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DOI: 10.4230/TGDK.3.1.4
CoaKG: A Contextualized Knowledge Graph Approach for Exploratory Search and Decision Making

Authors: Veronica dos Santos, Daniel Schwabe, Altigran Soares da Silva, and Sérgio Lifschitz

Published in: TGDK, Volume 3, Issue 1 (2025). Transactions on Graph Data and Knowledge, Volume 3, Issue 1

Abstract
In decision-making scenarios, an information need arises due to a knowledge gap when a decision-maker needs more knowledge to make a decision. Users may take the initiative to acquire knowledge to fill this gap through exploratory search approaches using Knowledge Graphs (KGs) as information sources, but their queries can be incomplete, inaccurate, and ambiguous. Although KGs have great potential for exploratory search, they are incomplete by nature. Besides, for both Crowd-sourced KGs and KGs constructed by integrating several different information sources of varying quality to be effectively consumed, there is a need for a Trust Layer. Our research aims to enrich and allow querying KGs to support context-aware exploration in decision-making scenarios. We propose a layered architecture for Context Augmented Knowledge Graphs-based Decision Support Systems with a Knowledge Layer that operates under a Dual Open World Assumption (DOWA). Under DOWA, the evaluation of the truthfulness of the information obtained from KGs depends on the context of its claims and the tasks carried out or intended (purpose). The Knowledge Layer comprises a Context Augmented KG (CoaKG) and a CoaKG Query Engine. The CoaKG contains contextual mappings to identify explicit context and rules to infer implicit context. The CoaKG Query Engine is designed as a query-answering approach that retrieves all contextualized answers from the CoaKG. A Proof of Concept (PoC) based on Wikidata was developed to evaluate the effectiveness of the Knowledge Layer.
Cite as

Veronica dos Santos, Daniel Schwabe, Altigran Soares da Silva, and Sérgio Lifschitz. CoaKG: A Contextualized Knowledge Graph Approach for Exploratory Search and Decision Making. In Transactions on Graph Data and Knowledge (TGDK), Volume 3, Issue 1, pp. 4:1-4:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@Article{dossantos_et_al:TGDK.3.1.4,
  author =	{dos Santos, Veronica and Schwabe, Daniel and da Silva, Altigran Soares and Lifschitz, S\'{e}rgio},
  title =	{{CoaKG: A Contextualized Knowledge Graph Approach for Exploratory Search and Decision Making}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{4:1--4:27},
  ISSN =	{2942-7517},
  year =	{2025},
  volume =	{3},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.3.1.4},
  URN =		{urn:nbn:de:0030-drops-236685},
  doi =		{10.4230/TGDK.3.1.4},
  annote =	{Keywords: Knowledge Graphs, Context Search, Decision Support}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.19
Dynamic Algorithms for Submodular Matching

Authors: Kiarash Banihashem, Leyla Biabani, Samira Goudarzi, MohammadTaghi Hajiaghayi, Peyman Jabbarzade, and Morteza Monemizadeh

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

Abstract
The Maximum Submodular Matching (MSM) problem is a generalization of the classical Maximum Weight Matching (MWM) problem. In this problem, given a monotone submodular function f: 2^E → ℝ^{≥ 0} defined over subsets of edges of a graph G(V, E), we are asked to return a matching whose submodular value is maximum among all matchings in graph G(V, E). In this paper, we consider this problem in a fully dynamic setting against an oblivious adversary. In this setting, we are given a sequence 𝒮 of insertions and deletions of edges of the underlying graph G(V, E), along with an oracle access to the monotone submodular function f. The goal is to maintain a matching M such that, at any time t of sequence 𝒮, its submodular value is a good approximation of the value of the optimal submodular matching while keeping the number of operations minimal. We develop the first dynamic algorithm for the submodular matching problem, in which we maintain a matching whose submodular value is within expected (8 + ε)-approximation of the optimal submodular matching at any time t of sequence 𝒮 using expected amortized poly(log n, 1/(ε)) update time. Our approach incorporates a range of novel techniques, notably the concept of Uniform Hierarchical Caches (UHC) data structure along with its invariants, which lead to the first algorithm for fully dynamic submodular matching and may be of independent interest for designing dynamic algorithms for other problems.
Cite as

