498 Search Results for "M�ller, P."


Volume

LIPIcs, Volume 148

14th International Symposium on Parameterized and Exact Computation (IPEC 2019)

IPEC 2019, September 11-13, 2019, Munich, Germany

Editors: Bart M. P. Jansen and Jan Arne Telle

Document
Containment of Regular Path Queries Under Path Constraints

Authors: Sylvain Salvati and Sophie Tison

Published in: LIPIcs, Volume 290, 27th International Conference on Database Theory (ICDT 2024)


Abstract
Data integrity is ensured by expressing constraints it should satisfy. One can also view constraints as data properties and take advantage of them for several tasks such as reasoning about data or accelerating query processing. In the context of graph databases, simple constraints can be expressed by means of path constraints while simple queries are modeled as regular path queries (RPQs). In this paper, we investigate the containment of RPQs under path constraints. We focus on word constraints that can be viewed as tuple-generating dependencies (TGDs) of the form ∀x_1,x_2, ∃y⁻, a_1(x_1,y_1) ∧ ... ∧ a_i(y_{i-1},y_i) ∧ ... ∧ a_n(y_{n-1},x_2) ⟶ ∃z⁻, b_1(x_1,z_1) ∧ ... ∧ b_i(z_{i-1},z_i) ∧ ... ∧ b_m(z_{m-1},x_2). Such a constraint means that whenever two nodes in a graph are connected by a path labeled a_1 … a_n, there is also a path labeled b_1 … b_m that connects them. Rewrite systems offer an abstract view of these TGDs: the rewrite rule a_1 … a_n → b_1 … b_m represents the previous constraint. A set of constraints 𝒞 is then represented by a rewrite system R and, when dealing with possibly infinite databases, a path query p is contained in a path query q under the constraints 𝒞 iff p rewrites to q with R. Contrary to what has been claimed in the literature we show that, when restricting to finite databases only, there are cases where a path query p is contained in a path query q under the constraints 𝒞 while p does not rewrite to q with R. More generally, we study the finite controllability of the containment of RPQs under word constraints, that is when this containment problem on unrestricted databases does coincide with the finite case. We give an exact characterisation of the cases where this equivalence holds. We then deduce the undecidability of the containment problem in the finite case even when RPQs are restricted to word queries. We prove several properties related to finite controllability, and in particular that it is undecidable. We also exhibit some classes of word constraints that ensure the finite controllability and the decidability of the containment problem.

Cite as

Sylvain Salvati and Sophie Tison. Containment of Regular Path Queries Under Path Constraints. In 27th International Conference on Database Theory (ICDT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 290, pp. 17:1-17:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{salvati_et_al:LIPIcs.ICDT.2024.17,
  author =	{Salvati, Sylvain and Tison, Sophie},
  title =	{{Containment of Regular Path Queries Under Path Constraints}},
  booktitle =	{27th International Conference on Database Theory (ICDT 2024)},
  pages =	{17:1--17:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-312-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{290},
  editor =	{Cormode, Graham and Shekelyan, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2024.17},
  URN =		{urn:nbn:de:0030-drops-197994},
  doi =		{10.4230/LIPIcs.ICDT.2024.17},
  annote =	{Keywords: Graph databases, rational path queries, query containment, TGDs, word constraints, rewrite systems, finite controllability, decision problems}
}
Document
Computing Data Distribution from Query Selectivities

Authors: Pankaj K. Agarwal, Rahul Raychaudhury, Stavros Sintos, and Jun Yang

Published in: LIPIcs, Volume 290, 27th International Conference on Database Theory (ICDT 2024)


