60 Search Results for "Held, Martin"

Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2025.158
Restricted CSPs and F-Free Digraph Algorithmics

Authors: Santiago Guzmán-Pro and Barnaby Martin

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

Abstract
In recent years, much attention has been placed on the complexity of graph homomorphism problems when the input is restricted to ℙ_k-free and ℙ_k-subgraph-free graphs. We consider the directed version of this research line, by addressing the question is it true that digraph homomorphism problems CSP(H) have a P versus NP-complete dichotomy when the input is restricted to ℙ→_k-free (resp. ℙ→_k-subgraph-free) digraphs? Our main contribution in this direction shows that if CSP(H) is NP-complete, then there is a positive integer N such that CSP(H) remains NP-hard even for ℙ→_N-subgraph-free digraphs. Moreover, CSP(H) becomes polynomial-time solvable for ℙ→_{N-1}-subgraph-free acyclic digraphs. We then verify the questions above for digraphs on three vertices and a family of smooth tournaments. We prove these results by establishing a connection between F-(subgraph)-free algorithmics and constraint satisfaction theory. On the way, we introduce restricted CSPs, i.e., problems of the form CSP(H) restricted to yes-instances of CSP(H') - these were called restricted homomorphism problems by Hell and Nešetřil. Another main result of this paper presents a P versus NP-complete dichotomy for these problems. Moreover, this complexity dichotomy is accompanied by an algebraic dichotomy in the spirit of the finite domain CSP dichotomy.
Cite as

Santiago Guzmán-Pro and Barnaby Martin. Restricted CSPs and F-Free Digraph Algorithmics. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 158:1-158:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{guzmanpro_et_al:LIPIcs.ICALP.2025.158,
  author =	{Guzm\'{a}n-Pro, Santiago and Martin, Barnaby},
  title =	{{Restricted CSPs and F-Free Digraph Algorithmics}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{158:1--158:21},
  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.2025.158},
  URN =		{urn:nbn:de:0030-drops-235352},
  doi =		{10.4230/LIPIcs.ICALP.2025.158},
  annote =	{Keywords: Digraph homomorphisms, constraint satisfaction problems, subgraph-free algorithmics}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2025.166
Limitations of Affine Integer Relaxations for Solving Constraint Satisfaction Problems

Authors: Moritz Lichter and Benedikt Pago

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

Abstract
We show that various recent algorithms for finite-domain constraint satisfaction problems (CSP), which are based on solving their affine integer relaxations, do not solve all tractable and not even all Maltsev CSPs. This rules them out as candidates for a universal polynomial-time CSP algorithm. The algorithms are ℤ-affine k-consistency, BLP+AIP, BA^{k}, and CLAP. We thereby answer a question by Brakensiek, Guruswami, Wrochna, and Živný [Joshua Brakensiek et al., 2020] whether a constant level of BA^{k}solves all tractable CSPs in the negative: Indeed, not even a sublinear level k suffices. We also refute a conjecture by Dalmau and Opršal [Víctor Dalmau and Jakub Opršal, 2024] (LICS 2024) that every CSP is either solved by ℤ-affine k-consistency or admits a Datalog reduction from 3-colorability. For the cohomological k-consistency algorithm, that is also based on affine relaxations, we show that it correctly solves our counterexample but fails on an NP-complete template.
Cite as

Moritz Lichter and Benedikt Pago. Limitations of Affine Integer Relaxations for Solving Constraint Satisfaction Problems. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 166:1-166:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lichter_et_al:LIPIcs.ICALP.2025.166,
  author =	{Lichter, Moritz and Pago, Benedikt},
  title =	{{Limitations of Affine Integer Relaxations for Solving Constraint Satisfaction Problems}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{166:1--166:17},
  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.2025.166},
  URN =		{urn:nbn:de:0030-drops-235431},
  doi =		{10.4230/LIPIcs.ICALP.2025.166},
  annote =	{Keywords: constraint satisfaction, affine relaxation, promise CSPs, \mathbb{Z}-affine k-consistency, cohomological k-consistency algorithm, Tseitin, graph isomorphism}
}
Document
Survey
DOI: 10.4230/TGDK.3.1.3
Uncertainty Management in the Construction of Knowledge Graphs: A Survey