Kiarash Banihashem, Leyla Biabani, Samira Goudarzi, MohammadTaghi Hajiaghayi, Peyman Jabbarzade, and Morteza Monemizadeh. Dynamic Algorithms for Submodular Matching. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 19:1-19:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{banihashem_et_al:LIPIcs.ICALP.2025.19,
  author =	{Banihashem, Kiarash and Biabani, Leyla and Goudarzi, Samira and Hajiaghayi, MohammadTaghi and Jabbarzade, Peyman and Monemizadeh, Morteza},
  title =	{{Dynamic Algorithms for Submodular Matching}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{19:1--19:21},
  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.2025.19},
  URN =		{urn:nbn:de:0030-drops-233969},
  doi =		{10.4230/LIPIcs.ICALP.2025.19},
  annote =	{Keywords: Matching, Submodular, Dynamic, Polylogarithmic}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.18
q-Partitioning Valuations: Exploring the Space Between Subadditive and Fractionally Subadditive Valuations

Authors: Kiril Bangachev and S. Matthew Weinberg

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

Abstract
For a set M of m elements, we define a decreasing chain of classes of normalized monotone-increasing valuation functions from 2^M to ℝ_{≥ 0}, parameterized by an integer q ∈ [2,m]. For a given q, we refer to the class as q-partitioning. A valuation function is subadditive if and only if it is 2-partitioning, and fractionally subadditive if and only if it is m-partitioning. Thus, our chain establishes an interpolation between subadditive and fractionally subadditive valuations. We show that this interpolation is smooth (q-partitioning valuations are "nearly" (q-1)-partitioning in a precise sense, Theorem 6), interpretable (the definition arises by analyzing the core of a cost-sharing game, à la the Bondareva-Shapley Theorem for fractionally subadditive valuations, Section 3.1), and non-trivial (the class of q-partitioning valuations is distinct for all q, Proposition 3). For domains where provable separations exist between subadditive and fractionally subadditive, we interpolate the stronger guarantees achievable for fractionally subadditive valuations to all q ∈ {2,…, m}. Two highlights are the following: 1) An Ω ((log log q)/(log log m))-competitive posted price mechanism for q-partitioning valuations. Note that this matches asymptotically the state-of-the-art for both subadditive (q = 2) [Paul Dütting et al., 2020], and fractionally subadditive (q = m) [Feldman et al., 2015]. 2) Two upper-tail concentration inequalities on 1-Lipschitz, q-partitioning valuations over independent items. One extends the state-of-the-art for q = m to q < m, the other improves the state-of-the-art for q = 2 for q > 2. Our concentration inequalities imply several corollaries that interpolate between subadditive and fractionally subadditive, for example: 𝔼[v(S)] ≤ (1 + 1/log q)Median[v(S)] + O(log q). To prove this, we develop a new isoperimetric inequality using Talagrand’s method of control by q points, which may be of independent interest. We also discuss other probabilistic inequalities and game-theoretic applications of q-partitioning valuations, and connections to subadditive MPH-k valuations [Tomer Ezra et al., 2019].
Cite as

Kiril Bangachev and S. Matthew Weinberg. q-Partitioning Valuations: Exploring the Space Between Subadditive and Fractionally Subadditive Valuations. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 18:1-18:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bangachev_et_al:LIPIcs.ICALP.2025.18,
  author =	{Bangachev, Kiril and Weinberg, S. Matthew},
  title =	{{q-Partitioning Valuations: Exploring the Space Between Subadditive and Fractionally Subadditive Valuations}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{18:1--18:20},
  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.2025.18},
  URN =		{urn:nbn:de:0030-drops-233956},
  doi =		{10.4230/LIPIcs.ICALP.2025.18},
  annote =	{Keywords: Subadditive Functions, Fractionally Subadditive Functions, Posted Price Mechanisms, Concentration Inequalities}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.16
Shared Randomness Helps with Local Distributed Problems

Authors: Alkida Balliu, Mohsen Ghaffari, Fabian Kuhn, Augusto Modanese, Dennis Olivetti, Mikaël Rabie, Jukka Suomela, and Jara Uitto

