3 Search Results for "Stieß, Julian"

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2026.94
When Does Sparsity Help for k-Independent Set in Hypergraphs and Other Boolean CSPs?

Authors: Timo Fritsch, Marvin Künnemann, Mirza Redzic, and Julian Stieß

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

Abstract
Consider the fundamental task of finding independent sets of (constant) size k in a given n-node hypergraph. How much is the time complexity affected by the sparsity of the input, i.e., the number of hyperedges m? Turán’s theorem implies that the problem is trivial if m = O(n^{2-ε}) for some ε > 0. Above that threshold (i.e., if m = Θ(n^γ) for some γ ≥ 2), we give a perhaps surprising algorithm with running time O(min{ n^({ω/3}k) + m^{k/3}, n^k}) (for k divisible by 3), which is essentially conditionally optimal for all γ ≥ 2, assuming the k-clique and 3-uniform hyperclique hypotheses (here, ω ≤ 2.372 denotes the matrix multiplication exponent). In fact, we obtain a more detailed time complexity that is sensitive to the arity distribution of the hyperedges. To study such phenomena in more generality, we study the time complexity of finding solutions of (constant) size k in sparse instances of Boolean constraint satisfaction problems, where n and m denote the number of variables and constraints, respectively. Our results include, among others: - an essentially full classification of the influence of sparsity for Boolean constraint families of binary arity. Of particular technical interest is a conditionally tight algorithm for the family consisting of the binary NAND and the binary Implication constraints, with a running time of Θ(m^{ω k/6 ± c}). - the identification of a large class of constraint families ℱ that exhibits a sharp phase transition: there is a threshold γ_ℱ such that the problem is trivial for m = O(n^{γ_ℱ-ε}), but requires essentially brute-force running time Θ(n^{k±c}) for m = Ω(n^{γ_ℱ}), assuming the 3-uniform hyperclique hypothesis. In general, we observe a rich landscape of time complexities. Notably, in many cases the combination of constraints display higher time complexity than either constraint alone.
Cite as

Timo Fritsch, Marvin Künnemann, Mirza Redzic, and Julian Stieß. When Does Sparsity Help for k-Independent Set in Hypergraphs and Other Boolean CSPs?. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 94:1-94:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{fritsch_et_al:LIPIcs.ICALP.2026.94,
  author =	{Fritsch, Timo and K\"{u}nnemann, Marvin and Redzic, Mirza and Stie{\ss}, Julian},
  title =	{{When Does Sparsity Help for k-Independent Set in Hypergraphs and Other Boolean CSPs?}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{94:1--94:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael 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.2026.94},
  URN =		{urn:nbn:de:0030-drops-264836},
  doi =		{10.4230/LIPIcs.ICALP.2026.94},
  annote =	{Keywords: Multivariate algorithmics, fine-grained complexity theory, classification theorems, algorithmic hypergraph theory}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.78
The Role of Regularity in (Hyper-)Clique Detection and Implications for Optimizing Boolean CSPs

Authors: Nick Fischer, Marvin Künnemann, Mirza Redžić, and Julian Stieß

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

Abstract
Is detecting a k-clique in k-partite regular (hyper-)graphs as hard as in the general case? Intuition suggests yes, but proving this - especially for hypergraphs - poses notable challenges. Concretely, we consider a strong notion of regularity in h-uniform hypergraphs, where we essentially require that any subset of at most h-1 is incident to a uniform number of hyperedges. Such notions are studied intensively in the combinatorial block design literature. We show that any f(k)n^{g(k)}-time algorithm for detecting k-cliques in such graphs transfers to an f'(k)n^{g(k)}-time algorithm for the general case, establishing a fine-grained equivalence between the h-uniform hyperclique hypothesis and its natural regular analogue. Equipped with this regularization result, we then fully resolve the fine-grained complexity of optimizing Boolean constraint satisfaction problems over assignments with k non-zeros. Our characterization depends on the maximum degree d of a constraint function. Specifically, if d ≤ 1, we obtain a linear-time solvable problem, if d = 2, the time complexity is essentially equivalent to k-clique detection, and if d ≥ 3 the problem requires exhaustive-search time under the 3-uniform hyperclique hypothesis. To obtain our hardness results, the regularization result plays a crucial role, enabling a very convenient approach when applied carefully. We believe that our regularization result will find further applications in the future.
Cite as

Nick Fischer, Marvin Künnemann, Mirza Redžić, and Julian Stieß. The Role of Regularity in (Hyper-)Clique Detection and Implications for Optimizing Boolean CSPs. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 78:1-78:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fischer_et_al:LIPIcs.ICALP.2025.78,
  author =	{Fischer, Nick and K\"{u}nnemann, Marvin and Red\v{z}i\'{c}, Mirza and Stie{\ss}, Julian},
  title =	{{The Role of Regularity in (Hyper-)Clique Detection and Implications for Optimizing Boolean CSPs}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{78:1--78:18},
  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.2025.78},
  URN =		{urn:nbn:de:0030-drops-234559},
  doi =		{10.4230/LIPIcs.ICALP.2025.78},
  annote =	{Keywords: fine-grained complexity theory, clique detections in hypergraphs, constraint satisfaction, parameterized algorithms}
}
Document
DOI: 10.4230/LIPIcs.SEA.2023.1
Engineering a Preprocessor for Symmetry Detection

Authors: Markus Anders, Pascal Schweitzer, and Julian Stieß

Published in: LIPIcs, Volume 265, 21st International Symposium on Experimental Algorithms (SEA 2023)

Abstract
State-of-the-art solvers for symmetry detection in combinatorial objects are becoming increasingly sophisticated software libraries. Most of the solvers were initially designed with inputs from combinatorics in mind (nauty, bliss, Traces, dejavu). They excel at dealing with a complicated core of the input. Others focus on practical instances that exhibit sparsity. They excel at dealing with comparatively easy but extremely large substructures of the input (saucy). In practice, these differences manifest in significantly diverging performances on different types of graph classes. We engineer a preprocessor for symmetry detection. The result is a tool designed to shrink sparse, large substructures of the input graph. On most of the practical instances, the preprocessor improves the overall running time significantly for many of the state-of-the-art solvers. At the same time, our benchmarks show that the additional overhead is negligible. Overall we obtain single algorithms with competitive performance across all benchmark graphs. As such, the preprocessor bridges the disparity between solvers that focus on combinatorial graphs and large practical graphs. In fact, on most of the practical instances the combined setup significantly outperforms previous state-of-the-art.
Cite as

Markus Anders, Pascal Schweitzer, and Julian Stieß. Engineering a Preprocessor for Symmetry Detection. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 1:1-1:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{anders_et_al:LIPIcs.SEA.2023.1,
  author =	{Anders, Markus and Schweitzer, Pascal and Stie{\ss}, Julian},
  title =	{{Engineering a Preprocessor for Symmetry Detection}},
  booktitle =	{21st International Symposium on Experimental Algorithms (SEA 2023)},
  pages =	{1:1--1:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-279-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{265},
  editor =	{Georgiadis, Loukas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2023.1},
  URN =		{urn:nbn:de:0030-drops-183511},
  doi =		{10.4230/LIPIcs.SEA.2023.1},
  annote =	{Keywords: graph isomorphism, automorphism groups, symmetry detection, preprocessors}
}
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