Authors: Lucas Jarnac, Yoan Chabot, and Miguel Couceiro

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

Abstract
Knowledge Graphs (KGs) are a major asset for companies thanks to their great flexibility in data representation and their numerous applications, e.g., vocabulary sharing, Q&A or recommendation systems. To build a KG, it is a common practice to rely on automatic methods for extracting knowledge from various heterogeneous sources. However, in a noisy and uncertain world, knowledge may not be reliable and conflicts between data sources may occur. Integrating unreliable data would directly impact the use of the KG, therefore such conflicts must be resolved. This could be done manually by selecting the best data to integrate. This first approach is highly accurate, but costly and time-consuming. That is why recent efforts focus on automatic approaches, which represent a challenging task since it requires handling the uncertainty of extracted knowledge throughout its integration into the KG. We survey state-of-the-art approaches in this direction and present constructions of both open and enterprise KGs. We then describe different knowledge extraction methods and discuss downstream tasks after knowledge acquisition, including KG completion using embedding models, knowledge alignment, and knowledge fusion in order to address the problem of knowledge uncertainty in KG construction. We conclude with a discussion on the remaining challenges and perspectives when constructing a KG taking into account uncertainty.
Cite as

Lucas Jarnac, Yoan Chabot, and Miguel Couceiro. Uncertainty Management in the Construction of Knowledge Graphs: A Survey. In Transactions on Graph Data and Knowledge (TGDK), Volume 3, Issue 1, pp. 3:1-3:48, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@Article{jarnac_et_al:TGDK.3.1.3,
  author =	{Jarnac, Lucas and Chabot, Yoan and Couceiro, Miguel},
  title =	{{Uncertainty Management in the Construction of Knowledge Graphs: A Survey}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{3:1--3:48},
  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.3.1.3},
  URN =		{urn:nbn:de:0030-drops-233733},
  doi =		{10.4230/TGDK.3.1.3},
  annote =	{Keywords: Knowledge reconciliation, Uncertainty, Heterogeneous sources, Knowledge graph construction}
}
Document
DOI: 10.4230/LIPIcs.ICDT.2025.9
Query Languages for Neural Networks

Authors: Martin Grohe, Christoph Standke, Juno Steegmans, and Jan Van den Bussche

Published in: LIPIcs, Volume 328, 28th International Conference on Database Theory (ICDT 2025)

Abstract
We lay the foundations for a database-inspired approach to interpreting and understanding neural network models by querying them using declarative languages. Towards this end we study different query languages, based on first-order logic, that mainly differ in their access to the neural network model. First-order logic over the reals naturally yields a language which views the network as a black box; only the input-output function defined by the network can be queried. This is essentially the approach of constraint query languages. On the other hand, a white-box language can be obtained by viewing the network as a weighted graph, and extending first-order logic with summation over weight terms. The latter approach is essentially an abstraction of SQL . In general, the two approaches are incomparable in expressive power, as we will show. Under natural circumstances, however, the white-box approach can subsume the black-box approach; this is our main result. We prove the result concretely for linear constraint queries over real functions definable by feedforward neural networks with a fixed number of hidden layers and piecewise linear activation functions.
Cite as

Martin Grohe, Christoph Standke, Juno Steegmans, and Jan Van den Bussche. Query Languages for Neural Networks. In 28th International Conference on Database Theory (ICDT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 328, pp. 9:1-9:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{grohe_et_al:LIPIcs.ICDT.2025.9,
  author =	{Grohe, Martin and Standke, Christoph and Steegmans, Juno and Van den Bussche, Jan},
  title =	{{Query Languages for Neural Networks}},
  booktitle =	{28th International Conference on Database Theory (ICDT 2025)},
  pages =	{9:1--9:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-364-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{328},
  editor =	{Roy, Sudeepa and Kara, Ahmet},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2025.9},
  URN =		{urn:nbn:de:0030-drops-229508},
  doi =		{10.4230/LIPIcs.ICDT.2025.9},
  annote =	{Keywords: Expressive power of query languages, Machine learning models, languages for interpretability, explainable AI}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.8
The Parameterized Complexity of Learning Monadic Second-Order Logic

