number of rounds, and produced only k(1+o(1)) centers whose cost is a super-constant approximation of k-center. In this work, we significantly improve upon the earlier results for the k-center problem for the fully scalable low-local-memory MPC model. In the low dimensional Euclidean case in ℝ^d, we present the first constant-round fully scalable MPC algorithm for (2+ε)-approximation. We push the ratio further to (1 + ε)-approximation albeit using slightly more (1 + ε)k centers. All these results naturally extends to slightly super-constant values of d. In the high-dimensional regime, we provide the first fully scalable MPC algorithm that in a constant number of rounds achieves an O(log n/ log log n)-approximation for k-center.
Cite as

Artur Czumaj, Guichen Gao, Mohsen Ghaffari, and Shaofeng H.-C. Jiang. Fully Scalable MPC Algorithms for Euclidean k-Center. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 64:1-64:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{czumaj_et_al:LIPIcs.ICALP.2025.64,
  author =	{Czumaj, Artur and Gao, Guichen and Ghaffari, Mohsen and Jiang, Shaofeng H.-C.},
  title =	{{Fully Scalable MPC Algorithms for Euclidean k-Center}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{64:1--64:20},
  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.2025.64},
  URN =		{urn:nbn:de:0030-drops-234416},
  doi =		{10.4230/LIPIcs.ICALP.2025.64},
  annote =	{Keywords: Massively Parallel Computing, Euclidean Spaces, k-Center Clustering}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.9
On the Quantum Time Complexity of Divide and Conquer

Authors: Jonathan Allcock, Jinge Bao, Aleksandrs Belovs, Troy Lee, and Miklos Santha

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

Abstract
In this work, we initiate a systematic study of the time complexity of quantum divide and conquer (QD&C) algorithms for classical problems, and propose a general framework for their analysis. We establish generic conditions under which search and minimization problems with classical divide and conquer algorithms are amenable to quantum speedup, and apply these theorems to various problems involving strings, integers, and geometric objects. These include Longest Distinct Substring, Klee's Coverage, several optimization problems on stock transactions, and k-Increasing Subsequence. For most of these problems our quantum time upper bounds match the quantum query lower bounds, up to polylogarithmic factors. We give a structured framework for describing and classifying a wide variety of QD&C algorithms so that quantum speedups can be more easily identified and applied, and prove general statements on QD&C time complexity covering a range of cases, accounting for the time required for all operations. In particular, we explicitly account for memory access operations in the commonly used QRAM (read-only) and QRAG (read-write) models, which are assumed to take unit time in the query model, and which require careful analysis when involved in recursion. Our generic QD&C theorems have several nice features. 1) To apply them, it suffices to come up with a classical divide and conquer algorithm satisfying the conditions of the theorem. The quantization of the algorithm is then completely handled by the theorem. This can make it easier to find applications which admit a quantum speedup, and contrast with dynamic programming algorithms which can be difficult to quantize due to their highly sequential nature. 2) As these theorems give bounds on time complexity, they can be applied to a greater range of problems than those based on query complexity, e.g., where the best-known quantum algorithms require super-linear time. 3) It can handle minimization problems as well as boolean functions, which allows us to improve on the query complexity result of Childs et al. [Childs et al., 2025] for k-Increasing Subsequence by a logarithmic factor.
Cite as

Jonathan Allcock, Jinge Bao, Aleksandrs Belovs, Troy Lee, and Miklos Santha. On the Quantum Time Complexity of Divide and Conquer. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 9:1-9:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{allcock_et_al:LIPIcs.ICALP.2025.9,
  author =	{Allcock, Jonathan and Bao, Jinge and Belovs, Aleksandrs and Lee, Troy and Santha, Miklos},
  title =	{{On the Quantum Time Complexity of Divide and Conquer}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{9:1--9:20},
  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.2025.9},
  URN =		{urn:nbn:de:0030-drops-233863},
  doi =		{10.4230/LIPIcs.ICALP.2025.9},
  annote =	{Keywords: Quantum Computing, Quantum Algorithms, Divide and Conquer}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.93
On Incremental Approximate Shortest Paths in Directed Graphs

Authors: Adam Górkiewicz and Adam Karczmarz

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

Abstract
In this paper, we show new data structures maintaining approximate shortest paths in sparse directed graphs with polynomially bounded non-negative edge weights under edge insertions. We give more efficient incremental (1+ε)-approximate APSP data structures that work against an adaptive adversary: a deterministic one with Õ(m^{3/2}n^{3/4}) total update time and a randomized one with Õ(m^{4/3}n^{5/6}) total update time. For sparse graphs, these both improve polynomially upon the best-known bound against an adaptive adversary [Karczmarz and Łącki, ESA 2019]. To achieve that, building on the ideas of [Chechik and Zhang, SODA 2021] and [Kyng, Meierhans and Probst Gutenberg, SODA 2022], we show a near-optimal (1+ε)-approximate incremental SSSP data structure for a special case when all edge updates are adjacent to the source, that might be of independent interest. We also describe a very simple and near-optimal offline incremental (1+ε)-approximate SSSP data structure. While online near-linear partially dynamic SSSP data structures have been elusive so far (except for dense instances), our result excludes using certain types of impossibility arguments to rule them out. Additionally, our offline solution leads to near-optimal and deterministic all-pairs bounded-leg shortest paths data structure for sparse graphs.
Cite as

Adam Górkiewicz and Adam Karczmarz. On Incremental Approximate Shortest Paths in Directed Graphs. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 93:1-93:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gorkiewicz_et_al:LIPIcs.ICALP.2025.93,
  author =	{G\'{o}rkiewicz, Adam and Karczmarz, Adam},
  title =	{{On Incremental Approximate Shortest Paths in Directed Graphs}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{93:1--93:20},
  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.2025.93},
  URN =		{urn:nbn:de:0030-drops-234700},
  doi =		{10.4230/LIPIcs.ICALP.2025.93},
  annote =	{Keywords: dynamic shortest paths, incremental shortest paths, offline dynamic algorithms}
}
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.SoCG.2025.51
Quantum Combine and Conquer and Its Applications to Sublinear Quantum Convex Hull and Maxima Set Construction

Authors: Shion Fukuzawa, Michael T. Goodrich, and Sandy Irani

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
We introduce a quantum algorithm design paradigm called combine and conquer, which is a quantum version of the "marriage-before-conquest" technique of Kirkpatrick and Seidel. In a quantum combine-and-conquer algorithm, one performs the essential computation of the combine step of a quantum divide-and-conquer algorithm prior to the conquer step while avoiding recursion. This model is better suited for the quantum setting, due to its non-recursive nature. We show the utility of this approach by providing quantum algorithms for 2D maxima set and convex hull problems for sorted point sets running in Õ(√{nh}) time, w.h.p., where h is the size of the output.
Cite as

Shion Fukuzawa, Michael T. Goodrich, and Sandy Irani. Quantum Combine and Conquer and Its Applications to Sublinear Quantum Convex Hull and Maxima Set Construction. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 51:1-51:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fukuzawa_et_al:LIPIcs.SoCG.2025.51,
  author =	{Fukuzawa, Shion and Goodrich, Michael T. and Irani, Sandy},
  title =	{{Quantum Combine and Conquer and Its Applications to Sublinear Quantum Convex Hull and Maxima Set Construction}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{51:1--51:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.51},
  URN =		{urn:nbn:de:0030-drops-232035},
  doi =		{10.4230/LIPIcs.SoCG.2025.51},
  annote =	{Keywords: quantum computing, computational geometry, divide and conquer, convex hulls, maxima sets}
}
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