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

Abstract
By prior work, we have many wonderful results related to distributed graph algorithms for problems that can be defined with local constraints; the formal framework used in prior work is locally checkable labeling problems (LCLs), introduced by Naor and Stockmeyer in the 1990s. It is known, for example, that if we have a deterministic algorithm that solves an LCL in o(log n) rounds, we can speed it up to O(log^* n) rounds, and if we have a randomized algorithm that solves an LCL in O(log^* n) rounds, we can derandomize it for free. It is also known that randomness helps with some LCL problems: there are LCL problems with randomized complexity Θ(log log n) and deterministic complexity Θ(log n). However, so far there have not been any LCL problems in which the use of shared randomness has been necessary; in all prior algorithms it has been enough that the nodes have access to their own private sources of randomness. Could it be the case that shared randomness never helps with LCLs? Could we have a general technique that takes any distributed graph algorithm for any LCL that uses shared randomness, and turns it into an equally fast algorithm where private randomness is enough? In this work we show that the answer is no. We present an LCL problem Π such that the round complexity of Π is Ω(√n) in the usual randomized LOCAL model (with private randomness), but if the nodes have access to a source of shared randomness, then the complexity drops to O(log n). As corollaries, we also resolve several other open questions related to the landscape of distributed computing in the context of LCL problems. In particular, problem Π demonstrates that distributed quantum algorithms for LCL problems strictly benefit from a shared quantum state. Problem Π also gives a separation between finitely dependent distributions and non-signaling distributions.
Cite as

Alkida Balliu, Mohsen Ghaffari, Fabian Kuhn, Augusto Modanese, Dennis Olivetti, Mikaël Rabie, Jukka Suomela, and Jara Uitto. Shared Randomness Helps with Local Distributed Problems. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{balliu_et_al:LIPIcs.ICALP.2025.16,
  author =	{Balliu, Alkida and Ghaffari, Mohsen and Kuhn, Fabian and Modanese, Augusto and Olivetti, Dennis and Rabie, Mika\"{e}l and Suomela, Jukka and Uitto, Jara},
  title =	{{Shared Randomness Helps with Local Distributed Problems}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{16:1--16:18},
  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.2025.16},
  URN =		{urn:nbn:de:0030-drops-233931},
  doi =		{10.4230/LIPIcs.ICALP.2025.16},
  annote =	{Keywords: Distributed computing, locally checkable labelings, shared randomness}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.17
Robust Contraction Decomposition for Minor-Free Graphs and Its Applications

Authors: Sayan Bandyapadhyay, William Lochet, Daniel Lokshtanov, Dániel Marx, Pranabendu Misra, Daniel Neuen, Saket Saurabh, Prafullkumar Tale, and Jie Xue

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

Abstract
We prove a robust contraction decomposition theorem for H-minor-free graphs, which states that given an H-minor-free graph G and an integer p, one can partition in polynomial time the vertices of G into p sets Z₁,… ,Z_p such that tw(G/(Z_i ⧵ Z')) = O(p + |Z'|) for all i ∈ [p] and Z' ⊆ Z_i. Here, tw(⋅) denotes the treewidth of a graph and G/(Z_i ⧵ Z') denotes the graph obtained from G by contracting all edges with both endpoints in Z_i ⧵ Z'. Our result generalizes earlier results by Klein [SICOMP 2008] and Demaine et al. [STOC 2011] based on partitioning E(G), and some recent theorems for planar graphs by Marx et al. [SODA 2022], for bounded-genus graphs (more generally, almost-embeddable graphs) by Bandyapadhyay et al. [SODA 2022], and for unit-disk graphs by Bandyapadhyay et al. [SoCG 2022]. The robust contraction decomposition theorem directly results in parameterized algorithms with running time 2^{Õ(√k)} ⋅ n^{O(1)} or n^{O(√k)} for every vertex/edge deletion problems on H-minor-free graphs that can be formulated as Permutation CSP Deletion or 2-Conn Permutation CSP Deletion. Consequently, we obtain the first subexponential-time parameterized algorithms for Subset Feedback Vertex Set, Subset Odd Cycle Transversal, Subset Group Feedback Vertex Set, 2-Conn Component Order Connectivity on H-minor-free graphs. For other problems which already have subexponential-time parameterized algorithms on H-minor-free graphs (e.g., Odd Cycle Transversal, Vertex Multiway Cut, Vertex Multicut, etc.), our theorem gives much simpler algorithms of the same running time.
Cite as

Sayan Bandyapadhyay, William Lochet, Daniel Lokshtanov, Dániel Marx, Pranabendu Misra, Daniel Neuen, Saket Saurabh, Prafullkumar Tale, and Jie Xue. Robust Contraction Decomposition for Minor-Free Graphs and Its Applications. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 17:1-17:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bandyapadhyay_et_al:LIPIcs.ICALP.2025.17,
  author =	{Bandyapadhyay, Sayan and Lochet, William and Lokshtanov, Daniel and Marx, D\'{a}niel and Misra, Pranabendu and Neuen, Daniel and Saurabh, Saket and Tale, Prafullkumar and Xue, Jie},
  title =	{{Robust Contraction Decomposition for Minor-Free Graphs and Its Applications}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{17:1--17:19},
  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.2025.17},
  URN =		{urn:nbn:de:0030-drops-233948},
  doi =		{10.4230/LIPIcs.ICALP.2025.17},
  annote =	{Keywords: subexponential time algorithms, graph decomposition, planar graphs, minor-free graphs, graph contraction}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.22
New Bounds for the Ideal Proof System in Positive Characteristic