Authors: Steffen van Bergerem, Martin Grohe, and Nina Runde

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract
Within the model-theoretic framework for supervised learning introduced by Grohe and Turán (TOCS 2004), we study the parameterized complexity of learning concepts definable in monadic second-order logic (MSO). We show that the problem of learning an MSO-definable concept from a training sequence of labeled examples is fixed-parameter tractable on graphs of bounded clique-width, and that it is hard for the parameterized complexity class para-NP on general graphs. It turns out that an important distinction to be made is between 1-dimensional and higher-dimensional concepts, where the instances of a k-dimensional concept are k-tuples of vertices of a graph. For the higher-dimensional case, we give a learning algorithm that is fixed-parameter tractable in the size of the graph, but not in the size of the training sequence, and we give a hardness result showing that this is optimal. By comparison, in the 1-dimensional case, we obtain an algorithm that is fixed-parameter tractable in both.
Cite as

Steffen van Bergerem, Martin Grohe, and Nina Runde. The Parameterized Complexity of Learning Monadic Second-Order Logic. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{vanbergerem_et_al:LIPIcs.CSL.2025.8,
  author =	{van Bergerem, Steffen and Grohe, Martin and Runde, Nina},
  title =	{{The Parameterized Complexity of Learning Monadic Second-Order Logic}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{8:1--8:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.8},
  URN =		{urn:nbn:de:0030-drops-227651},
  doi =		{10.4230/LIPIcs.CSL.2025.8},
  annote =	{Keywords: monadic second-order definable concept learning, agnostic probably approximately correct learning, parameterized complexity, clique-width, fixed-parameter tractable, Boolean classification, supervised learning, monadic second-order logic}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.23
Density-Sensitive Algorithms for (Δ + 1)-Edge Coloring

Authors: Sayan Bhattacharya, Martín Costa, Nadav Panski, and Shay Solomon

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
Vizing’s theorem asserts the existence of a (Δ+1)-edge coloring for any graph G, where Δ = Δ(G) denotes the maximum degree of G. Several polynomial time (Δ+1)-edge coloring algorithms are known, and the state-of-the-art running time (up to polylogarithmic factors) is Õ(min{m √n, m Δ}), by Gabow, Nishizeki, Kariv, Leven and Terada from 1985, where n and m denote the number of vertices and edges in the graph, respectively. Recently, Sinnamon shaved off a polylog(n) factor from the time bound of Gabow et al. The arboricity α = α(G) of a graph G is the minimum number of edge-disjoint forests into which its edge set can be partitioned, and it is a measure of the graph’s "uniform density". While α ≤ Δ in any graph, many natural and real-world graphs exhibit a significant separation between α and Δ. In this work we design a (Δ+1)-edge coloring algorithm with a running time of Õ(min{m √n, m Δ})⋅ α/Δ, thus improving the longstanding time barrier by a factor of α/Δ. In particular, we achieve a near-linear runtime for bounded arboricity graphs (i.e., α = Õ(1)) as well as when α = Õ(Δ/√n). Our algorithm builds on Gabow et al.’s and Sinnamon’s algorithms, and can be viewed as a density-sensitive refinement of them.
Cite as

Sayan Bhattacharya, Martín Costa, Nadav Panski, and Shay Solomon. Density-Sensitive Algorithms for (Δ + 1)-Edge Coloring. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 23:1-23:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bhattacharya_et_al:LIPIcs.ESA.2024.23,
  author =	{Bhattacharya, Sayan and Costa, Mart{\'\i}n and Panski, Nadav and Solomon, Shay},
  title =	{{Density-Sensitive Algorithms for (\Delta + 1)-Edge Coloring}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{23:1--23:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John 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.2024.23},
  URN =		{urn:nbn:de:0030-drops-210945},
  doi =		{10.4230/LIPIcs.ESA.2024.23},
  annote =	{Keywords: Graph Algorithms, Edge Coloring, Arboricity}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2024.33
Compiling with Arrays

Authors: David Richter, Timon Böhler, Pascal Weisenburger, and Mira Mezini

Published in: LIPIcs, Volume 313, 38th European Conference on Object-Oriented Programming (ECOOP 2024)

