19 Search Results for "Wolf, Petra"

Document
DOI: 10.4230/LIPIcs.MFCS.2024.36
Distance to Transitivity: New Parameters for Taming Reachability in Temporal Graphs

Authors: Arnaud Casteigts, Nils Morawietz, and Petra Wolf

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

Abstract
A temporal graph is a graph whose edges only appear at certain points in time. Reachability in these graphs is defined in terms of paths that traverse the edges in chronological order (temporal paths). This form of reachability is neither symmetric nor transitive, the latter having important consequences on the computational complexity of even basic questions, such as computing temporal connected components. In this paper, we introduce several parameters that capture how far a temporal graph 𝒢 is from being transitive, namely, vertex-deletion distance to transitivity and arc-modification distance to transitivity, both being applied to the reachability graph of 𝒢. We illustrate the impact of these parameters on the temporal connected component problem, obtaining several tractability results in terms of fixed-parameter tractability and polynomial kernels. Significantly, these results are obtained without restrictions of the underlying graph, the snapshots, or the lifetime of the input graph. As such, our results isolate the impact of non-transitivity and confirm the key role that it plays in the hardness of temporal graph problems.
Cite as

Arnaud Casteigts, Nils Morawietz, and Petra Wolf. Distance to Transitivity: New Parameters for Taming Reachability in Temporal Graphs. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 36:1-36:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{casteigts_et_al:LIPIcs.MFCS.2024.36,
  author =	{Casteigts, Arnaud and Morawietz, Nils and Wolf, Petra},
  title =	{{Distance to Transitivity: New Parameters for Taming Reachability in Temporal Graphs}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{36:1--36:17},
  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.2024.36},
  URN =		{urn:nbn:de:0030-drops-205923},
  doi =		{10.4230/LIPIcs.MFCS.2024.36},
  annote =	{Keywords: Temporal graphs, Parameterized complexity, Reachability, Transitivity}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.81
Monoids of Upper Triangular Matrices over the Boolean Semiring

Authors: Andrew Ryzhikov and Petra Wolf

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

Abstract
Given a finite set 𝒜 of square matrices and a square matrix B, all of the same dimension, the membership problem asks if B belongs to the monoid ℳ(𝒜) generated by 𝒜. The rank one problem asks if there is a matrix of rank one in ℳ(𝒜). We study the membership and the rank one problems in the case where all matrices are upper triangular matrices over the Boolean semiring. We characterize the computational complexity of these problems, and identify their PSPACE-complete and NP-complete special cases. We then consider, for a set 𝒜 of matrices from the same class, the problem of finding in ℳ(𝒜) a matrix of minimum rank with no zero rows. We show that the minimum rank of such matrix can be computed in linear time.We also characterize the space complexity of this problem depending on the size of 𝒜, and apply all these results to the ergodicity problem asking if ℳ(𝒜) contains a matrix with a column consisting of all ones. Finally, we show that our results give better upper bounds for the case where each row of every matrix in 𝒜 contains at most one non-zero entry than for the general case.
Cite as

Andrew Ryzhikov and Petra Wolf. Monoids of Upper Triangular Matrices over the Boolean Semiring. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 81:1-81:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ryzhikov_et_al:LIPIcs.MFCS.2024.81,
  author =	{Ryzhikov, Andrew and Wolf, Petra},
  title =	{{Monoids of Upper Triangular Matrices over the Boolean Semiring}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{81:1--81:18},
  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.2024.81},
  URN =		{urn:nbn:de:0030-drops-206377},
  doi =		{10.4230/LIPIcs.MFCS.2024.81},
  annote =	{Keywords: matrix monoids, membership, rank, ergodicity, partially ordered automata}
}
Document
DOI: 10.4230/LIPIcs.SAND.2024.12
Parameterized Algorithms for Multi-Label Periodic Temporal Graph Realization

Authors: Thomas Erlebach, Nils Morawietz, and Petra Wolf

Published in: LIPIcs, Volume 292, 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)

