91 Search Results for "Fischer, Stefan"

Document
DOI: 10.4230/LIPIcs.STACS.2026.5
On the Complexity of Language Membership for Probabilistic Words

Authors: Antoine Amarilli, Mikaël Monet, Paul Raphaël, and Sylvain Salvati

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
We study the membership problem to context-free languages L (CFLs) on probabilistic words, that specify for each position a probability distribution on the letters (assuming independence across positions). Our task is to compute, given a probabilistic word, what is the probability that a word drawn according to the distribution belongs to L. This problem generalizes the problem of counting how many words of length n belong to L, or of counting how many completions of a partial word belong to L. We show that this problem is in polynomial time for unambiguous context-free languages (uCFLs), but can be #P-hard already for unions of two linear uCFLs. More generally, we show that the problem is in polynomial time for so-called poly-slicewise-unambiguous languages, where given a length n we can tractably compute an uCFL for the words of length n in the language. This class includes some inherently ambiguous languages, and implies the tractability of bounded CFLs and of languages recognized by unambiguous polynomial-time counter automata; but we show that the problem can be #P-hard for nondeterministic counter automata, even for Parikh automata with a single counter. We then introduce classes of circuits from knowledge compilation which we use for tractable counting, and show that this covers the tractability of poly-slicewise-unambiguous languages and of some CFLs that are not poly-slicewise-unambiguous. Extending these circuits with negation further allows us to show tractability for the language of primitive words, and for the language of concatenations of two palindromes. We finally show the conditional undecidability of the meta-problem that asks, given a CFG, whether the probabilistic membership problem for that CFG is tractable or #P-hard.
Cite as

Antoine Amarilli, Mikaël Monet, Paul Raphaël, and Sylvain Salvati. On the Complexity of Language Membership for Probabilistic Words. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 5:1-5:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{amarilli_et_al:LIPIcs.STACS.2026.5,
  author =	{Amarilli, Antoine and Monet, Mika\"{e}l and Rapha\"{e}l, Paul and Salvati, Sylvain},
  title =	{{On the Complexity of Language Membership for Probabilistic Words}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{5:1--5:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.5},
  URN =		{urn:nbn:de:0030-drops-254943},
  doi =		{10.4230/LIPIcs.STACS.2026.5},
  annote =	{Keywords: Automaton, probabilistic words, context-free grammar, membership problem}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.73
Colouring Probe H-Free Graphs

Authors: Daniël Paulusma, Johannes Rauch, and Erik Jan van Leeuwen

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
The NP-complete problems Colouring and k-Colouring (k ≥ 3) are well studied on H-free graphs, i.e., graphs that do not contain some fixed graph H as an induced subgraph. We research to what extent the known polynomial-time algorithms for H-free graphs can be generalized if we only know some of the edges of the input graph. We do this by considering the classical probe graph model introduced in the early nineties. For a graph H, a partitioned probe H-free graph (G,P,N) consists of a graph G = (V,E), together with a set P ⊆ V of probes and an independent set N = V ⧵ P of non-probes, such that G+F is H-free for some edge set F ⊆ binom(N,2). We show the following: - We fully classify Colouring on partitioned probe H-free graphs and show that the obtained complexity dichotomy differs from the known dichotomy of Colouring for H-free graphs. - We fully classify 3-Colouring on partitioned probe P_t-free graphs: we prove polynomial-time solvability for t ≤ 5 and NP-completeness for t ≥ 6. In contrast, 3-Colouring on P_t-free graphs is known to be polynomial-time solvable for t ≤ 7 and quasi-polynomial-time solvable for t ≥ 8. Our main result is our polynomial-time algorithm for 3-Colouring on partitioned P₅-free graphs. For this result, and also for all our other polynomial-time results, we do not need to know the edge set F; we only need to know its existence. Moreover, the class of probe P₅-free graphs includes not only paths of arbitrary length but even all bipartite graphs and is much richer than the class of P₅-free graphs. The latter is also evidenced by the fact that there exist graph problems, such as Matching Cut, that are known to be polynomial-time solvable for P₅-free graphs but NP-complete for partitioned probe P₅-free graphs. In particular, unlike the class of 3-colourable P₅-free graphs, the class of 3-colourable probe P₅-free graphs has unbounded mim-width. Hence, our polynomial-time result for 3-Colouring for probe P₅-free graphs suggests that there may be another, deeper overarching reason why 3-Colouring is polynomial-time solvable for P₅-free graphs.
Cite as