Authors: Amik Raj Behera, Nutan Limaye, Varun Ramanathan, and Srikanth Srinivasan

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

Abstract
In this work, we prove upper and lower bounds over fields of positive characteristics for several fragments of the Ideal Proof System (IPS), an algebraic proof system introduced by Grochow and Pitassi (J. ACM 2018). Our results extend the works of Forbes, Shpilka, Tzameret, and Wigderson (Theory of Computing 2021) and also of Govindasamy, Hakoniemi, and Tzameret (FOCS 2022). These works primarily focused on proof systems over fields of characteristic 0, and we are able to extend these results to positive characteristic. The question of proving general IPS lower bounds over positive characteristic is motivated by the important question of proving AC⁰[p]-Frege lower bounds. This connection was observed by Grochow and Pitassi (J. ACM 2018). Additional motivation comes from recent developments in algebraic complexity theory due to Forbes (CCC 2024) who showed how to extend previous lower bounds over characteristic 0 to positive characteristic. In our work, we adapt the functional lower bound method of Forbes et al. (Theory of Computing 2021) to prove exponential-size lower bounds for various subsystems of IPS. In order to establish these size lower bounds, we first prove a tight degree lower bound for a variant of Subset Sum over positive characteristic. This forms the core of all our lower bounds. Additionally, we derive upper bounds for the instances presented above. We show that they have efficient constant-depth IPS refutations. This demonstrates that constant-depth IPS refutations are stronger than the proof systems considered above even in positive characteristic. We also show that constant-depth IPS can efficiently refute a general class of instances, namely all symmetric instances, thereby further uncovering the strength of these algebraic proofs in positive characteristic.
Cite as

Amik Raj Behera, Nutan Limaye, Varun Ramanathan, and Srikanth Srinivasan. New Bounds for the Ideal Proof System in Positive Characteristic. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 22:1-22:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{behera_et_al:LIPIcs.ICALP.2025.22,
  author =	{Behera, Amik Raj and Limaye, Nutan and Ramanathan, Varun and Srinivasan, Srikanth},
  title =	{{New Bounds for the Ideal Proof System in Positive Characteristic}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{22:1--22:20},
  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.2025.22},
  URN =		{urn:nbn:de:0030-drops-233992},
  doi =		{10.4230/LIPIcs.ICALP.2025.22},
  annote =	{Keywords: Ideal Proof Systems, Algebraic Complexity, Positive Characteristic}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.23
On the Instance Optimality of Detecting Collisions and Subgraphs

Authors: Omri Ben-Eliezer, Tomer Grossman, and Moni Naor

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

Abstract
Suppose you are given a function f: [n] → [n] via (black-box) query access to the function. You are looking to find something local, like a collision (a pair x ≠ y s.t. f(x) = f(y)). The question is whether knowing the "shape" of the function helps you or not (by shape we mean that some permutation of the function is known). Formally, we investigate the unlabeled instance optimality of substructure detection problems in graphs and functions. A problem is g(n)-instance optimal if it admits an algorithm A satisfying that for any possible input, the (randomized) query complexity of A is at most g(n) times larger than the query complexity of any algorithm A' which solves the same problem while holding an unlabeled copy of the input (i.e., any A' that "knows the structure of the input"). Our results point to a trichotomy of unlabeled instance optimality among substructure detection problems in graphs and functions: - A few very simple properties have an O(1)-instance optimal algorithm. - Most properties of graphs and functions, with examples such as containing a fixed point or a 3-collision in functions, or a triangle in graphs, are n^{c}-far from instance optimal for some constant c > 0. - The problems of collision detection in functions and finding a claw in a graph serve as a middle ground between the two regimes. We show that these two properties are not Ω(log n)-instance optimal, and conjecture that this bound is tight. We provide evidence towards this conjecture, by proving that finding a claw in a graph is O(log(n))-instance optimal among all input graphs for which the query complexity of an algorithm holding an unlabeled certificate is O(√{n/(log n)}).
Cite as

