11 Search Results for "Larose, Benoit"

Document
DOI: 10.4230/LIPIcs.SoCG.2026.93
Simplicial Approximation to CW Complexes with Spherical Delaunay Triangulations

Authors: Raphaël Tinarrage

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
Simplicial approximation provides a framework for constructing simplicial complexes that are homotopy equivalent to a given manifold, provided a CW structure is explicitly known. However, its conventional implementation quickly becomes intractable on a computer: barycentric subdivision produces poorly shaped simplices, and the star condition introduces many vertices. To address these limitations, this article develops a subdivision scheme based on spherical Delaunay triangulations, which attains better refinement properties than barycentric subdivisions. Moreover, the star condition is reframed as two independent problems, one geometric and the other combinatorial, respectively tackled in the language of locally equiconnected spaces and the list homomorphism problem, allowing an exponential reduction in the number of vertices. Via a prototype implementation, we obtain simplicial complexes homotopy equivalent to Grassmannians and Stiefel manifolds up to dimension 5.
Cite as

Raphaël Tinarrage. Simplicial Approximation to CW Complexes with Spherical Delaunay Triangulations. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 93:1-93:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{tinarrage:LIPIcs.SoCG.2026.93,
  author =	{Tinarrage, Rapha\"{e}l},
  title =	{{Simplicial Approximation to CW Complexes with Spherical Delaunay Triangulations}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{93:1--93:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.93},
  URN =		{urn:nbn:de:0030-drops-258991},
  doi =		{10.4230/LIPIcs.SoCG.2026.93},
  annote =	{Keywords: Triangulation of manifolds, Simplicial approximation, CW complexes, Delaunay complexes, List homomorphism problem, Topological Data Analysis}
}
Document
DOI: 10.4230/LIPIcs.FUN.2026.15
Spells for Quantum Programmers: Expressive High-Level Commands in Qutes

Authors: Simone Faro, Francesco Pio Marino, and Gabriele Messina

Published in: LIPIcs, Volume 366, 13th International Conference on Fun with Algorithms (FUN 2026)

Abstract
Classical computers are powerful but fundamentally mundane: they operate through explicit, step-by-step instructions that force programmers to think locally and procedurally. Quantum technologies, by contrast, resemble magical instruments, capable of acting on superpositions, correlations, and entire collections of states at once. Yet, despite their magical nature, quantum computers are still programmed as if they were ordinary machines, relying on long sequences of low-level operations that obscure the underlying algorithmic ideas. Magic, however, is not performed by improvisation alone: it requires a spellbook. In this paper we position Qutes as a book of spells for quantum programmers, providing high-level commands that capture complex quantum behaviour behind concise and expressive syntax. We focus on the manipulation of quantum arrays, which naturally arise in many algorithms but are notoriously cumbersome to manage at the circuit level. We introduce three new array-oriented spells in Qutes: global initialization, parallel pairwise comparison, and parallel (optionally controlled) swap. Individually, these spells encapsulate non-trivial quantum procedures; when combined, they enable programmers to express algorithms in a way that is immediate, readable, and surprisingly elegant. As a final demonstration, we show how these spells can be assembled to produce a remarkably compact implementation of Bubble Sort. While algorithmically simple, this example illustrates a broader message: when the right abstractions are available, quantum programming can feel less like engineering machinery and more like magic.
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Simone Faro, Francesco Pio Marino, and Gabriele Messina. Spells for Quantum Programmers: Expressive High-Level Commands in Qutes. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 15:1-15:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{faro_et_al:LIPIcs.FUN.2026.15,
  author =	{Faro, Simone and Marino, Francesco Pio and Messina, Gabriele},
  title =	{{Spells for Quantum Programmers: Expressive High-Level Commands in Qutes}},
  booktitle =	{13th International Conference on Fun with Algorithms (FUN 2026)},
  pages =	{15:1--15:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-417-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{366},
  editor =	{Iacono, John},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2026.15},
  URN =		{urn:nbn:de:0030-drops-257349},
  doi =		{10.4230/LIPIcs.FUN.2026.15},
  annote =	{Keywords: Quantum programming languages, High-level abstractions, Quantum arrays}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.5
Kernelization for H-Coloring