Daniël Paulusma, Johannes Rauch, and Erik Jan van Leeuwen. Colouring Probe H-Free Graphs. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 73:1-73:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{paulusma_et_al:LIPIcs.STACS.2026.73,
  author =	{Paulusma, Dani\"{e}l and Rauch, Johannes and van Leeuwen, Erik Jan},
  title =	{{Colouring Probe H-Free Graphs}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{73:1--73:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.73},
  URN =		{urn:nbn:de:0030-drops-255621},
  doi =		{10.4230/LIPIcs.STACS.2026.73},
  annote =	{Keywords: colouring, probe graph, forbidden induced subgraph, complexity dichotomy}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.79
Mind the Gap. Doubling Constant Parametrization of Weighted Problems: TSP, Max-Cut, and More

Authors: Mihail Stoian

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
Despite much research, hard weighted problems still resist super-polynomial improvements over their textbook solution. On the other hand, the unweighted versions of these problems have recently witnessed the sought-after speedups. Currently, the only way to repurpose the algorithm of the unweighted version for the weighted version is to employ a polynomial embedding of the input weights. This, however, introduces a pseudo-polynomial factor into the running time, which becomes impractical for arbitrarily weighted instances. In this paper, we introduce a new way to repurpose the algorithm of the unweighted problem. Specifically, we show that the time complexity of several well-known NP-hard problems operating over the (min, +) and (max, +) semirings, such as TSP, Weighted Max-Cut, and Edge-Weighted k-Clique, is proportional to that of their unweighted versions when the set of input weights has small doubling. We achieve this by a meta-algorithm that converts the input weights into polynomially bounded integers using the recent constructive Freiman’s theorem by Randolph and Węgrzycki [ESA 2024] before applying the polynomial embedding.
Cite as

Mihail Stoian. Mind the Gap. Doubling Constant Parametrization of Weighted Problems: TSP, Max-Cut, and More. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 79:1-79:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{stoian:LIPIcs.STACS.2026.79,
  author =	{Stoian, Mihail},
  title =	{{Mind the Gap. Doubling Constant Parametrization of Weighted Problems: TSP, Max-Cut, and More}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{79:1--79:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.79},
  URN =		{urn:nbn:de:0030-drops-255680},
  doi =		{10.4230/LIPIcs.STACS.2026.79},
  annote =	{Keywords: doubling constant parametrization, weighted problems, traveling salesman, weighted max-cut, edge-weighted k-clique}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.28
Conditional Complexity Hardness: Monotone Circuit Size, Matrix Rigidity, and Tensor Rank

Authors: Nikolai Chukhin, Alexander S. Kulikov, Ivan Mihajlin, and Arina Smirnova