Abstract
In the periodic temporal graph realization problem introduced by Klobas et al. [SAND '24] one is given a period Δ and an n× n matrix D of desired fastest travel times, and the task is to decide if there is a simple periodic temporal graph with period Δ such that the fastest travel time between any pair of vertices matches the one specified by D. We generalize the problem from simple temporal graphs to temporal graphs where each edge can appear up to 𝓁 times in each period, for some given integer 𝓁. For the resulting problem Multi-Label Periodic TGR, we show that it is fixed-parameter tractable for parameter n and for parameter vc+Δ, where vc is the vertex cover number of the underlying graph. We also show the existence of a polynomial kernel for parameter nu+d_max, where nu is the number of non-universal vertices of the underlying graph and d_max is the largest entry of D. Furthermore, we show that the problem is NP-hard for each 𝓁 ≥ 5, even if the underlying graph is a tree, a case that was known to be solvable in polynomial time if the task is to construct a simple periodic temporal graph, that is, if 𝓁 = 1.
Cite as

Thomas Erlebach, Nils Morawietz, and Petra Wolf. Parameterized Algorithms for Multi-Label Periodic Temporal Graph Realization. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{erlebach_et_al:LIPIcs.SAND.2024.12,
  author =	{Erlebach, Thomas and Morawietz, Nils and Wolf, Petra},
  title =	{{Parameterized Algorithms for Multi-Label Periodic Temporal Graph Realization}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{12:1--12:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.12},
  URN =		{urn:nbn:de:0030-drops-198909},
  doi =		{10.4230/LIPIcs.SAND.2024.12},
  annote =	{Keywords: Fixed-Parameter Tractability, Almost-Clique, Kernelization, Dynamic Network, Temporal Graph}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2023.1
Kernelizing Temporal Exploration Problems

Authors: Emmanuel Arrighi, Fedor V. Fomin, Petr A. Golovach, and Petra Wolf

Published in: LIPIcs, Volume 285, 18th International Symposium on Parameterized and Exact Computation (IPEC 2023)

Abstract
We study the kernelization of exploration problems on temporal graphs. A temporal graph consists of a finite sequence of snapshot graphs 𝒢 = (G₁, G₂, … , G_L) that share a common vertex set but might have different edge sets. The non-strict temporal exploration problem (NS-TEXP for short) introduced by Erlebach and Spooner, asks if a single agent can visit all vertices of a given temporal graph where the edges traversed by the agent are present in non-strict monotonous time steps, i.e., the agent can move along the edges of a snapshot graph with infinite speed. The exploration must at the latest be completed in the last snapshot graph. The optimization variant of this problem is the k-arb NS-TEXP problem, where the agent’s task is to visit at least k vertices of the temporal graph. We show that under standard computational complexity assumptions, neither of the problems NS-TEXP nor k-arb NS-TEXP allow for polynomial kernels in the standard parameters: number of vertices n, lifetime L, number of vertices to visit k, and maximal number of connected components per time step γ; as well as in the combined parameters L+k, L + γ, and k+γ. On the way to establishing these lower bounds, we answer a couple of questions left open by Erlebach and Spooner. We also initiate the study of structural kernelization by identifying a new parameter of a temporal graph p(𝒢) = ∑_{i=1}^L (|E(G_i)|) - |V(G)| + 1. Informally, this parameter measures how dynamic the temporal graph is. Our main algorithmic result is the construction of a polynomial (in p(𝒢)) kernel for the more general Weighted k-arb NS-TEXP problem, where weights are assigned to the vertices and the task is to find a temporal walk of weight at least k.
Cite as

Emmanuel Arrighi, Fedor V. Fomin, Petr A. Golovach, and Petra Wolf. Kernelizing Temporal Exploration Problems. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 1:1-1:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{arrighi_et_al:LIPIcs.IPEC.2023.1,
  author =	{Arrighi, Emmanuel and Fomin, Fedor V. and Golovach, Petr A. and Wolf, Petra},
  title =	{{Kernelizing Temporal Exploration Problems}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{1:1--1:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-305-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{285},
  editor =	{Misra, Neeldhara and Wahlstr\"{o}m, Magnus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.1},
  URN =		{urn:nbn:de:0030-drops-194201},
  doi =		{10.4230/LIPIcs.IPEC.2023.1},
  annote =	{Keywords: Temporal graph, temporal exploration, computational complexity, kernel}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2023.2
Cluster Editing with Overlapping Communities

Authors: Emmanuel Arrighi, Matthias Bentert, Pål Grønås Drange, Blair D. Sullivan, and Petra Wolf