Abstract
We are given a set 𝒵 = {(R_1,s_1), …, (R_n,s_n)}, where each R_i is a range in ℝ^d, such as rectangle or ball, and s_i ∈ [0,1] denotes its selectivity. The goal is to compute a small-size discrete data distribution 𝒟 = {(q₁,w₁),…, (q_m,w_m)}, where q_j ∈ ℝ^d and w_j ∈ [0,1] for each 1 ≤ j ≤ m, and ∑_{1≤j≤m} w_j = 1, such that 𝒟 is the most consistent with 𝒵, i.e., err_p(𝒟,𝒵) = 1/n ∑_{i = 1}ⁿ |s_i - ∑_{j=1}^m w_j⋅1(q_j ∈ R_i)|^p is minimized. In a database setting, 𝒵 corresponds to a workload of range queries over some table, together with their observed selectivities (i.e., fraction of tuples returned), and 𝒟 can be used as compact model for approximating the data distribution within the table without accessing the underlying contents. In this paper, we obtain both upper and lower bounds for this problem. In particular, we show that the problem of finding the best data distribution from selectivity queries is NP-complete. On the positive side, we describe a Monte Carlo algorithm that constructs, in time O((n+δ^{-d}) δ^{-2} polylog n), a discrete distribution 𝒟̃ of size O(δ^{-2}), such that err_p(𝒟̃,𝒵) ≤ min_𝒟 err_p(𝒟,𝒵)+δ (for p = 1,2,∞) where the minimum is taken over all discrete distributions. We also establish conditional lower bounds, which strongly indicate the infeasibility of relative approximations as well as removal of the exponential dependency on the dimension for additive approximations. This suggests that significant improvements to our algorithm are unlikely.

Cite as

Pankaj K. Agarwal, Rahul Raychaudhury, Stavros Sintos, and Jun Yang. Computing Data Distribution from Query Selectivities. In 27th International Conference on Database Theory (ICDT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 290, pp. 18:1-18:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{agarwal_et_al:LIPIcs.ICDT.2024.18,
  author =	{Agarwal, Pankaj K. and Raychaudhury, Rahul and Sintos, Stavros and Yang, Jun},
  title =	{{Computing Data Distribution from Query Selectivities}},
  booktitle =	{27th International Conference on Database Theory (ICDT 2024)},
  pages =	{18:1--18:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-312-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{290},
  editor =	{Cormode, Graham and Shekelyan, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2024.18},
  URN =		{urn:nbn:de:0030-drops-198007},
  doi =		{10.4230/LIPIcs.ICDT.2024.18},
  annote =	{Keywords: selectivity queries, discrete distributions, Multiplicative Weights Update, eps-approximation, learnable functions, depth problem, arrangement}
}
Document
Approximate Circular Pattern Matching Under Edit Distance

Authors: Panagiotis Charalampopoulos, Solon P. Pissis, Jakub Radoszewski, Wojciech Rytter, Tomasz Waleń, and Wiktor Zuba

Published in: LIPIcs, Volume 289, 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)


Abstract
In the k-Edit Circular Pattern Matching (k-Edit CPM) problem, we are given a length-n text T, a length-m pattern P, and a positive integer threshold k, and we are to report all starting positions of the substrings of T that are at edit distance at most k from some cyclic rotation of P. In the decision version of the problem, we are to check if any such substring exists. Very recently, Charalampopoulos et al. [ESA 2022] presented 𝒪(nk²)-time and 𝒪(nk log³ k)-time solutions for the reporting and decision versions of k-Edit CPM, respectively. Here, we show that the reporting and decision versions of k-Edit CPM can be solved in 𝒪(n+(n/m) k⁶) time and 𝒪(n+(n/m) k⁵ log³ k) time, respectively, thus obtaining the first algorithms with a complexity of the type 𝒪(n+(n/m) poly(k)) for this problem. Notably, our algorithms run in 𝒪(n) time when m = Ω(k⁶) and are superior to the previous respective solutions when m = ω(k⁴). We provide a meta-algorithm that yields efficient algorithms in several other interesting settings, such as when the strings are given in a compressed form (as straight-line programs), when the strings are dynamic, or when we have a quantum computer. We obtain our solutions by exploiting the structure of approximate circular occurrences of P in T, when T is relatively short w.r.t. P. Roughly speaking, either the starting positions of approximate occurrences of rotations of P form 𝒪(k⁴) intervals that can be computed efficiently, or some rotation of P is almost periodic (is at a small edit distance from a string with small period). Dealing with the almost periodic case is the most technically demanding part of this work; we tackle it using properties of locked fragments (originating from [Cole and Hariharan, SICOMP 2002]).