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
Proving complexity lower bounds remains a challenging task: currently, we only know how to prove conditional uniform (algorithm) lower bounds and nonuniform (circuit) lower bounds in restricted circuit models. About a decade ago, Williams (STOC 2010) showed how to derive nonuniform lower bounds from uniform upper bounds: roughly, by designing a fast algorithm for checking satisfiability of circuits, one gets a lower bound for this circuit class. Since then, a number of results of this kind have been proved. For example, Jahanjou et al. (ICALP 2015) and Carmosino et al. (ITCS 2016) proved that if NSETH fails, then E^{NP} has series-parallel circuit size ω(n). One can also derive nonuniform lower bounds from nondeterministic uniform lower bounds. Perhaps the most well-known example is the Karp-Lipton theorem (STOC 1980): if Σ₂ ≠ Π₂, then NP ⊄ P/poly. Some recent examples include the following. Nederlof (STOC 2020) proved a lower bound on the matrix multiplication tensor rank under an assumption that TSP cannot be solved faster than in 2ⁿ time. Belova et al. (SODA 2024) proved that there exists an explicit polynomial family of arithmetic circuit size Ω(n^{δ}), for any δ > 0, assuming that MAX-3-SAT cannot be solved faster than in 2ⁿ nondeterministic time. Williams (FOCS 2024) proved an exponential lower bound for ETHR ∘ ETHR circuits under the Orthogonal Vectors conjecture. Whereas all the lower bounds above are proved under strong assumptions that might eventually be refuted, the revealed connections are of great interest and may still give further insights: one may be able to weaken the used assumptions or to construct generators from other fine-grained reductions. In this paper, we continue developing this line of research and show how uniform nondeterministic lower bounds can be used to construct generators of various types of combinatorial objects that are notoriously hard to analyze: Boolean functions of high circuit size, matrices of high rigidity, and tensors of high rank. Specifically, we prove the following. - If, for some ε and k, k-SAT cannot be solved in input-oblivious co-nondeterministic time O(2^{(1/2+ε)n}), then there exists a monotone Boolean function family in coNP of monotone circuit size 2^{Ω(n / log n)}. Combining this with the result above, we get win-win circuit lower bounds: either E^{NP{}} requires series-parallel circuits of size ω(n) or coNP requires monotone circuits of size 2^{Ω(n / log n)}. - If, for all ε > 0, MAX-3-SAT cannot be solved in co-nondeterministic time O(2^{(1 - ε)n}), then there exist small families of matrices with rigidity exceeding the best known constructions as well as small families of three-dimensional tensors of rank n^{1+Δ}, for some Δ > 0.
Cite as

Nikolai Chukhin, Alexander S. Kulikov, Ivan Mihajlin, and Arina Smirnova. Conditional Complexity Hardness: Monotone Circuit Size, Matrix Rigidity, and Tensor Rank. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 28:1-28:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chukhin_et_al:LIPIcs.STACS.2026.28,
  author =	{Chukhin, Nikolai and Kulikov, Alexander S. and Mihajlin, Ivan and Smirnova, Arina},
  title =	{{Conditional Complexity Hardness: Monotone Circuit Size, Matrix Rigidity, and Tensor Rank}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{28:1--28:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.28},
  URN =		{urn:nbn:de:0030-drops-255177},
  doi =		{10.4230/LIPIcs.STACS.2026.28},
  annote =	{Keywords: computational complexity, circuit complexity, lower bounds, conditional lower bounds, monotone circuits, matrix rigidity, tensor rank, arithmetic circuits, fine-grained complexity}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.15
How to Use Nondeterminism in Cryptography

Authors: Marshall Ball and Peter Crawford-Kahrl

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
Nondeterministic reductions have yielded powerful results in the theory of computational complexity, yet are effectively useless in a cryptographic context. The reason for this is simple, a nondeterministic polynomial time adversary can trivially break almost any cryptographic primitive by simply guessing the "key." In order to use this powerful nondeterministic tool kit in the cryptographic context, we initiate the study of cryptography against adversaries with limited nondeterminism: polynomial time nondeterministic algorithms that are restricted to just a few bits of nondeterminism. We demonstrate that limited nondeterministic security is sufficient to prove two foundational results that have eluded our grasp for decades: dream hardness amplification, and extracting ω(log n) hardcore bits.
Cite as

Marshall Ball and Peter Crawford-Kahrl. How to Use Nondeterminism in Cryptography. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 15:1-15:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ball_et_al:LIPIcs.ITCS.2026.15,
  author =	{Ball, Marshall and Crawford-Kahrl, Peter},
  title =	{{How to Use Nondeterminism in Cryptography}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{15:1--15:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.15},
  URN =		{urn:nbn:de:0030-drops-253024},
  doi =		{10.4230/LIPIcs.ITCS.2026.15},
  annote =	{Keywords: limited nondeterminism, cryptography, computational complexity, hardness amplification, pseudorandom generators, hardcore bits}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.54
Testable Algorithms for Approximately Counting Edges and Triangles in Sublinear Time and Space