Published in: LIPIcs, Volume 285, 18th International Symposium on Parameterized and Exact Computation (IPEC 2023)

Abstract
Cluster Editing, also known as correlation clustering, is a well-studied graph modification problem. In this problem, one is given a graph and allowed to perform up to k edge additions and deletions to transform it into a cluster graph, i.e., a graph consisting of a disjoint union of cliques. However, in real-world networks, clusters are often overlapping. For example, in social networks, a person might belong to several communities - e.g. those corresponding to work, school, or neighborhood. Another strong motivation comes from language networks where trying to cluster words with similar usage can be confounded by homonyms, that is, words with multiple meanings like "bat". The recently introduced operation of vertex splitting is one natural approach to incorporating such overlap into Cluster Editing. First used in the context of graph drawing, this operation allows a vertex v to be replaced by two vertices whose combined neighborhood is the neighborhood of v (and thus v can belong to more than one cluster). The problem of transforming a graph into a cluster graph using at most k edge additions, edge deletions, or vertex splits is called Cluster Editing with Vertex Splitting and is known to admit a polynomial kernel with respect to k and an O(9^{k²} + n + m)-time (parameterized) algorithm. However, it was not known whether the problem is NP-hard, a question which was originally asked by Abu-Khzam et al. [Combinatorial Optimization, 2018]. We answer this in the affirmative. We further give an improved algorithm running in O(2^{7klog k} + n + m) time.
Cite as

Emmanuel Arrighi, Matthias Bentert, Pål Grønås Drange, Blair D. Sullivan, and Petra Wolf. Cluster Editing with Overlapping Communities. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 2:1-2:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{arrighi_et_al:LIPIcs.IPEC.2023.2,
  author =	{Arrighi, Emmanuel and Bentert, Matthias and Drange, P\r{a}l Gr{\o}n\r{a}s and Sullivan, Blair D. and Wolf, Petra},
  title =	{{Cluster Editing with Overlapping Communities}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{2:1--2:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-305-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{285},
  editor =	{Misra, Neeldhara and Wahlstr\"{o}m, Magnus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.2},
  URN =		{urn:nbn:de:0030-drops-194218},
  doi =		{10.4230/LIPIcs.IPEC.2023.2},
  annote =	{Keywords: graph modification, correlation clustering, vertex splitting, NP-hardness, parameterized algorithm}
}
Document
PACE Solver Description
DOI: 10.4230/LIPIcs.IPEC.2023.39
PACE Solver Description: Zygosity

Authors: Emmanuel Arrighi, Pål Grønås Drange, Kenneth Langedal, Farhad Vadiee, Martin Vatshelle, and Petra Wolf

Published in: LIPIcs, Volume 285, 18th International Symposium on Parameterized and Exact Computation (IPEC 2023)

Abstract
The graph parameter twin-width was recently introduced by Bonnet et al. Twin-width is a parameter that measures a graph’s similarity to a cograph, which is a graph that can be reduced to a single vertex by repeatedly contracting twins. This brief description introduces Zygosity, a heuristic for computing a low-width contraction sequence that achieved second place in the 2023 edition of Parameterized Algorithms and Computational Experiments Challenge (PACE). Zygosity starts by repeatedly contracting twins. Then, any attached trees are contracted down to a single pendant vertex. The remaining graph is then contracted using a randomized greedy algorithm.
Cite as

Emmanuel Arrighi, Pål Grønås Drange, Kenneth Langedal, Farhad Vadiee, Martin Vatshelle, and Petra Wolf. PACE Solver Description: Zygosity. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 39:1-39:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{arrighi_et_al:LIPIcs.IPEC.2023.39,
  author =	{Arrighi, Emmanuel and Drange, P\r{a}l Gr{\o}n\r{a}s and Langedal, Kenneth and Vadiee, Farhad and Vatshelle, Martin and Wolf, Petra},
  title =	{{PACE Solver Description: Zygosity}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{39:1--39:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-305-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{285},
  editor =	{Misra, Neeldhara and Wahlstr\"{o}m, Magnus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.39},
  URN =		{urn:nbn:de:0030-drops-194583},
  doi =		{10.4230/LIPIcs.IPEC.2023.39},
  annote =	{Keywords: Twin-width, randomized greedy algorithm}
}
Document
DOI: 10.4230/LIPIcs.STACS.2022.20
Symmetry and Quantum Query-To-Communication Simulation