Authors: Yael Berkman and Ishay Haviv

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
For a fixed graph H, the H-Coloring problem asks whether a given graph admits an edge-preserving function from its vertex set to that of H. A seminal theorem of Hell and Nešetřil asserts that the H-Coloring problem is NP-hard whenever H is loopless and non-bipartite. A result of Jansen and Pieterse implies that for every graph H, the H-Coloring problem parameterized by the vertex cover number k admits a kernel with O(k^Δ(H)) vertices and bit-size bounded by O(k^Δ(H)⋅log k), where Δ(H) denotes the maximum degree in H. For the case where H is a complete graph on at least three vertices, this kernel size nearly matches conditional lower bounds established by Jansen and Kratsch and by Jansen and Pieterse. This paper presents new upper and lower bounds on the kernel size of H-Coloring problems parameterized by the vertex cover number. The upper bounds arise from two kernelization algorithms. The first is purely combinatorial, and its size is governed by a structural quantity of the graph H, called the non-adjacency witness number. As applications, we obtain kernels whose size is bounded by a fixed polynomial for natural classes of graphs H with unbounded maximum degree, such as planar graphs and, more broadly, graphs with bounded degeneracy. More strikingly, we show that for almost every graph H, the degree of the polynomial that bounds the size of our combinatorial kernel grows only logarithmically in Δ(H). Our second kernel leverages linear-algebraic tools and involves the notion of faithful independent representations of graphs. It strengthens the general bound from prior work and, among other applications, yields near-optimal kernels for problems concerning the dimension of orthogonal graph representations over finite fields. We complement our kernelization results with conditional lower bounds, thereby nearly settling the kernel complexity of the problem for various target graphs H.
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Yael Berkman and Ishay Haviv. Kernelization for H-Coloring. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 5:1-5:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{berkman_et_al:LIPIcs.IPEC.2025.5,
  author =	{Berkman, Yael and Haviv, Ishay},
  title =	{{Kernelization for H-Coloring}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{5:1--5:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.5},
  URN =		{urn:nbn:de:0030-drops-251376},
  doi =		{10.4230/LIPIcs.IPEC.2025.5},
  annote =	{Keywords: Kernelization, Graph coloring, Graph homomorphism}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.34
Adaptive Query Algorithms for Relational Structures Based on Homomorphism Counts

Authors: Balder ten Cate, Phokion G. Kolaitis, and Arnar Á. Kristjánsson

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
A query algorithm based on homomorphism counts is a procedure to decide membership for a class of finite relational structures using only homomorphism count queries. A left query algorithm can ask the number of homomorphisms from any structure to the input structure and a right query algorithm can ask the number of homomorphisms from the input structure to any other structure. We systematically compare the expressive power of different types of left or right query algorithms, including non-adaptive query algorithms, adaptive query algorithms that can ask a bounded number of queries, and adaptive query algorithms that can ask an unbounded number of queries. We also consider query algorithms where the homomorphism counting is done over the Boolean semiring 𝔹, meaning that only the existence of a homomorphism is recorded, not the precise number of them.
Cite as

Balder ten Cate, Phokion G. Kolaitis, and Arnar Á. Kristjánsson. Adaptive Query Algorithms for Relational Structures Based on Homomorphism Counts. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 34:1-34:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{tencate_et_al:LIPIcs.MFCS.2025.34,
  author =	{ten Cate, Balder and Kolaitis, Phokion G. and Kristj\'{a}nsson, Arnar \'{A}.},
  title =	{{Adaptive Query Algorithms for Relational Structures Based on Homomorphism Counts}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{34:1--34:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.34},
  URN =		{urn:nbn:de:0030-drops-241413},
  doi =		{10.4230/LIPIcs.MFCS.2025.34},
  annote =	{Keywords: Query algorithms, homomorphisms, homomorphism counts, directed graphs, relational structures, Datalog, constraint satisfaction}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.37
Satisfiability of Commutative vs. Non-Commutative CSPs