Authors: Talya Eden, Ronitt Rubinfeld, and Arsen Vasilyan

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
We consider the fundamental problems of approximately counting the numbers of edges and triangles in a graph in sublinear time. Previous algorithms for these tasks are significantly more efficient under a promise that the arboricity of the graph is bounded by some parameter ̅α. However, when this promise is violated, the estimates given by these algorithms are no longer guaranteed to be correct. For the triangle counting task, we give an algorithm that requires no promise on the input graph G, and computes a (1±ε)-approximation for the number of triangles t in G in time O^*((m⋅ α(G))/t + m/(t^{2/3)}), where α(G) is the arboricity of the graph. The algorithm can be used on any graph G (no prior knowledge of the arboricity α(G) is required), and the algorithm adapts its run-time on the fly based on the graph G. We accomplish this by trying a sequence of candidate values α̃ for α(G) and using a novel algorithm in the framework of testable algorithms. This ensures that wrong candidates α̃ cannot lead to wrong estimates: if the advice is incorrect, the algorithm either succeeds despite this or detects this and continues with a new candidate. Once the algorithm accepts the candidate, its output is guaranteed to be correct with high probability. We prove that this approach preserves - up to an additive overhead - the dramatic efficiency gains obtainable when good arboricity bounds are known in advance, while ensuring robustness against misleading advice. We further complement this result with a lower bound, showing that such an overhead is unavoidable whenever the advice may be faulty. We further demonstrate implications of our results for triangle counting in the streaming model.
Cite as

Talya Eden, Ronitt Rubinfeld, and Arsen Vasilyan. Testable Algorithms for Approximately Counting Edges and Triangles in Sublinear Time and Space. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 54:1-54:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{eden_et_al:LIPIcs.ITCS.2026.54,
  author =	{Eden, Talya and Rubinfeld, Ronitt and Vasilyan, Arsen},
  title =	{{Testable Algorithms for Approximately Counting Edges and Triangles in Sublinear Time and Space}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{54:1--54:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.54},
  URN =		{urn:nbn:de:0030-drops-253417},
  doi =		{10.4230/LIPIcs.ITCS.2026.54},
  annote =	{Keywords: Sublinear Algorithms, Triangle Counting, Edge Counting, Arboricity}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.36
Beyond 2-Edge-Connectivity: Algorithms and Impossibility for Content-Oblivious Leader Election

Authors: Yi-Jun Chang, Lyuting Chen, and Haoran Zhou

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
The content-oblivious model, introduced by Censor-Hillel, Cohen, Gelles, and Sela (PODC 2022; Distributed Computing 2023), captures an extremely weak form of communication where nodes can only send asynchronous, content-less pulses. They showed that in 2-edge-connected networks, any distributed algorithm can be simulated in the content-oblivious model, provided that a unique leader is designated a priori. Subsequent works of Frei, Gelles, Ghazy, and Nolin (DISC 2024) and Chalopin et al. (DISC 2025) developed content-oblivious leader election algorithms, first for unoriented rings and then for general 2-edge-connected graphs. These results establish that all graph problems are solvable in content-oblivious, 2-edge-connected networks. Much less is known about networks that are not 2-edge-connected. Censor-Hillel, Cohen, Gelles, and Sela showed that no non-constant function f(x,y) can be computed correctly by two parties using content-oblivious communication over a single edge, where one party holds x and the other holds y. This seemingly ruled out many natural graph problems on non-2-edge-connected graphs. In this work, we show that, with the knowledge of network topology G, leader election is possible in a wide range of graphs. Our main contributions are as follows: Impossibility: Graphs symmetric about an edge admit no randomized terminating leader election algorithm, even when nodes have unique identifiers and full knowledge of G. Leader election algorithms: Trees that are not symmetric about any edge admit a quiescently terminating leader election algorithm with topology knowledge, even in anonymous networks, using O(n²) messages, where n is the number of nodes. Moreover, even-diameter trees admit a terminating leader election given only the knowledge of the network diameter D = 2r, with message complexity O(nr). Necessity of topology knowledge: In the family of graphs 𝒢 = {P₃, P₅}, both the 3-path P₃ and the 5-path P₅ admit a quiescently terminating leader election if nodes know the topology exactly. However, if nodes only know that the underlying topology belongs to 𝒢, then terminating leader election is impossible.
Cite as