Omri Ben-Eliezer, Tomer Grossman, and Moni Naor. On the Instance Optimality of Detecting Collisions and Subgraphs. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 23:1-23:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{beneliezer_et_al:LIPIcs.ICALP.2025.23,
  author =	{Ben-Eliezer, Omri and Grossman, Tomer and Naor, Moni},
  title =	{{On the Instance Optimality of Detecting Collisions and Subgraphs}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{23:1--23:14},
  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.2025.23},
  URN =		{urn:nbn:de:0030-drops-234002},
  doi =		{10.4230/LIPIcs.ICALP.2025.23},
  annote =	{Keywords: instance optimality, instance complexity, unlabeled certificate, subgraph detection, collision detection}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.21
Multiparty Communication Complexity of Collision-Finding and Cutting Planes Proofs of Concise Pigeonhole Principles

Authors: Paul Beame and Michael Whitmeyer

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

Abstract
We prove several results concerning the communication complexity of a collision-finding problem, each of which has applications to the complexity of cutting-plane proofs, which make inferences based on integer linear inequalities. In particular, we prove an Ω(n^{1-1/k} log k /2^k) lower bound on the k-party number-in-hand communication complexity of collision-finding. This implies a 2^{n^{1-o(1)}} lower bound on the size of tree-like cutting-planes refutations of the bit pigeonhole principle CNFs, which are compact and natural propositional encodings of the negation of the pigeonhole principle, improving on the best previous lower bound of 2^{Ω(√n)}. Using the method of density-restoring partitions, we also extend that previous lower bound to the full range of pigeonhole parameters. Finally, using a refinement of a bottleneck-counting framework of Haken and Cook and Sokolov for DAG-like communication protocols, we give a 2^{Ω(n^{1/4})} lower bound on the size of fully general (not necessarily tree-like) cutting planes refutations of the same bit pigeonhole principle formulas, improving on the best previous lower bound of 2^{Ω(n^{1/8})}.
Cite as

Paul Beame and Michael Whitmeyer. Multiparty Communication Complexity of Collision-Finding and Cutting Planes Proofs of Concise Pigeonhole Principles. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 21:1-21:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{beame_et_al:LIPIcs.ICALP.2025.21,
  author =	{Beame, Paul and Whitmeyer, Michael},
  title =	{{Multiparty Communication Complexity of Collision-Finding and Cutting Planes Proofs of Concise Pigeonhole Principles}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{21:1--21:20},
  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.2025.21},
  URN =		{urn:nbn:de:0030-drops-233982},
  doi =		{10.4230/LIPIcs.ICALP.2025.21},
  annote =	{Keywords: Proof Complexity, Communication Complexity}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.20
Improved Approximation Algorithms for Capacitated Network Design and Flexible Graph Connectivity

Authors: Ishan Bansal, Joe Cheriyan, Sanjeev Khanna, and Miles Simmons

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

Abstract
We present improved approximation algorithms for some problems in the related areas of Capacitated Network Design and Flexible Graph Connectivity. In the Cap-k-ECSS problem, we are given a graph G = (V,E) whose edges have non-negative costs and positive integer capacities, and the goal is to find a minimum-cost edge-set F such that every non-trivial cut of the graph G' = (V,F) has capacity at least k. Let n = |V| and let u_{min} (respectively, u_{max}) denote the minimum (respectively, maximum) capacity of an edge; assume that u_{max} ≤ k. We present an O(log({k}/u_{min}))-approximation algorithm for the Cap-k-ECSS problem, asymptotically improving upon the previous best approximation ratio of min(O(log{n}), k, 2u_{max}, 6 ⋅ {⌈ k/u_{min} ⌉}) whenever log(k/u_{min}) = o(log{n}) and u_{max} is sufficiently large. In the (p,q)-Flexible Graph Connectivity problem, denoted (p,q)-FGC, the input is a graph G = (V, E) where E is partitioned into safe and unsafe edges, and the goal is to find a minimum-cost edge-set F such that the subgraph G' = (V, F) remains p-edge connected upon removal of any q unsafe edges from F. We present an 8-approximation algorithm for the (1,q)-FGC problem that improves upon the previous best approximation ratio of (q+1). Both of our results are obtained by using natural LP relaxations strengthened with the knapsack-cover inequalities, and then, during the rounding process, utilizing a recent O(1)-approximation algorithm for the Cover Small Cuts problem. In the latter problem, the goal is to find a minimum-cost set of links such that each non-trivial cut of capacity less than a specified value is covered by a link. We also show that the problem of covering small cuts inherently arises in another variant of (p,q)-FGC. Specifically, we give Cook reductions that preserve approximation ratios within O(1) factors between the (2,q)-FGC problem and the 2-Cover Small Cuts problem; in the latter problem, each small cut needs to be covered by two links.
Cite as