Authors: Andrei A. Bulatov and Stanislav Živný

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

Abstract
The Mermin-Peres magic square is a celebrated example of a system of Boolean linear equations that is not (classically) satisfiable but is satisfiable via linear operators on a Hilbert space of dimension four. A natural question is then, for what kind of problems such a phenomenon occurs? Atserias, Kolaitis, and Severini answered this question for all Boolean Constraint Satisfaction Problems (CSPs): For 0-Valid-SAT, 1-Valid-SAT, 2-SAT, Horn-SAT, and Dual Horn-SAT, classical satisfiability and operator satisfiability is the same and thus there is no gap; for all other Boolean CSPs, these notions differ as there are gaps, i.e., there are unsatisfiable instances that are satisfiable via operators on Hilbert spaces. We generalize their result to CSPs on arbitrary finite domains and give an almost complete classification: First, we show that NP-hard CSPs admit a separation between classical satisfiability and satisfiability via operators on finite- and infinite-dimensional Hilbert spaces. Second, we show that tractable CSPs of bounded width have no satisfiability gaps of any kind. Finally, we show that tractable CSPs of unbounded width can simulate, in a satisfiability-gap-preserving fashion, linear equations over an Abelian group of prime order p; for such CSPs, we obtain a separation of classical satisfiability and satisfiability via operators on infinite-dimensional Hilbert spaces. Furthermore, if p = 2, such CSPs also have gaps separating classical satisfiability and satisfiability via operators on finite- and infinite-dimensional Hilbert spaces.
Cite as

Andrei A. Bulatov and Stanislav Živný. Satisfiability of Commutative vs. Non-Commutative CSPs. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 37:1-37:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bulatov_et_al:LIPIcs.ICALP.2025.37,
  author =	{Bulatov, Andrei A. and \v{Z}ivn\'{y}, Stanislav},
  title =	{{Satisfiability of Commutative vs. Non-Commutative CSPs}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{37:1--37:18},
  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.2025.37},
  URN =		{urn:nbn:de:0030-drops-234149},
  doi =		{10.4230/LIPIcs.ICALP.2025.37},
  annote =	{Keywords: constraint satisfaction, quantum CSP, operator CSP}
}
Document
DOI: 10.4230/LIPIcs.ICDT.2025.13
Symmetric Linear Arc Monadic Datalog and Gadget Reductions

Authors: Manuel Bodirsky and Florian Starke

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

Abstract
A Datalog program solves a constraint satisfaction problem (CSP) if and only if it derives the goal predicate precisely on the unsatisfiable instances of the CSP. There are three Datalog fragments that are particularly important for finite-domain constraint satisfaction: arc monadic Datalog, linear Datalog, and symmetric linear Datalog, each having good computational properties. We consider the fragment of Datalog where we impose all of these restrictions simultaneously, i.e., we study symmetric linear arc monadic (slam) Datalog. We characterise the CSPs that can be solved by a slam Datalog program as those that have a gadget reduction to a particular Boolean constraint satisfaction problem. We also present exact characterisations in terms of a homomorphism duality (which we call unfolded caterpillar duality), and in universal-algebraic terms (using known minor conditions, namely the existence of quasi Maltsev operations and k-absorptive operations of arity nk, for all n,k ≥ 1). Our characterisations also imply that the question whether a given finite-domain CSP can be expressed by a slam Datalog program is decidable.
Cite as

Manuel Bodirsky and Florian Starke. Symmetric Linear Arc Monadic Datalog and Gadget Reductions. In 28th International Conference on Database Theory (ICDT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 328, pp. 13:1-13:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bodirsky_et_al:LIPIcs.ICDT.2025.13,
  author =	{Bodirsky, Manuel and Starke, Florian},
  title =	{{Symmetric Linear Arc Monadic Datalog and Gadget Reductions}},
  booktitle =	{28th International Conference on Database Theory (ICDT 2025)},
  pages =	{13:1--13:20},
  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.2025.13},
  URN =		{urn:nbn:de:0030-drops-229548},
  doi =		{10.4230/LIPIcs.ICDT.2025.13},
  annote =	{Keywords: Datalog, Gadget Reductions, Homomorphism Dualities, Minor Conditions}
}
Document
DOI: 10.4230/LIPIcs.ESA.2021.58
QCSP on Reflexive Tournaments

Authors: Benoît Larose, Petar Marković, Barnaby Martin, Daniël Paulusma, Siani Smith, and Stanislav Živný

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
We give a complexity dichotomy for the Quantified Constraint Satisfaction Problem QCSP(H) when H is a reflexive tournament. It is well-known that reflexive tournaments can be split into a sequence of strongly connected components H₁,…,H_n so that there exists an edge from every vertex of H_i to every vertex of H_j if and only if i < j. We prove that if H has both its initial and final strongly connected component (possibly equal) of size 1, then QCSP(H) is in NL and otherwise QCSP(H) is NP-hard.
Cite as