Yi-Jun Chang, Lyuting Chen, and Haoran Zhou. Beyond 2-Edge-Connectivity: Algorithms and Impossibility for Content-Oblivious Leader Election. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 36:1-36:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chang_et_al:LIPIcs.ITCS.2026.36,
  author =	{Chang, Yi-Jun and Chen, Lyuting and Zhou, Haoran},
  title =	{{Beyond 2-Edge-Connectivity: Algorithms and Impossibility for Content-Oblivious Leader Election}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{36:1--36:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.36},
  URN =		{urn:nbn:de:0030-drops-253239},
  doi =		{10.4230/LIPIcs.ITCS.2026.36},
  annote =	{Keywords: Asynchronous model, fault tolerance, quiescent termination}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2025.10
Computing in a Faulty Congested Clique

Authors: Keren Censor-Hillel and Pedro Soto

Published in: LIPIcs, Volume 361, 29th International Conference on Principles of Distributed Systems (OPODIS 2025)

Abstract
We study a Faulty Congested Clique model, in which an adversary may fail nodes in the network throughout the computation. We show that any task of O(nlog{n})-bit input per node can be solved in roughly n rounds, where n is the size of the network. This nearly matches the linear upper bound on the complexity of the non-faulty Congested Clique model for such problems, by learning the entire input, and it holds in the faulty model even with a linear number of faults. Our main contribution is that we establish that one can do much better by looking more closely at the computation. Given a deterministic algorithm 𝒜 for the non-faulty Congested Clique model, we show how to transform it into an algorithm 𝒜' for the faulty model, with an overhead that could be as small as some logarithmic-in-n factor, by considering refined complexity measures of 𝒜. As an exemplifying application of our approach, we show that the O(n^{1/3})-round complexity of semi-ring matrix multiplication [Censor{-}Hillel, Kaski, Korhonen, Lenzen, Paz, Suomela, PODC 2015] remains the same up to polylog factors in the faulty model, even if the adversary can fail 99% of the nodes (or any other constant fraction).
Cite as

Keren Censor-Hillel and Pedro Soto. Computing in a Faulty Congested Clique. In 29th International Conference on Principles of Distributed Systems (OPODIS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 361, pp. 10:1-10:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{censorhillel_et_al:LIPIcs.OPODIS.2025.10,
  author =	{Censor-Hillel, Keren and Soto, Pedro},
  title =	{{Computing in a Faulty Congested Clique}},
  booktitle =	{29th International Conference on Principles of Distributed Systems (OPODIS 2025)},
  pages =	{10:1--10:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-409-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{361},
  editor =	{Arusoaie, Andrei and Onica, Emanuel and Spear, Michael and Tucci-Piergiovanni, Sara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2025.10},
  URN =		{urn:nbn:de:0030-drops-251833},
  doi =		{10.4230/LIPIcs.OPODIS.2025.10},
  annote =	{Keywords: distributed computing, graph algorithms, computing with faults}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.8
Binary k-Center with Missing Entries: Structure Leads to Tractability

Authors: Tobias Friedrich, Kirill Simonov, and Farehe Soheil

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

Abstract
k-Center clustering is a fundamental classification problem, where the task is to categorize the given collection of entities into k clusters and come up with a representative for each cluster, so that the maximum distance between an entity and its representative is minimized. In this work, we focus on the setting where the entities are represented by binary vectors with missing entries, which model incomplete categorical data. This version of the problem has wide applications, from predictive analytics to bioinformatics. Our main finding is that the problem, which is notoriously hard from the classical complexity viewpoint, becomes tractable as soon as the known entries are sparse and exhibit a certain structure. Formally, we show fixed-parameter tractable algorithms for the parameters vertex cover, fracture number, and treewidth of the row-column graph, which encodes the positions of the known entries of the matrix. Additionally, we tie the complexity of the 1-cluster variant of the problem, which is famous under the name Closest String, to the complexity of solving integer linear programs with few constraints. This implies, in particular, that improving upon the running times of our algorithms would lead to more efficient algorithms for integer linear programming in general.
Cite as