Authors: Sourav Chakraborty, Arkadev Chattopadhyay, Peter Høyer, Nikhil S. Mande, Manaswi Paraashar, and Ronald de Wolf

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Abstract
Buhrman, Cleve and Wigderson (STOC'98) showed that for every Boolean function f : {-1,1}ⁿ → {-1,1} and G ∈ {AND₂, XOR₂}, the bounded-error quantum communication complexity of the composed function f∘G equals O(𝖰(f) log n), where 𝖰(f) denotes the bounded-error quantum query complexity of f. This is achieved by Alice running the optimal quantum query algorithm for f, using a round of O(log n) qubits of communication to implement each query. This is in contrast with the classical setting, where it is easy to show that 𝖱^{cc}(f∘G) ≤ 2𝖱(f), where 𝖱^{cc} and 𝖱 denote bounded-error communication and query complexity, respectively. Chakraborty et al. (CCC'20) exhibited a total function for which the log n overhead in the BCW simulation is required. This established the somewhat surprising fact that quantum reductions are in some cases inherently more expensive than classical reductions. We improve upon their result in several ways. - We show that the log n overhead is not required when f is symmetric (i.e., depends only on the Hamming weight of its input), generalizing a result of Aaronson and Ambainis for the Set-Disjointness function (Theory of Computing'05). Our upper bound assumes a shared entangled state, though for most symmetric functions the assumed number of entangled qubits is less than the communication and hence could be part of the communication. - In order to prove the above, we design an efficient distributed version of noisy amplitude amplification that allows us to prove the result when f is the OR function. This also provides a different, and arguably simpler, proof of Aaronson and Ambainis’s O(√n) communication upper bound for Set-Disjointness. - In view of our first result above, one may ask whether the log n overhead in the BCW simulation can be avoided even when f is transitive, which is a weaker notion of symmetry. We give a strong negative answer by showing that the log n overhead is still necessary for some transitive functions even when we allow the quantum communication protocol an error probability that can be arbitrarily close to 1/2 (this corresponds to the unbounded-error model of communication). - We also give, among other things, a general recipe to construct functions for which the log n overhead is required in the BCW simulation in the bounded-error communication model, even if the parties are allowed to share an arbitrary prior entangled state for free.
Cite as

Sourav Chakraborty, Arkadev Chattopadhyay, Peter Høyer, Nikhil S. Mande, Manaswi Paraashar, and Ronald de Wolf. Symmetry and Quantum Query-To-Communication Simulation. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 20:1-20:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{chakraborty_et_al:LIPIcs.STACS.2022.20,
  author =	{Chakraborty, Sourav and Chattopadhyay, Arkadev and H{\o}yer, Peter and Mande, Nikhil S. and Paraashar, Manaswi and de Wolf, Ronald},
  title =	{{Symmetry and Quantum Query-To-Communication Simulation}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{20:1--20:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.20},
  URN =		{urn:nbn:de:0030-drops-158309},
  doi =		{10.4230/LIPIcs.STACS.2022.20},
  annote =	{Keywords: Classical and quantum communication complexity, query-to-communication-simulation, quantum computing}
}
Document
DOI: 10.4230/LIPIcs.STACS.2022.35
Improved Quantum Lower and Upper Bounds for Matrix Scaling

Authors: Sander Gribling and Harold Nieuwboer

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Abstract
Matrix scaling is a simple to state, yet widely applicable linear-algebraic problem: the goal is to scale the rows and columns of a given non-negative matrix such that the rescaled matrix has prescribed row and column sums. Motivated by recent results on first-order quantum algorithms for matrix scaling, we investigate the possibilities for quantum speedups for classical second-order algorithms, which comprise the state-of-the-art in the classical setting. We first show that there can be essentially no quantum speedup in terms of the input size in the high-precision regime: any quantum algorithm that solves the matrix scaling problem for n × n matrices with at most m non-zero entries and with 𝓁₂-error ε = Θ~(1/m) must make Ω(m) queries to the matrix, even when the success probability is exponentially small in n. Additionally, we show that for ε ∈ [1/n,1/2], any quantum algorithm capable of producing ε/100-𝓁₁-approximations of the row-sum vector of a (dense) normalized matrix uses Ω(n/ε) queries, and that there exists a constant ε₀ > 0 for which this problem takes Ω(n^{1.5}) queries. To complement these results we give improved quantum algorithms in the low-precision regime: with quantum graph sparsification and amplitude estimation, a box-constrained Newton method can be sped up in the large-ε regime, and outperforms previous quantum algorithms. For entrywise-positive matrices, we find an ε-𝓁₁-scaling in time O~(n^{1.5}/ε²), whereas the best previously known bounds were O~(n²polylog(1/ε)) (classical) and O~(n^{1.5}/ε³) (quantum).
Cite as