Benoît Larose, Petar Marković, Barnaby Martin, Daniël Paulusma, Siani Smith, and Stanislav Živný. QCSP on Reflexive Tournaments. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 58:1-58:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{larose_et_al:LIPIcs.ESA.2021.58,
  author =	{Larose, Beno\^{i}t and Markovi\'{c}, Petar and Martin, Barnaby and Paulusma, Dani\"{e}l and Smith, Siani and \v{Z}ivn\'{y}, Stanislav},
  title =	{{QCSP on Reflexive Tournaments}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{58:1--58:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus 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.2021.58},
  URN =		{urn:nbn:de:0030-drops-146392},
  doi =		{10.4230/LIPIcs.ESA.2021.58},
  annote =	{Keywords: computational complexity, algorithmic graph theory, quantified constraints, universal algebra, constraint satisfaction}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2019.29
Dismantlability, Connectedness, and Mixing in Relational Structures

Authors: Raimundo Briceño, Andrei A. Bulatov, Víctor Dalmau, and Benoît Larose

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
The Constraint Satisfaction Problem (CSP) and its counting counterpart appears under different guises in many areas of mathematics, computer science, statistical physics, and elsewhere. Its structural and algorithmic properties have demonstrated to play a crucial role in many of those applications. For instance, topological properties of the solution set such as connectedness is related to the hardness of CSPs over random structures. In approximate counting and statistical physics, where CSPs emerge in the form of spin systems, mixing properties and the uniqueness of Gibbs measures have been heavily exploited for approximating partition functions or the free energy of spin systems. Additionally, in the decision CSPs, structural properties of the relational structures involved - like, for example, dismantlability - and their logical characterizations have been instrumental for determining the complexity and other properties of the problem. In spite of the great diversity of those features, there are some eerie similarities between them. These were observed and made more precise in the case of graph homomorphisms by Brightwell and Winkler, who showed that the structural property of dismantlability of the target graph, the connectedness of the set of homomorphisms, good mixing properties of the corresponding spin system, and the uniqueness of Gibbs measure are all equivalent. In this paper we go a step further and demonstrate similar connections for arbitrary CSPs. This requires much deeper understanding of dismantling and the structure of the solution space in the case of relational structures, and new refined concepts of mixing introduced by Briceño. In addition, we develop properties related to the study of valid extensions of a given partially defined homomorphism, an approach that turns out to be novel even in the graph case. We also add to the mix the combinatorial property of finite duality and its logic counterpart, FO-definability, studied by Larose, Loten, and Tardif.
Cite as

Raimundo Briceño, Andrei A. Bulatov, Víctor Dalmau, and Benoît Larose. Dismantlability, Connectedness, and Mixing in Relational Structures. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 29:1-29:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{briceno_et_al:LIPIcs.ICALP.2019.29,
  author =	{Brice\~{n}o, Raimundo and Bulatov, Andrei A. and Dalmau, V{\'\i}ctor and Larose, Beno\^{i}t},
  title =	{{Dismantlability, Connectedness, and Mixing in Relational Structures}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{29:1--29:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.29},
  URN =		{urn:nbn:de:0030-drops-106059},
  doi =		{10.4230/LIPIcs.ICALP.2019.29},
  annote =	{Keywords: relational structure, constraint satisfaction problem, homomorphism, mixing properties, Gibbs measure}
}
Document
DOI: 10.4230/LIPIcs.STACS.2018.49
Surjective H-Colouring over Reflexive Digraphs

Authors: Benoit Larose, Barnaby Martin, and Daniel Paulusma

Published in: LIPIcs, Volume 96, 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)

Abstract
The Surjective H-Colouring problem is to test if a given graph allows a vertex-surjective homomorphism to a fixed graph H. The complexity of this problem has been well studied for undirected (partially) reflexive graphs. We introduce endo-triviality, the property of a structure that all of its endomorphisms that do not have range of size 1 are automorphisms, as a means to obtain complexity-theoretic classifications of Surjective H-Colouring in the case of reflexive digraphs. Chen [2014] proved, in the setting of constraint satisfaction problems, that Surjective H-Colouring is NP-complete if H has the property that all of its polymorphisms are essentially unary. We give the first concrete application of his result by showing that every endo-trivial reflexive digraph H has this property. We then use the concept of endo-triviality to prove, as our main result, a dichotomy for Surjective H-Colouring when H is a reflexive tournament: if H is transitive, then Surjective H-Colouring is in NL, otherwise it is NP-complete. By combining this result with some known and new results we obtain a complexity classification for Surjective H-Colouring when H is a partially reflexive digraph of size at most 3.
Cite as