Tobias Friedrich, Kirill Simonov, and Farehe Soheil. Binary k-Center with Missing Entries: Structure Leads to Tractability. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{friedrich_et_al:LIPIcs.IPEC.2025.8,
  author =	{Friedrich, Tobias and Simonov, Kirill and Soheil, Farehe},
  title =	{{Binary k-Center with Missing Entries: Structure Leads to Tractability}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{8:1--8:19},
  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.2025.8},
  URN =		{urn:nbn:de:0030-drops-251403},
  doi =		{10.4230/LIPIcs.IPEC.2025.8},
  annote =	{Keywords: Clustering, Missing Entries, k-Center, Parameterized Algorithms}
}
Document
Poster Abstract
DOI: 10.4230/LIPIcs.GD.2025.52
Investigating Crossing Perception in 3D Graph Visualisation (Poster Abstract)

Authors: Ying Zhang, Niklas Gröne, Giuseppe Liotta, Falk Schreiber, and Karsten Klein

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

Abstract
Human perception and understanding of graph drawings is influenced by a variety of impact factors for which quality measures such as the number of crossings are used as a proxy indicator. For the more and more common stereoscopic 3D (S3D) graph visualisations, evidence is required to better understand graph perception and its relation to quality measures. We investigate the perception of crossing configurations in S3D graph visualisations and present the results of a study.
Cite as

Ying Zhang, Niklas Gröne, Giuseppe Liotta, Falk Schreiber, and Karsten Klein. Investigating Crossing Perception in 3D Graph Visualisation (Poster Abstract). In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 52:1-52:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{zhang_et_al:LIPIcs.GD.2025.52,
  author =	{Zhang, Ying and Gr\"{o}ne, Niklas and Liotta, Giuseppe and Schreiber, Falk and Klein, Karsten},
  title =	{{Investigating Crossing Perception in 3D Graph Visualisation}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{52:1--52:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.52},
  URN =		{urn:nbn:de:0030-drops-250381},
  doi =		{10.4230/LIPIcs.GD.2025.52},
  annote =	{Keywords: Graph Perception, Stereoscopic 3D Graph Visualisation, Crossing Configurations}
}
Document
DOI: 10.4230/LIPIcs.GD.2025.17
Visualizing Treewidth

Authors: Alvin Chiu, Thomas Depian, David Eppstein, Michael T. Goodrich, and Martin Nöllenburg

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

Abstract
A witness drawing of a graph is a visualization that clearly shows a given property of a graph. We study and implement various drawing paradigms for witness drawings to clearly show that graphs have bounded pathwidth or treewidth. Our approach draws the tree decomposition or path decomposition as a tree of bags, with induced subgraphs shown in each bag, and with "tracks" for each graph vertex connecting its copies in multiple bags. Within bags, we optimize the vertex layout to avoid crossings of edges and tracks. We implement a visualization prototype for crossing minimization using dynamic programming for graphs of small width and heuristic approaches for graphs of larger width. We introduce a taxonomy of drawing styles, which render the subgraph for each bag as an arc diagram with one or two pages or as a circular layout with straight-line edges, and we render tracks either with straight lines or with orbital-radial paths.
Cite as

Alvin Chiu, Thomas Depian, David Eppstein, Michael T. Goodrich, and Martin Nöllenburg. Visualizing Treewidth. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 17:1-17:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chiu_et_al:LIPIcs.GD.2025.17,
  author =	{Chiu, Alvin and Depian, Thomas and Eppstein, David and Goodrich, Michael T. and N\"{o}llenburg, Martin},
  title =	{{Visualizing Treewidth}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{17:1--17:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.17},
  URN =		{urn:nbn:de:0030-drops-250034},
  doi =		{10.4230/LIPIcs.GD.2025.17},
  annote =	{Keywords: Graph drawing, witness drawings, pathwidth, treewidth}
}
Document
DOI: 10.4230/LIPIcs.GD.2025.11
Towards a Better Understanding of Graph Perception in Immersive Environments