Abstract
Linear algebra computations are foundational for neural networks and machine learning, often handled through arrays. While many functional programming languages feature lists and recursion, arrays in linear algebra demand constant-time access and bulk operations. To bridge this gap, some languages represent arrays as (eager) functions instead of lists. In this paper, we connect this idea to a formal logical foundation by interpreting functions as the usual negative types from polarized type theory, and arrays as the corresponding dual positive version of the function type. Positive types are defined to have a single elimination form whose computational interpretation is pattern matching. Just like (positive) product types bind two variables during pattern matching, (positive) array types bind variables with multiplicity during pattern matching. We follow a similar approach for Booleans by introducing conditionally-defined variables. The positive formulation for the array type enables us to combine typed partial evaluation and common subexpression elimination into an elegant algorithm whose result enjoys a property we call maximal fission, which we argue can be beneficial for further optimizations. For this purpose, we present the novel intermediate representation indexed administrative normal form (A_{i}NF), which relies on the formal logical foundation of the positive formulation for the array type to facilitate maximal loop fission and subsequent optimizations. A_{i}NF is normal with regard to commuting conversion for both let-bindings and for-loops, leading to flat and maximally fissioned terms. We mechanize the translation and normalization from a simple surface language to A_{i}NF, establishing that the process terminates, preserves types, and produces maximally fissioned terms.
Cite as

David Richter, Timon Böhler, Pascal Weisenburger, and Mira Mezini. Compiling with Arrays. In 38th European Conference on Object-Oriented Programming (ECOOP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 313, pp. 33:1-33:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{richter_et_al:LIPIcs.ECOOP.2024.33,
  author =	{Richter, David and B\"{o}hler, Timon and Weisenburger, Pascal and Mezini, Mira},
  title =	{{Compiling with Arrays}},
  booktitle =	{38th European Conference on Object-Oriented Programming (ECOOP 2024)},
  pages =	{33:1--33:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-341-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{313},
  editor =	{Aldrich, Jonathan and Salvaneschi, Guido},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2024.33},
  URN =		{urn:nbn:de:0030-drops-208823},
  doi =		{10.4230/LIPIcs.ECOOP.2024.33},
  annote =	{Keywords: array languages, functional programming, domain-specific languages, normalization by evaluation, common subexpression elimination, polarity, positive function type, intrinsic types}
}
Document
DOI: 10.4230/LIPIcs.ITP.2024.13
Completeness of Asynchronous Session Tree Subtyping in Coq

Authors: Burak Ekici and Nobuko Yoshida

Published in: LIPIcs, Volume 309, 15th International Conference on Interactive Theorem Proving (ITP 2024)

Abstract
Multiparty session types (MPST) serve as a foundational framework for formally specifying and verifying message passing protocols. Asynchronous subtyping in MPST allows for typing optimised programs preserving type safety and deadlock freedom under asynchronous interactions where the message order is preserved and sending is non-blocking. The optimisation is obtained by message reordering, which allows for sending messages earlier or receiving them later. Sound subtyping algorithms have been extensively studied and implemented as part of various programming languages and tools including C, Rust and C-MPI. However, formalising all such permutations under sequencing, selection, branching and recursion in session types is an intricate task. Additionally, checking asynchronous subtyping has been proven to be undecidable. This paper introduces the first formalisation of asynchronous subtyping in MPST within the Coq proof assistant. We first decompose session types into session trees that do not involve branching and selection, and then establish a coinductive refinement relation over them to govern subtyping. To showcase our formalisation, we prove example subtyping schemas that appear in the literature, all of which cannot be verified, at the same time, by any of the existing decidable sound algorithms. Additionally, we take the (inductive) negation of the refinement relation from a prior work by Ghilezan et al. [Ghilezan et al., 2023] and re-implement it, significantly reducing the number of rules (from eighteen to eight). We establish the completeness of subtyping with respect to its negation in Coq, addressing the issues concerning the negation rules outlined in the previous work [Ghilezan et al., 2023]. In the formalisation, we use the greatest fixed point of the least fixed point technique, facilitated by the paco library, to define coinductive predicates. We employ parametrised coinduction to prove their properties. The formalisation consists of roughly 10K lines of Coq code, accessible at: https://github.com/ekiciburak/sessionTreeST/tree/itp2024.
Cite as