Sander Gribling and Harold Nieuwboer. Improved Quantum Lower and Upper Bounds for Matrix Scaling. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 35:1-35:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{gribling_et_al:LIPIcs.STACS.2022.35,
  author =	{Gribling, Sander and Nieuwboer, Harold},
  title =	{{Improved Quantum Lower and Upper Bounds for Matrix Scaling}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{35:1--35:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.35},
  URN =		{urn:nbn:de:0030-drops-158458},
  doi =		{10.4230/LIPIcs.STACS.2022.35},
  annote =	{Keywords: Matrix scaling, quantum algorithms, lower bounds}
}
Document
DOI: 10.4230/LIPIcs.STACS.2022.49
One-Way Communication Complexity and Non-Adaptive Decision Trees

Authors: Nikhil S. Mande, Swagato Sanyal, and Suhail Sherif

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Abstract
We study the relationship between various one-way communication complexity measures of a composed function with the analogous decision tree complexity of the outer function. We consider two gadgets: the AND function on 2 inputs, and the Inner Product on a constant number of inputs. More generally, we show the following when the gadget is Inner Product on 2b input bits for all b ≥ 2, denoted IP. - If f is a total Boolean function that depends on all of its n input bits, then the bounded-error one-way quantum communication complexity of f∘IP equals Ω(n(b-1)). - If f is a partial Boolean function, then the deterministic one-way communication complexity of f∘IP is at least Ω(b ⋅ 𝖣_{dt}^ → (f)), where 𝖣_{dt}^ → (f) denotes non-adaptive decision tree complexity of f. To prove our quantum lower bound, we first show a lower bound on the VC-dimension of f∘IP. We then appeal to a result of Klauck [STOC'00], which immediately yields our quantum lower bound. Our deterministic lower bound relies on a combinatorial result independently proven by Ahlswede and Khachatrian [Adv. Appl. Math.'98], and Frankl and Tokushige [Comb.'99]. It is known due to a result of Montanaro and Osborne [arXiv'09] that the deterministic one-way communication complexity of f∘XOR equals the non-adaptive parity decision tree complexity of f. In contrast, we show the following when the inner gadget is the AND function on 2 input bits. - There exists a function for which even the quantum non-adaptive AND decision tree complexity of f is exponentially large in the deterministic one-way communication complexity of f∘AND. - However, for symmetric functions f, the non-adaptive AND decision tree complexity of f is at most quadratic in the (even two-way) communication complexity of f∘AND. In view of the first bullet, a lower bound on non-adaptive AND decision tree complexity of f does not lift to a lower bound on one-way communication complexity of f∘AND. The proof of the first bullet above uses the well-studied Odd-Max-Bit function. For the second bullet, we first observe a connection between the one-way communication complexity of f and the Möbius sparsity of f, and then give a lower bound on the Möbius sparsity of symmetric functions. An upper bound on the non-adaptive AND decision tree complexity of symmetric functions follows implicitly from prior work on combinatorial group testing; for the sake of completeness, we include a proof of this result. It is well known that the rank of the communication matrix of a function F is an upper bound on its deterministic one-way communication complexity. This bound is known to be tight for some F. However, in our final result we show that this is not the case when F = f∘AND. More precisely we show that for all f, the deterministic one-way communication complexity of F = f∘AND is at most (rank(M_{F}))(1 - Ω(1)), where M_{F} denotes the communication matrix of F.
Cite as

Nikhil S. Mande, Swagato Sanyal, and Suhail Sherif. One-Way Communication Complexity and Non-Adaptive Decision Trees. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 49:1-49:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{mande_et_al:LIPIcs.STACS.2022.49,
  author =	{Mande, Nikhil S. and Sanyal, Swagato and Sherif, Suhail},
  title =	{{One-Way Communication Complexity and Non-Adaptive Decision Trees}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{49:1--49:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.49},
  URN =		{urn:nbn:de:0030-drops-158598},
  doi =		{10.4230/LIPIcs.STACS.2022.49},
  annote =	{Keywords: Decision trees, communication complexity, composed Boolean functions}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2021.34
On the Complexity of Intersection Non-emptiness for Star-Free Language Classes