Authors: Lin Zhang, Yao Wang, Ying Zhang, Wilhelm Kerle-Malcharek, Karsten Klein, Falk Schreiber, and Andreas Bulling

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

Abstract
As Immersive Analytics (IA) increasingly uses Virtual Reality (VR) for stereoscopic 3D (S3D) graph visualisation, it is crucial to understand how users perceive network structures in these immersive environments. However, little is known about how humans read S3D graphs during task solving, and how gaze behaviour indicates task performance. To address this gap, we report a user study with 18 participants asked to perform three analytical tasks on S3D graph visualisations in a VR environment. Our findings reveal systematic relationships between network structural properties and gaze behaviour. Based on these insights, we contribute a comprehensive eye tracking methodology for analysing human perception in immersive environments and establish eye tracking as a valuable tool for objectively evaluating cognitive load in S3D graph visualisation.
Cite as

Lin Zhang, Yao Wang, Ying Zhang, Wilhelm Kerle-Malcharek, Karsten Klein, Falk Schreiber, and Andreas Bulling. Towards a Better Understanding of Graph Perception in Immersive Environments. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 11:1-11:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{zhang_et_al:LIPIcs.GD.2025.11,
  author =	{Zhang, Lin and Wang, Yao and Zhang, Ying and Kerle-Malcharek, Wilhelm and Klein, Karsten and Schreiber, Falk and Bulling, Andreas},
  title =	{{Towards a Better Understanding of Graph Perception in Immersive Environments}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{11:1--11:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.11},
  URN =		{urn:nbn:de:0030-drops-249976},
  doi =		{10.4230/LIPIcs.GD.2025.11},
  annote =	{Keywords: Stereoscopic 3D, Graph Visualisation, Eye Tracking, Graph Perception}
}
Document
DOI: 10.4230/LIPIcs.GD.2025.39
Optimizing Wiggle in Storylines

Authors: Alexander Dobler, Tim Hegemann, Martin Nöllenburg, and Alexander Wolff

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

Abstract
A storyline visualization shows interactions between characters over time. Each character is represented by an x-monotone curve. Time is mapped to the x-axis, and groups of characters that interact at a particular point t in time must be ordered consecutively in the y-dimension at x = t. The predominant objective in storyline optimization so far has been the minimization of crossings between (blocks of) characters. Building on this work, we investigate another important, but less studied quality criterion, namely the minimization of wiggle, i.e., the amount of vertical movement of the characters over time. Given a storyline instance together with an ordering of the characters at any point in time, we show that wiggle count minimization is NP-complete. In contrast, we provide algorithms based on mathematical programming to solve linear wiggle height minimization and quadratic wiggle height minimization efficiently. Finally, we introduce a new method for routing character curves that focuses on keeping distances between neighboring curves constant as long as they run in parallel. We have implemented our algorithms, and we conduct a case study that explores the differences between the three optimization objectives. We use existing benchmark data, but we also present a new use case for storylines, namely the visualization of rolling stock schedules in railway operation.
Cite as

Alexander Dobler, Tim Hegemann, Martin Nöllenburg, and Alexander Wolff. Optimizing Wiggle in Storylines. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 39:1-39:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dobler_et_al:LIPIcs.GD.2025.39,
  author =	{Dobler, Alexander and Hegemann, Tim and N\"{o}llenburg, Martin and Wolff, Alexander},
  title =	{{Optimizing Wiggle in Storylines}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{39:1--39:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.39},
  URN =		{urn:nbn:de:0030-drops-250252},
  doi =		{10.4230/LIPIcs.GD.2025.39},
  annote =	{Keywords: Storyline visualization, wiggle minimization, NP-complete, linear programming, quadratic programming, experimental analysis}
}
Document
DOI: 10.4230/LIPIcs.GD.2025.37
Show Me Your Best Side: Characteristics of User-Preferred Perspectives for 3D Graph Drawings

Authors: Lucas Joos, Gavin J. Mooney, Maximilian T. Fischer, Daniel A. Keim, Falk Schreiber, Helen C. Purchase, and Karsten Klein