Burak Ekici and Nobuko Yoshida. Completeness of Asynchronous Session Tree Subtyping in Coq. In 15th International Conference on Interactive Theorem Proving (ITP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 309, pp. 13:1-13:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ekici_et_al:LIPIcs.ITP.2024.13,
  author =	{Ekici, Burak and Yoshida, Nobuko},
  title =	{{Completeness of Asynchronous Session Tree Subtyping in Coq}},
  booktitle =	{15th International Conference on Interactive Theorem Proving (ITP 2024)},
  pages =	{13:1--13:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-337-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{309},
  editor =	{Bertot, Yves and Kutsia, Temur and Norrish, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2024.13},
  URN =		{urn:nbn:de:0030-drops-207418},
  doi =		{10.4230/LIPIcs.ITP.2024.13},
  annote =	{Keywords: asynchronous multiparty session types, session trees, subtyping, Coq}
}
Document
DOI: 10.4230/LIPIcs.ITP.2024.12
A Modular Formalization of Superposition in Isabelle/HOL

Authors: Martin Desharnais, Balazs Toth, Uwe Waldmann, Jasmin Blanchette, and Sophie Tourret

Published in: LIPIcs, Volume 309, 15th International Conference on Interactive Theorem Proving (ITP 2024)

Abstract
Superposition is an efficient proof calculus for reasoning about first-order logic with equality that is implemented in many automatic theorem provers. It works by saturating the given set of clauses and is refutationally complete, meaning that if the set is inconsistent, the saturation will contain a contradiction. In this work, we restructured the completeness proof to cleanly separate the ground (i.e., variable-free) and nonground aspects, and we formalized the result in Isabelle/HOL. We relied on the IsaFoR library for first-order terms and on the Isabelle saturation framework.
Cite as

Martin Desharnais, Balazs Toth, Uwe Waldmann, Jasmin Blanchette, and Sophie Tourret. A Modular Formalization of Superposition in Isabelle/HOL. In 15th International Conference on Interactive Theorem Proving (ITP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 309, pp. 12:1-12:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{desharnais_et_al:LIPIcs.ITP.2024.12,
  author =	{Desharnais, Martin and Toth, Balazs and Waldmann, Uwe and Blanchette, Jasmin and Tourret, Sophie},
  title =	{{A Modular Formalization of Superposition in Isabelle/HOL}},
  booktitle =	{15th International Conference on Interactive Theorem Proving (ITP 2024)},
  pages =	{12:1--12:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-337-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{309},
  editor =	{Bertot, Yves and Kutsia, Temur and Norrish, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2024.12},
  URN =		{urn:nbn:de:0030-drops-207401},
  doi =		{10.4230/LIPIcs.ITP.2024.12},
  annote =	{Keywords: Superposition, verification, first-order logic, higher-order logic}
}
Document
DOI: 10.4230/LIPIcs.CP.2024.19
An Efficient Local Search Solver for Mixed Integer Programming

Authors: Peng Lin, Mengchuan Zou, and Shaowei Cai

Published in: LIPIcs, Volume 307, 30th International Conference on Principles and Practice of Constraint Programming (CP 2024)

Abstract
Mixed integer programming (MIP) is a fundamental model in operations research. Local search is a powerful method for solving hard problems, but the development of local search solvers for MIP still needs to be explored. This work develops an efficient local search solver for solving MIP, called Local-MIP. We propose two new operators for MIP to adaptively modify variables for optimizing the objective function and satisfying constraints, respectively. Furthermore, we design a new weighting scheme to dynamically balance the priority between the objective function and each constraint, and propose a two-level scoring function structure to hierarchically guide the search for high-quality feasible solutions. Experiments are conducted on seven public benchmarks to compare Local-MIP with state-of-the-art MIP solvers, which demonstrate that Local-MIP significantly outperforms CPLEX, HiGHS, SCIP and Feasibility Jump, and is competitive with the most powerful commercial solver Gurobi. Moreover, Local-MIP establishes 4 new records for MIPLIB open instances.
Cite as