Authors: Emmanuel Arrighi, Henning Fernau, Stefan Hoffmann, Markus Holzer, Ismaël Jecker, Mateus de Oliveira Oliveira, and Petra Wolf

Published in: LIPIcs, Volume 213, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)

Abstract
In the Intersection Non-emptiness problem, we are given a list of finite automata A_1, A_2,… , A_m over a common alphabet Σ as input, and the goal is to determine whether some string w ∈ Σ^* lies in the intersection of the languages accepted by the automata in the list. We analyze the complexity of the Intersection Non-emptiness problem under the promise that all input automata accept a language in some level of the dot-depth hierarchy, or some level of the Straubing-Thérien hierarchy. Automata accepting languages from the lowest levels of these hierarchies arise naturally in the context of model checking. We identify a dichotomy in the dot-depth hierarchy by showing that the problem is already NP-complete when all input automata accept languages of the levels B_0 or B_{1/2} and already PSPACE-hard when all automata accept a language from the level B_1. Conversely, we identify a tetrachotomy in the Straubing-Thérien hierarchy. More precisely, we show that the problem is in AC^0 when restricted to level L_0; complete for L or NL, depending on the input representation, when restricted to languages in the level L_{1/2}; NP-complete when the input is given as DFAs accepting a language in L_1 or L_{3/2}; and finally, PSPACE-complete when the input automata accept languages in level L_2 or higher. Moreover, we show that the proof technique used to show containment in NP for DFAs accepting languages in L_1 or L_{3/2} does not generalize to the context of NFAs. To prove this, we identify a family of languages that provide an exponential separation between the state complexity of general NFAs and that of partially ordered NFAs. To the best of our knowledge, this is the first superpolynomial separation between these two models of computation.
Cite as

Emmanuel Arrighi, Henning Fernau, Stefan Hoffmann, Markus Holzer, Ismaël Jecker, Mateus de Oliveira Oliveira, and Petra Wolf. On the Complexity of Intersection Non-emptiness for Star-Free Language Classes. In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, pp. 34:1-34:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{arrighi_et_al:LIPIcs.FSTTCS.2021.34,
  author =	{Arrighi, Emmanuel and Fernau, Henning and Hoffmann, Stefan and Holzer, Markus and Jecker, Isma\"{e}l and de Oliveira Oliveira, Mateus and Wolf, Petra},
  title =	{{On the Complexity of Intersection Non-emptiness for Star-Free Language Classes}},
  booktitle =	{41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
  pages =	{34:1--34:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-215-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{213},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021.34},
  URN =		{urn:nbn:de:0030-drops-155456},
  doi =		{10.4230/LIPIcs.FSTTCS.2021.34},
  annote =	{Keywords: Intersection Non-emptiness Problem, Star-Free Languages, Straubing-Th\'{e}rien Hierarchy, dot-depth Hierarchy, Commutative Languages, Complexity}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2021.8
Order Reconfiguration Under Width Constraints

Authors: Emmanuel Arrighi, Henning Fernau, Mateus de Oliveira Oliveira, and Petra Wolf

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)

Abstract
In this work, we consider the following order reconfiguration problem: Given a graph G together with linear orders ω and ω' of the vertices of G, can one transform ω into ω' by a sequence of swaps of adjacent elements in such a way that at each time step the resulting linear order has cutwidth (pathwidth) at most k? We show that this problem always has an affirmative answer when the input linear orders ω and ω' have cutwidth (pathwidth) at most k/2. Using this result, we establish a connection between two apparently unrelated problems: the reachability problem for two-letter string rewriting systems and the graph isomorphism problem for graphs of bounded cutwidth. This opens an avenue for the study of the famous graph isomorphism problem using techniques from term rewriting theory.
Cite as