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

Abstract
The visual analysis of graphs in 3D has become increasingly popular, accelerated by the rise of immersive technology, such as augmented and virtual reality. Unlike 2D drawings, 3D graph layouts are highly viewpoint-dependent, making perspective selection critical for revealing structural and relational patterns. Despite its importance, there is limited empirical evidence guiding what constitutes an effective or preferred viewpoint from the user’s perspective. In this paper, we present a systematic investigation into user-preferred viewpoints in 3D graph visualisations. We conducted a controlled study with 23 participants in a virtual reality environment, where users selected their most and least preferred viewpoints for 36 different graphs varying in size and layout. From this data, enriched by qualitative feedback, we distil common strategies underlying viewpoint choice. We further analyse the alignment of user preferences with classical 2D aesthetic criteria (e.g., Crossings), 3D-specific measures (e.g., Node-Node Occlusion), and introduce a novel measure capturing the perceivability of a graph’s principal axes (Isometric Viewpoint Deviation). Our data-driven analysis indicates that Stress, Crossings, Gabriel Ratio, Edge-Node Overlap, and Isometric Viewpoint Deviation are key indicators of viewpoint preference. Beyond our findings, we contribute a publicly available dataset consisting of the graphs and computed aesthetic measures, supporting further research and the development of viewpoint evaluation measures for 3D graph drawing.
Cite as

Lucas Joos, Gavin J. Mooney, Maximilian T. Fischer, Daniel A. Keim, Falk Schreiber, Helen C. Purchase, and Karsten Klein. Show Me Your Best Side: Characteristics of User-Preferred Perspectives for 3D Graph Drawings. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 37:1-37:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{joos_et_al:LIPIcs.GD.2025.37,
  author =	{Joos, Lucas and Mooney, Gavin J. and Fischer, Maximilian T. and Keim, Daniel A. and Schreiber, Falk and Purchase, Helen C. and Klein, Karsten},
  title =	{{Show Me Your Best Side: Characteristics of User-Preferred Perspectives for 3D Graph Drawings}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{37:1--37:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.37},
  URN =		{urn:nbn:de:0030-drops-250236},
  doi =		{10.4230/LIPIcs.GD.2025.37},
  annote =	{Keywords: Graph Aesthetics, Immersive 3D, Node-Link Diagrams, Empirical Evaluation}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.30
Team Formation and Applications

Authors: Yuval Emek, Shay Kutten, Ido Rafael, and Gadi Taubenfeld

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
A novel long-lived distributed problem, called Team Formation (TF), is introduced together with a message- and time-efficient randomized algorithm. The problem is defined over the asynchronous model with a complete communication graph, using bounded size messages, where a certain fraction of the nodes may experience a generalized, strictly stronger, version of initial failures. The goal of a TF algorithm is to assemble tokens injected by the environment, in a distributed manner, into teams of size σ, where σ is a parameter of the problem. The usefulness of TF is demonstrated by using it to derive efficient algorithms for many distributed problems. Specifically, we show that various (one-shot as well as long-lived) distributed problems reduce to TF. This includes well-known (and extensively studied) distributed problems such as several versions of leader election and threshold detection. For example, we are the first to break the linear message complexity bound for asynchronous implicit leader election. We also improve the time complexity of message-optimal algorithms for asynchronous explicit leader election. Other distributed problems that reduce to TF are new ones, including matching players in online gaming platforms, a generalization of gathering, constructing a perfect matching in an induced subgraph of the complete graph, and more. To complement our positive contribution, we establish a tight lower bound on the message complexity of TF algorithms.
Cite as

Yuval Emek, Shay Kutten, Ido Rafael, and Gadi Taubenfeld. Team Formation and Applications. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 30:1-30:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{emek_et_al:LIPIcs.DISC.2025.30,
  author =	{Emek, Yuval and Kutten, Shay and Rafael, Ido and Taubenfeld, Gadi},
  title =	{{Team Formation and Applications}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{30:1--30:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.30},
  URN =		{urn:nbn:de:0030-drops-248474},
  doi =		{10.4230/LIPIcs.DISC.2025.30},
  annote =	{Keywords: asynchronous message-passing, complete communication graph, initial failures, leader election, matching}
}
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