Peng Lin, Mengchuan Zou, and Shaowei Cai. An Efficient Local Search Solver for Mixed Integer Programming. In 30th International Conference on Principles and Practice of Constraint Programming (CP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 307, pp. 19:1-19:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{lin_et_al:LIPIcs.CP.2024.19,
  author =	{Lin, Peng and Zou, Mengchuan and Cai, Shaowei},
  title =	{{An Efficient Local Search Solver for Mixed Integer Programming}},
  booktitle =	{30th International Conference on Principles and Practice of Constraint Programming (CP 2024)},
  pages =	{19:1--19:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-336-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{307},
  editor =	{Shaw, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2024.19},
  URN =		{urn:nbn:de:0030-drops-207041},
  doi =		{10.4230/LIPIcs.CP.2024.19},
  annote =	{Keywords: Mixed Integer Programming, Local Search, Operator, Scoring Function}
}
Document
DOI: 10.4230/LIPIcs.CP.2024.22
Learning Lagrangian Multipliers for the Travelling Salesman Problem

Authors: Augustin Parjadis, Quentin Cappart, Bistra Dilkina, Aaron Ferber, and Louis-Martin Rousseau

Published in: LIPIcs, Volume 307, 30th International Conference on Principles and Practice of Constraint Programming (CP 2024)

Abstract
Lagrangian relaxation is a versatile mathematical technique employed to relax constraints in an optimization problem, enabling the generation of dual bounds to prove the optimality of feasible solutions and the design of efficient propagators in constraint programming (such as the weighted circuit constraint). However, the conventional process of deriving Lagrangian multipliers (e.g., using subgradient methods) is often computationally intensive, limiting its practicality for large-scale or time-sensitive problems. To address this challenge, we propose an innovative unsupervised learning approach that harnesses the capabilities of graph neural networks to exploit the problem structure, aiming to generate accurate Lagrangian multipliers efficiently. We apply this technique to the well-known Held-Karp Lagrangian relaxation for the traveling salesman problem. The core idea is to predict accurate Lagrangian multipliers and to employ them as a warm start for generating Held-Karp relaxation bounds. These bounds are subsequently utilized to enhance the filtering process carried out by branch-and-bound algorithms. In contrast to much of the existing literature, which primarily focuses on finding feasible solutions, our approach operates on the dual side, demonstrating that learning can also accelerate the proof of optimality. We conduct experiments across various distributions of the metric traveling salesman problem, considering instances with up to 200 cities. The results illustrate that our approach can improve the filtering level of the weighted circuit global constraint, reduce the optimality gap by a factor two for unsolved instances up to a timeout, and reduce the execution time for solved instances by 10%.
Cite as

Augustin Parjadis, Quentin Cappart, Bistra Dilkina, Aaron Ferber, and Louis-Martin Rousseau. Learning Lagrangian Multipliers for the Travelling Salesman Problem. In 30th International Conference on Principles and Practice of Constraint Programming (CP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 307, pp. 22:1-22:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{parjadis_et_al:LIPIcs.CP.2024.22,
  author =	{Parjadis, Augustin and Cappart, Quentin and Dilkina, Bistra and Ferber, Aaron and Rousseau, Louis-Martin},
  title =	{{Learning Lagrangian Multipliers for the Travelling Salesman Problem}},
  booktitle =	{30th International Conference on Principles and Practice of Constraint Programming (CP 2024)},
  pages =	{22:1--22:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-336-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{307},
  editor =	{Shaw, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2024.22},
  URN =		{urn:nbn:de:0030-drops-207076},
  doi =		{10.4230/LIPIcs.CP.2024.22},
  annote =	{Keywords: Lagrangian relaxation, unsupervised learning, graph neural network}
}
Document
DOI: 10.4230/LIPIcs.WABI.2024.5
Memoization on Shared Subtrees Accelerates Computations on Genealogical Forests

Authors: Lukas Hübner and Alexandros Stamatakis

Published in: LIPIcs, Volume 312, 24th International Workshop on Algorithms in Bioinformatics (WABI 2024)