Emmanuel Arrighi, Henning Fernau, Mateus de Oliveira Oliveira, and Petra Wolf. Order Reconfiguration Under Width Constraints. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 8:1-8:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{arrighi_et_al:LIPIcs.MFCS.2021.8,
  author =	{Arrighi, Emmanuel and Fernau, Henning and de Oliveira Oliveira, Mateus and Wolf, Petra},
  title =	{{Order Reconfiguration Under Width Constraints}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{8:1--8:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.8},
  URN =		{urn:nbn:de:0030-drops-144486},
  doi =		{10.4230/LIPIcs.MFCS.2021.8},
  annote =	{Keywords: Parameterized Complexity, Order Reconfiguration, String Rewriting Systems}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2021.77
A Timecop’s Chase Around the Table

Authors: Nils Morawietz and Petra Wolf

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)

Abstract
We consider the cops and robbers game variant consisting of one cop and one robber on time-varying graphs (TVG). The considered TVGs are edge periodic graphs, i.e., for each edge, a binary string s_e determines in which time step the edge is present, namely the edge e is present in time step t if and only if the string s_e contains a 1 at position t mod |s_e|. This periodicity allows for a compact representation of an infinite TVG. We prove that even for very simple underlying graphs, i.e., directed and undirected cycles the problem whether a cop-winning strategy exists is NP-hard and W[1]-hard parameterized by the number of vertices. Our second main result are matching lower bounds for the ratio between the length of the underlying cycle and the least common multiple (lcm) of the lengths of binary strings describing edge-periodicies over which the graph is robber-winning. Our third main result improves the previously known EXPTIME upper bound for Periodic Cop & Robber on general edge periodic graphs to PSPACE-membership.
Cite as

Nils Morawietz and Petra Wolf. A Timecop’s Chase Around the Table. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 77:1-77:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{morawietz_et_al:LIPIcs.MFCS.2021.77,
  author =	{Morawietz, Nils and Wolf, Petra},
  title =	{{A Timecop’s Chase Around the Table}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{77:1--77:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.77},
  URN =		{urn:nbn:de:0030-drops-145176},
  doi =		{10.4230/LIPIcs.MFCS.2021.77},
  annote =	{Keywords: Time variable graph, Edge periodic cycle, Game of cops and robbers, Computational complexity}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2021.18
Decomposing Permutation Automata

Authors: Ismaël Jecker, Nicolas Mazzocchi, and Petra Wolf

Published in: LIPIcs, Volume 203, 32nd International Conference on Concurrency Theory (CONCUR 2021)

Abstract
A deterministic finite automaton (DFA) 𝒜 is composite if its language L(𝒜) can be decomposed into an intersection ⋂_{i = 1}^k L(𝒜_i) of languages of smaller DFAs. Otherwise, 𝒜 is prime. This notion of primality was introduced by Kupferman and Mosheiff in 2013, and while they proved that we can decide whether a DFA is composite, the precise complexity of this problem is still open, with a doubly-exponential gap between the upper and lower bounds. In this work, we focus on permutation DFAs, i.e., those for which the transition monoid is a group. We provide an NP algorithm to decide whether a permutation DFA is composite, and show that the difficulty of this problem comes from the number of non-accepting states of the instance: we give a fixed-parameter tractable algorithm with the number of rejecting states as the parameter. Moreover, we investigate the class of commutative permutation DFAs. Their structural properties allow us to decide compositionality in NL, and even in LOGSPACE if the alphabet size is fixed. Despite this low complexity, we show that complex behaviors still arise in this class: we provide a family of composite DFAs each requiring polynomially many factors with respect to its size. We also consider the variant of the problem that asks whether a DFA is k-factor composite, that is, decomposable into k smaller DFAs, for some given integer k ∈ ℕ. We show that, for commutative permutation DFAs, restricting the number of factors makes the decision computationally harder, and yields a problem with tight bounds: it is NP-complete. Finally, we show that in general, this problem is in PSPACE, and it is in LOGSPACE for DFAs with a singleton alphabet.
Cite as