Benoit Larose, Barnaby Martin, and Daniel Paulusma. Surjective H-Colouring over Reflexive Digraphs. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 49:1-49:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{larose_et_al:LIPIcs.STACS.2018.49,
  author =	{Larose, Benoit and Martin, Barnaby and Paulusma, Daniel},
  title =	{{Surjective H-Colouring over Reflexive Digraphs}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{49:1--49:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-062-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{96},
  editor =	{Niedermeier, Rolf and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2018.49},
  URN =		{urn:nbn:de:0030-drops-84882},
  doi =		{10.4230/LIPIcs.STACS.2018.49},
  annote =	{Keywords: Surjective H-Coloring, Computational Complexity, Algorithmic Graph Theory, Universal Algebra, Constraint Satisfaction}
}
Document
DOI: 10.4230/DFU.Vol7.15301.267
Algebra and the Complexity of Digraph CSPs: a Survey

Authors: Benoit Larose

Published in: Dagstuhl Follow-Ups, Volume 7, The Constraint Satisfaction Problem: Complexity and Approximability (2017)

Abstract
We present a brief survey of some of the key results on the interplay between algebraic and graph-theoretic methods in the study of the complexity of digraph-based constraint satisfaction problems.
Cite as

Benoit Larose. Algebra and the Complexity of Digraph CSPs: a Survey. In The Constraint Satisfaction Problem: Complexity and Approximability. Dagstuhl Follow-Ups, Volume 7, pp. 267-285, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InCollection{larose:DFU.Vol7.15301.267,
  author =	{Larose, Benoit},
  title =	{{Algebra and the Complexity of Digraph CSPs: a Survey}},
  booktitle =	{The Constraint Satisfaction Problem: Complexity and Approximability},
  pages =	{267--285},
  series =	{Dagstuhl Follow-Ups},
  ISBN =	{978-3-95977-003-3},
  ISSN =	{1868-8977},
  year =	{2017},
  volume =	{7},
  editor =	{Krokhin, Andrei and Zivny, Stanislav},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DFU.Vol7.15301.267},
  URN =		{urn:nbn:de:0030-drops-69677},
  doi =		{10.4230/DFU.Vol7.15301.267},
  annote =	{Keywords: Constraint satisfaction problems, Polymorphisms, Digraphs}
}
Document
DOI: 10.4230/LIPIcs.STACS.2010.2467
The Complexity of the List Homomorphism Problem for Graphs

Authors: László Egri, Andrei Krokhin, Benoit Larose, and Pascal Tesson

Published in: LIPIcs, Volume 5, 27th International Symposium on Theoretical Aspects of Computer Science (2010)

Abstract
We completely classify the computational complexity of the list $\bH$-colouring problem for graphs (with possible loops) in combinatorial and algebraic terms: for every graph $\bH$ the problem is either NP-complete, NL-complete, L-complete or is first-order definable; descriptive complexity equivalents are given as well via Datalog and its fragments. Our algebraic characterisations match important conjectures in the study of constraint satisfaction problems.
Cite as

László Egri, Andrei Krokhin, Benoit Larose, and Pascal Tesson. The Complexity of the List Homomorphism Problem for Graphs. In 27th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 5, pp. 335-346, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

Copy BibTex To Clipboard

@InProceedings{egri_et_al:LIPIcs.STACS.2010.2467,
  author =	{Egri, L\'{a}szl\'{o} and Krokhin, Andrei and Larose, Benoit and Tesson, Pascal},
  title =	{{The Complexity of the List Homomorphism Problem for Graphs}},
  booktitle =	{27th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{335--346},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-16-3},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{5},
  editor =	{Marion, Jean-Yves and Schwentick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2010.2467},
  URN =		{urn:nbn:de:0030-drops-24675},
  doi =		{10.4230/LIPIcs.STACS.2010.2467},
  annote =	{Keywords: Graph homomorphism, constraint satisfaction problem, complexity, universal algebra, Datalog}
}
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