Ishan Bansal, Joe Cheriyan, Sanjeev Khanna, and Miles Simmons. Improved Approximation Algorithms for Capacitated Network Design and Flexible Graph Connectivity. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 20:1-20:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bansal_et_al:LIPIcs.ICALP.2025.20,
  author =	{Bansal, Ishan and Cheriyan, Joe and Khanna, Sanjeev and Simmons, Miles},
  title =	{{Improved Approximation Algorithms for Capacitated Network Design and Flexible Graph Connectivity}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{20:1--20:20},
  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.2025.20},
  URN =		{urn:nbn:de:0030-drops-233973},
  doi =		{10.4230/LIPIcs.ICALP.2025.20},
  annote =	{Keywords: Approximation algorithms, Capacitated network design, Covering small cuts, Edge-connectivity of graphs, f-Connectivity problem, Flexible Graph Connectivity, Knapsack-cover inequalities}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.24
Counting Permutation Patterns with Multidimensional Trees

Authors: Gal Beniamini and Nir Lavee

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

Abstract
We consider the well-studied pattern-counting problem: given a permutation π ∈ 𝕊_n and an integer k > 1, count the number of order-isomorphic occurrences of every pattern τ ∈ 𝕊_k in π. Our first result is an 𝒪̃(n²)-time algorithm for k = 6 and k = 7. The proof relies heavily on a new family of graphs that we introduce, called pattern-trees. Every such tree corresponds to an integer linear combination of permutations in 𝕊_k, and is associated with linear extensions of partially ordered sets. We design an evaluation algorithm for these combinations, and apply it to a family of linearly-independent trees. For k = 8, we show a barrier: the subspace spanned by trees in the previous family has dimension exactly |𝕊₈| - 1, one less than required. Our second result is an 𝒪̃(n^{7/4})-time algorithm for k = 5. This algorithm extends the framework of pattern-trees by speeding-up their evaluation in certain cases. A key component of the proof is the introduction of pair-rectangle-trees, a data structure for dominance counting.
Cite as

Gal Beniamini and Nir Lavee. Counting Permutation Patterns with Multidimensional Trees. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 24:1-24:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{beniamini_et_al:LIPIcs.ICALP.2025.24,
  author =	{Beniamini, Gal and Lavee, Nir},
  title =	{{Counting Permutation Patterns with Multidimensional Trees}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{24:1--24:18},
  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.2025.24},
  URN =		{urn:nbn:de:0030-drops-234018},
  doi =		{10.4230/LIPIcs.ICALP.2025.24},
  annote =	{Keywords: Pattern counting, patterns, permutations}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.52
Relative-Error Testing of Conjunctions and Decision Lists

Authors: Xi Chen, William Pires, Toniann Pitassi, and Rocco A. Servedio

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

Abstract
We study the relative-error property testing model for Boolean functions that was recently introduced in the work of [X. Chen et al., 2025]. In relative-error testing, the testing algorithm gets uniform random satisfying assignments as well as black-box queries to f, and it must accept f with high probability whenever f has the property that is being tested and reject any f that is relative-error far from having the property. Here the relative-error distance from f to a function g is measured with respect to |f^{-1}(1)| rather than with respect to the entire domain size 2ⁿ as in the Hamming distance measure that is used in the standard model; thus, unlike the standard model, relative-error testing allows us to study the testability of sparse Boolean functions that have few satisfying assignments. It was shown in [X. Chen et al., 2025] that relative-error testing is at least as difficult as standard-model property testing, but for many natural and important Boolean function classes the precise relationship between the two notions is unknown. In this paper we consider the well-studied and fundamental properties of being a conjunction and being a decision list. In the relative-error setting, we give an efficient one-sided error tester for conjunctions with running time and query complexity O(1/ε). Secondly, we give a two-sided relative-error Õ(1/ε) tester for decision lists, matching the query complexity of the state-of-the-art algorithm in the standard model [Nader H. Bshouty, 2020; I. Diakonikolas et al., 2007].
Cite as