Ismaël Jecker, Nicolas Mazzocchi, and Petra Wolf. Decomposing Permutation Automata. In 32nd International Conference on Concurrency Theory (CONCUR 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 203, pp. 18:1-18:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{jecker_et_al:LIPIcs.CONCUR.2021.18,
  author =	{Jecker, Isma\"{e}l and Mazzocchi, Nicolas and Wolf, Petra},
  title =	{{Decomposing Permutation Automata}},
  booktitle =	{32nd International Conference on Concurrency Theory (CONCUR 2021)},
  pages =	{18:1--18:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-203-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{203},
  editor =	{Haddad, Serge and Varacca, Daniele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2021.18},
  URN =		{urn:nbn:de:0030-drops-143956},
  doi =		{10.4230/LIPIcs.CONCUR.2021.18},
  annote =	{Keywords: Deterministic finite automata (DFA), Permutation automata, Commutative languages, Decomposition, Regular Languages, Primality}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2020.9
Width Notions for Ordering-Related Problems

Authors: Emmanuel Arrighi, Henning Fernau, Mateus de Oliveira Oliveira, and Petra Wolf

Published in: LIPIcs, Volume 182, 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)

Abstract
We are studying a weighted version of a linear extension problem, given some finite partial order ρ, called Completion of an Ordering. While this problem is NP-complete, we show that it lies in FPT when parameterized by the interval width of ρ. This ordering problem can be used to model several ordering problems stemming from diverse application areas, such as graph drawing, computational social choice, or computer memory management. Each application yields a special ρ. We also relate the interval width of ρ to parameterizations such as maximum range that have been introduced earlier in these applications, sometimes improving on parameterized algorithms that have been developed for these parameterizations before. This approach also gives some practical sub-exponential time algorithms for ordering problems.
Cite as

Emmanuel Arrighi, Henning Fernau, Mateus de Oliveira Oliveira, and Petra Wolf. Width Notions for Ordering-Related Problems. In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, pp. 9:1-9:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{arrighi_et_al:LIPIcs.FSTTCS.2020.9,
  author =	{Arrighi, Emmanuel and Fernau, Henning and de Oliveira Oliveira, Mateus and Wolf, Petra},
  title =	{{Width Notions for Ordering-Related Problems}},
  booktitle =	{40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)},
  pages =	{9:1--9:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-174-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{182},
  editor =	{Saxena, Nitin and Simon, Sunil},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2020.9},
  URN =		{urn:nbn:de:0030-drops-132505},
  doi =		{10.4230/LIPIcs.FSTTCS.2020.9},
  annote =	{Keywords: Parameterized algorithms, interval width, linear extension, one-sided crossing minimization, Kemeny rank aggregation, grouping by swapping}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2020.45
Synchronization of Deterministic Visibly Push-Down Automata

Authors: Henning Fernau and Petra Wolf

Published in: LIPIcs, Volume 182, 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)

Abstract
We generalize the concept of synchronizing words for finite automata, which map all states of the automata to the same state, to deterministic visibly push-down automata. Here, a synchronizing word w does not only map all states to the same state but also fulfills some conditions on the stack content of each run after reading w. We consider three types of these stack constraints: after reading w, the stack (1) is empty in each run, (2) contains the same sequence of stack symbols in each run, or (3) contains an arbitrary sequence which is independent of the other runs. We show that in contrast to general deterministic push-down automata, it is decidable for deterministic visibly push-down automata whether there exists a synchronizing word with each of these stack constraints, more precisely, the problems are in EXPTIME. Under the constraint (1), the problem is even in P. For the sub-classes of deterministic very visibly push-down automata, the problem is in P for all three types of constraints. We further study variants of the synchronization problem where the number of turns in the stack height behavior caused by a synchronizing word is restricted, as well as the problem of synchronizing a variant of a sequential transducer, which shows some visibly behavior, by a word that synchronizes the states and produces the same output on all runs.
Cite as

Henning Fernau and Petra Wolf. Synchronization of Deterministic Visibly Push-Down Automata. In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, pp. 45:1-45:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{fernau_et_al:LIPIcs.FSTTCS.2020.45,
  author =	{Fernau, Henning and Wolf, Petra},
  title =	{{Synchronization of Deterministic Visibly Push-Down Automata}},
  booktitle =	{40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)},
  pages =	{45:1--45:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-174-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{182},
  editor =	{Saxena, Nitin and Simon, Sunil},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2020.45},
  URN =		{urn:nbn:de:0030-drops-132861},
  doi =		{10.4230/LIPIcs.FSTTCS.2020.45},
  annote =	{Keywords: Synchronizing word, Deterministic visibly push-down automata, Deterministc finite atuomata, Finite-turn push-down automata, Sequential transducer, Computational complexity}
}
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