Abstract
The field of population genetics attempts to advance our understanding of evolutionary processes. It has applications, for example, in medical research, wildlife conservation, and - in conjunction with recent advances in ancient DNA sequencing technology - studying human migration patterns over the past few thousand years. The basic toolbox of population genetics includes genealogical trees, which describe the shared evolutionary history among individuals of the same species. They are calculated on the basis of genetic variations. However, in recombining organisms, a single tree is insufficient to describe the evolutionary history of the whole genome. Instead, a collection of correlated trees can be used, where each describes the evolutionary history of a consecutive region of the genome. The current corresponding state of-the-art data structure, tree sequences, compresses these genealogical trees via edit operations when moving from one tree to the next along the genome instead of storing the full, often redundant, description for each tree. We propose a new data structure, genealogical forests, which compresses the set of genealogical trees into a DAG. In this DAG identical subtrees that are shared across the input trees are encoded only once, thereby allowing for straight-forward memoization of intermediate results. Additionally, we provide a C++ implementation of our proposed data structure, called gfkit, which is 2.1 to 11.2 (median 4.0) times faster than the state-of-the-art tool on empirical and simulated datasets at computing important population genetics statistics such as the Allele Frequency Spectrum, Patterson’s f, the Fixation Index, Tajima’s D, pairwise Lowest Common Ancestors, and others. On Lowest Common Ancestor queries with more than two samples as input, gfkit scales asymptotically better than the state-of-the-art, and is thus up to 990 times faster. In conclusion, our proposed data structure compresses genealogical trees by storing shared subtrees only once, thereby enabling straight-forward memoization of intermediate results, yielding a substantial runtime reduction and a potentially more intuitive data representation over the state-of-the-art. Our improvements will boost the development of novel analyses and models in the field of population genetics and increases scalability to ever-growing genomic datasets.
Cite as

Lukas Hübner and Alexandros Stamatakis. Memoization on Shared Subtrees Accelerates Computations on Genealogical Forests. In 24th International Workshop on Algorithms in Bioinformatics (WABI 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 312, pp. 5:1-5:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hubner_et_al:LIPIcs.WABI.2024.5,
  author =	{H\"{u}bner, Lukas and Stamatakis, Alexandros},
  title =	{{Memoization on Shared Subtrees Accelerates Computations on Genealogical Forests}},
  booktitle =	{24th International Workshop on Algorithms in Bioinformatics (WABI 2024)},
  pages =	{5:1--5:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-340-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{312},
  editor =	{Pissis, Solon P. and Sung, Wing-Kin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2024.5},
  URN =		{urn:nbn:de:0030-drops-206499},
  doi =		{10.4230/LIPIcs.WABI.2024.5},
  annote =	{Keywords: bioinformatics, population genetics, algorithms}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.82
An Algorithmic Meta Theorem for Homomorphism Indistinguishability

Authors: Tim Seppelt

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
Two graphs G and H are homomorphism indistinguishable over a family of graphs ℱ if for all graphs F ∈ ℱ the number of homomorphisms from F to G is equal to the number of homomorphism from F to H. Many natural equivalence relations comparing graphs such as (quantum) isomorphism, cospectrality, and logical equivalences can be characterised as homomorphism indistinguishability relations over various graph classes. The wealth of such results motivates a more fundamental study of homomorphism indistinguishability. From a computational perspective, the central object of interest is the decision problem HomInd(ℱ) which asks to determine whether two input graphs G and H are homomorphism indistinguishable over a fixed graph class ℱ. The problem HomInd(ℱ) is known to be decidable only for few graph classes ℱ. Due to a conjecture by Roberson (2022) and results by Seppelt (MFCS 2023), homomorphism indistinguishability relations over minor-closed graph classes are of special interest. We show that HomInd(ℱ) admits a randomised polynomial-time algorithm for every minor-closed graph class ℱ of bounded treewidth. This result extends to a version of HomInd where the graph class ℱ is specified by a sentence in counting monadic second-order logic and a bound k on the treewidth, which are given as input. For fixed k, this problem is randomised fixed-parameter tractable. If k is part of the input, then it is coNP- and coW[1]-hard. Addressing a problem posed by Berkholz (2012), we show coNP-hardness by establishing that deciding indistinguishability under the k-dimensional Weisfeiler-Leman algorithm is coNP-hard when k is part of the input.
Cite as

Tim Seppelt. An Algorithmic Meta Theorem for Homomorphism Indistinguishability. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 82:1-82:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{seppelt:LIPIcs.MFCS.2024.82,
  author =	{Seppelt, Tim},
  title =	{{An Algorithmic Meta Theorem for Homomorphism Indistinguishability}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{82:1--82:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.82},
  URN =		{urn:nbn:de:0030-drops-206387},
  doi =		{10.4230/LIPIcs.MFCS.2024.82},
  annote =	{Keywords: homomorphism indistinguishability, graph homomorphism, graph minor, recognisability, randomised algorithm, Courcelle’s Theorem}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2024.148
An Order out of Nowhere: A New Algorithm for Infinite-Domain CSPs