Xi Chen, William Pires, Toniann Pitassi, and Rocco A. Servedio. Relative-Error Testing of Conjunctions and Decision Lists. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 52:1-52:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chen_et_al:LIPIcs.ICALP.2025.52,
  author =	{Chen, Xi and Pires, William and Pitassi, Toniann and Servedio, Rocco A.},
  title =	{{Relative-Error Testing of Conjunctions and Decision Lists}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{52:1--52:18},
  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.2025.52},
  URN =		{urn:nbn:de:0030-drops-234291},
  doi =		{10.4230/LIPIcs.ICALP.2025.52},
  annote =	{Keywords: Property Testing, Relative Error}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.53
Cut-Preserving Vertex Sparsifiers for Planar and Quasi-Bipartite Graphs

Authors: Yu Chen and Zihan Tan

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

Abstract
We study vertex sparsification for preserving cuts. Given a graph G with a subset |T| = k of its vertices called terminals, a quality-q cut sparsifier is a graph G' that contains T, such that, for any partition (T₁,T₂) of T into non-empty subsets, the value of the min-cut in G' separating T₁ from T₂ is within factor q from the value of the min-cut in G separating T₁ from T₂. The construction of cut sparsifiers with good (small) quality and size has been a central problem in graph compression for years. Planar graphs and quasi-bipartite graphs are two important special families studied in this research direction. The main results in this paper are new cut sparsifier constructions for them in the high-quality regime (where q = 1 or 1+{ε} for small {ε} > 0). We first show that every planar graph admits a planar quality-(1+{ε}) cut sparsifier of size Õ(k/poly({ε})), which is in sharp contrast with the lower bound of 2^{Ω(k)} for the quality-1 case. We then show that every quasi-bipartite graph admits a quality-1 cut sparsifier of size 2^{Õ(k²)}. This is the second to improve over the doubly-exponential bound for general graphs (previously only planar graphs have been shown to have single-exponential size quality-1 cut sparsifiers). Lastly, we show that contraction, a common approach for constructing cut sparsifiers adopted in most previous works, does not always give optimal bounds for cut sparsifiers. We demonstrate this by showing that the optimal size bound for quality-(1+{ε}) contraction-based cut sparsifiers for quasi-bipartite graphs lies in the range [k^{̃Ω(1/{ε})},k^{O(1/{ε}²)}], while in previous work an upper bound of Õ(k/{ε}²) was achieved via a non-contraction approach.
Cite as

Yu Chen and Zihan Tan. Cut-Preserving Vertex Sparsifiers for Planar and Quasi-Bipartite Graphs. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 53:1-53:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chen_et_al:LIPIcs.ICALP.2025.53,
  author =	{Chen, Yu and Tan, Zihan},
  title =	{{Cut-Preserving Vertex Sparsifiers for Planar and Quasi-Bipartite Graphs}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{53:1--53:20},
  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.2025.53},
  URN =		{urn:nbn:de:0030-drops-234304},
  doi =		{10.4230/LIPIcs.ICALP.2025.53},
  annote =	{Keywords: Termianl Cut, Graph Sparsification}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.54
Decay of Correlation for Edge Colorings When q > 3Δ

Authors: Zejia Chen, Yulin Wang, Chihao Zhang, and Zihan Zhang

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

Abstract
We examine various perspectives on the decay of correlation for the uniform distribution over proper q-edge colorings of graphs with maximum degree Δ. First, we establish the coupling independence property when q ≥ 3Δ for general graphs. Together with the recent work of Chen, Feng, Guo, Zhang and Zou (2024), this result implies a fully polynomial-time approximation scheme (FPTAS) for counting the number of proper q-edge colorings. Next, we prove the strong spatial mixing property on trees, provided that q > (3+o(1))Δ. The strong spatial mixing property is derived from the spectral independence property of a version of the weighted edge coloring distribution, which is established using the matrix trickle-down method developed in Abdolazimi, Liu and Oveis Gharan (FOCS, 2021) and Wang, Zhang and Zhang (STOC, 2024). Finally, we show that the weak spatial mixing property holds on trees with maximum degree Δ if and only if q ≥ 2Δ-1.
Cite as

Zejia Chen, Yulin Wang, Chihao Zhang, and Zihan Zhang. Decay of Correlation for Edge Colorings When q > 3Δ. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 54:1-54:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chen_et_al:LIPIcs.ICALP.2025.54,
  author =	{Chen, Zejia and Wang, Yulin and Zhang, Chihao and Zhang, Zihan},
  title =	{{Decay of Correlation for Edge Colorings When q \rangle 3\Delta}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{54:1--54:18},
  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.2025.54},
  URN =		{urn:nbn:de:0030-drops-234314},
  doi =		{10.4230/LIPIcs.ICALP.2025.54},
  annote =	{Keywords: Strong Spatial Mixing, Edge Coloring, Approximate Counting}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.55
Optimal Oblivious Subspace Embeddings with Near-Optimal Sparsity