Authors: Antoine Mottet, Tomáš Nagy, and Michael Pinsker

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We consider the problem of satisfiability of sets of constraints in a given set of finite uniform hypergraphs. While the problem under consideration is similar in nature to the problem of satisfiability of constraints in graphs, the classical complexity reduction to finite-domain CSPs that was used in the proof of the complexity dichotomy for such problems cannot be used as a black box in our case. We therefore introduce an algorithmic technique inspired by classical notions from the theory of finite-domain CSPs, and prove its correctness based on symmetries that depend on a linear order that is external to the structures under consideration. Our second main result is a P/NP-complete complexity dichotomy for such problems over many sets of uniform hypergraphs. The proof is based on the translation of the problem into the framework of constraint satisfaction problems (CSPs) over infinite uniform hypergraphs. Our result confirms in particular the Bodirsky-Pinsker conjecture for CSPs of first-order reducts of some homogeneous hypergraphs. This forms a vast generalization of previous work by Bodirsky-Pinsker (STOC'11) and Bodirsky-Martin-Pinsker-Pongrácz (ICALP'16) on graph satisfiability.
Cite as

Antoine Mottet, Tomáš Nagy, and Michael Pinsker. An Order out of Nowhere: A New Algorithm for Infinite-Domain CSPs. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 148:1-148:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{mottet_et_al:LIPIcs.ICALP.2024.148,
  author =	{Mottet, Antoine and Nagy, Tom\'{a}\v{s} and Pinsker, Michael},
  title =	{{An Order out of Nowhere: A New Algorithm for Infinite-Domain CSPs}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{148:1--148:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.148},
  URN =		{urn:nbn:de:0030-drops-202912},
  doi =		{10.4230/LIPIcs.ICALP.2024.148},
  annote =	{Keywords: Constraint Satisfaction Problems, Hypergraphs, Polymorphisms}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.7
Finer-Grained Reductions in Fine-Grained Hardness of Approximation

Authors: Elie Abboud and Noga Ron-Zewi

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We investigate the relation between δ and ε required for obtaining a (1+δ)-approximation in time N^{2-ε} for closest pair problems under various distance metrics, and for other related problems in fine-grained complexity. Specifically, our main result shows that if it is impossible to (exactly) solve the (bichromatic) inner product (IP) problem for vectors of dimension c log N in time N^{2-ε}, then there is no (1+δ)-approximation algorithm for (bichromatic) Euclidean Closest Pair running in time N^{2-2ε}, where δ ≈ (ε/c)² (where ≈ hides polylog factors). This improves on the prior result due to Chen and Williams (SODA 2019) which gave a smaller polynomial dependence of δ on ε, on the order of δ ≈ (ε/c)⁶. Our result implies in turn that no (1+δ)-approximation algorithm exists for Euclidean closest pair for δ ≈ ε⁴, unless an algorithmic improvement for IP is obtained. This in turn is very close to the approximation guarantee of δ ≈ ε³ for Euclidean closest pair, given by the best known algorithm of Almam, Chan, and Williams (FOCS 2016). By known reductions, a similar result follows for a host of other related problems in fine-grained hardness of approximation. Our reduction combines the hardness of approximation framework of Chen and Williams, together with an MA communication protocol for IP over a small alphabet, that is inspired by the MA protocol of Chen (Theory of Computing, 2020).
Cite as

Elie Abboud and Noga Ron-Zewi. Finer-Grained Reductions in Fine-Grained Hardness of Approximation. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 7:1-7:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{abboud_et_al:LIPIcs.ICALP.2024.7,
  author =	{Abboud, Elie and Ron-Zewi, Noga},
  title =	{{Finer-Grained Reductions in Fine-Grained Hardness of Approximation}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{7:1--7:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.7},
  URN =		{urn:nbn:de:0030-drops-201507},
  doi =		{10.4230/LIPIcs.ICALP.2024.7},
  annote =	{Keywords: Fine-grained complexity, conditional lower bound, fine-grained reduction, Approximation algorithms, Analysis of algorithms, Computational geometry, Computational and structural complexity theory}
}
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