Authors: Shabarish Chenakkod, Michał Dereziński, and Xiaoyu Dong

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

Abstract
An oblivious subspace embedding is a random m× n matrix Π such that, for any d-dimensional subspace, with high probability Π preserves the norms of all vectors in that subspace within a 1±ε factor. In this work, we give an oblivious subspace embedding with the optimal dimension m = Θ(d/ε²) that has a near-optimal sparsity of Õ(1/ε) non-zero entries per column of Π. This is the first result to nearly match the conjecture of Nelson and Nguyen [FOCS 2013] in terms of the best sparsity attainable by an optimal oblivious subspace embedding, improving on a prior bound of Õ(1/ε⁶) non-zeros per column [Chenakkod et al., STOC 2024]. We further extend our approach to the non-oblivious setting, proposing a new family of Leverage Score Sparsified embeddings with Independent Columns, which yield faster runtimes for matrix approximation and regression tasks. In our analysis, we develop a new method which uses a decoupling argument together with the cumulant method for bounding the edge universality error of isotropic random matrices. To achieve near-optimal sparsity, we combine this general-purpose approach with new trace inequalities that leverage the specific structure of our subspace embedding construction.
Cite as

Shabarish Chenakkod, Michał Dereziński, and Xiaoyu Dong. Optimal Oblivious Subspace Embeddings with Near-Optimal Sparsity. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 55:1-55:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chenakkod_et_al:LIPIcs.ICALP.2025.55,
  author =	{Chenakkod, Shabarish and Derezi\'{n}ski, Micha{\l} and Dong, Xiaoyu},
  title =	{{Optimal Oblivious Subspace Embeddings with Near-Optimal Sparsity}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{55:1--55:20},
  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.2025.55},
  URN =		{urn:nbn:de:0030-drops-234324},
  doi =		{10.4230/LIPIcs.ICALP.2025.55},
  annote =	{Keywords: Randomized linear algebra, matrix sketching, subspace embeddings}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.49
Submodular Hypergraph Partitioning: Metric Relaxations and Fast Algorithms via an Improved Cut-Matching Game

Authors: Antares Chen, Lorenzo Orecchia, and Erasmo Tani

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

Abstract
Despite there being significant work on developing spectral- [Chan et al., 2018; Lau et al., 2023; Kwok et al., 2022], and metric-embedding-based [Louis and Makarychev, 2016] approximation algorithms for hypergraph conductance, little is known regarding the approximability of other hypergraph partitioning objectives. This work proposes algorithms for a general model of hypergraph partitioning that unifies both undirected and directed versions of many well-studied partitioning objectives. The first contribution of this paper introduces polymatroidal cut functions, a large class of cut functions amenable to approximation algorithms via metric embeddings and routing multicommodity flows. We demonstrate a simple O(√{log n})-approximation, where n is the number of vertices in the hypergraph, for these problems by rounding relaxations to metrics of negative-type. The second contribution of this paper generalizes the cut-matching game framework of Khandekar et al. [Khandekar et al., 2007] to tackle polymatroidal cut functions. This yields an almost-linear time O(log n)-approximation algorithm for standard versions of undirected and directed hypergraph partitioning [Kwok et al., 2022]. A technical contribution of our construction is a novel cut-matching game, which greatly relaxes the set of allowed actions by the cut player and allows for the use of approximate s-t maximum flows by the matching player. We believe this to be of independent interest.
Cite as

Antares Chen, Lorenzo Orecchia, and Erasmo Tani. Submodular Hypergraph Partitioning: Metric Relaxations and Fast Algorithms via an Improved Cut-Matching Game. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 49:1-49:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chen_et_al:LIPIcs.ICALP.2025.49,
  author =	{Chen, Antares and Orecchia, Lorenzo and Tani, Erasmo},
  title =	{{Submodular Hypergraph Partitioning: Metric Relaxations and Fast Algorithms via an Improved Cut-Matching Game}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{49:1--49:16},
  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.2025.49},
  URN =		{urn:nbn:de:0030-drops-234261},
  doi =		{10.4230/LIPIcs.ICALP.2025.49},
  annote =	{Keywords: Hypergraph Partitioning, Cut Improvement, Cut-Matching Game}
}
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