Cite as

Panagiotis Charalampopoulos, Solon P. Pissis, Jakub Radoszewski, Wojciech Rytter, Tomasz Waleń, and Wiktor Zuba. Approximate Circular Pattern Matching Under Edit Distance. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 24:1-24:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{charalampopoulos_et_al:LIPIcs.STACS.2024.24,
  author =	{Charalampopoulos, Panagiotis and Pissis, Solon P. and Radoszewski, Jakub and Rytter, Wojciech and Wale\'{n}, Tomasz and Zuba, Wiktor},
  title =	{{Approximate Circular Pattern Matching Under Edit Distance}},
  booktitle =	{41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)},
  pages =	{24:1--24:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-311-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{289},
  editor =	{Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2024.24},
  URN =		{urn:nbn:de:0030-drops-197346},
  doi =		{10.4230/LIPIcs.STACS.2024.24},
  annote =	{Keywords: circular pattern matching, approximate pattern matching, edit distance}
}
Document
Extended Abstract
Noisy Decoding by Shallow Circuits with Parities: Classical and Quantum (Extended Abstract)

Authors: Jop Briët, Harry Buhrman, Davi Castro-Silva, and Niels M. P. Neumann

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)


Abstract
We consider the problem of decoding corrupted error correcting codes with NC⁰[⊕] circuits in the classical and quantum settings. We show that any such classical circuit can correctly recover only a vanishingly small fraction of messages, if the codewords are sent over a noisy channel with positive error rate. Previously this was known only for linear codes with large dual distance, whereas our result applies to any code. By contrast, we give a simple quantum circuit that correctly decodes the Hadamard code with probability Ω(ε²) even if a (1/2 - ε)-fraction of a codeword is adversarially corrupted. Our classical hardness result is based on an equidistribution phenomenon for multivariate polynomials over a finite field under biased input-distributions. This is proved using a structure-versus-randomness strategy based on a new notion of rank for high-dimensional polynomial maps that may be of independent interest. Our quantum circuit is inspired by a non-local version of the Bernstein-Vazirani problem, a technique to generate "poor man’s cat states" by Watts et al., and a constant-depth quantum circuit for the OR function by Takahashi and Tani.

Cite as

Jop Briët, Harry Buhrman, Davi Castro-Silva, and Niels M. P. Neumann. Noisy Decoding by Shallow Circuits with Parities: Classical and Quantum (Extended Abstract). In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 21:1-21:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{briet_et_al:LIPIcs.ITCS.2024.21,
  author =	{Bri\"{e}t, Jop and Buhrman, Harry and Castro-Silva, Davi and Neumann, Niels M. P.},
  title =	{{Noisy Decoding by Shallow Circuits with Parities: Classical and Quantum (Extended Abstract)}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{21:1--21:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.21},
  URN =		{urn:nbn:de:0030-drops-195490},
  doi =		{10.4230/LIPIcs.ITCS.2024.21},
  annote =	{Keywords: Coding theory, circuit complexity, quantum complexity theory, higher-order Fourier analysis, non-local games}
}
Document
Space-Optimal Profile Estimation in Data Streams with Applications to Symmetric Functions

Authors: Justin Y. Chen, Piotr Indyk, and David P. Woodruff

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)


Abstract
We revisit the problem of estimating the profile (also known as the rarity) in the data stream model. Given a sequence of m elements from a universe of size n, its profile is a vector ϕ whose i-th entry ϕ_i represents the number of distinct elements that appear in the stream exactly i times. A classic paper by Datar and Muthukrishan from 2002 gave an algorithm which estimates any entry ϕ_i up to an additive error of ± ε D using O(1/ε² (log n + log m)) bits of space, where D is the number of distinct elements in the stream. In this paper, we considerably improve on this result by designing an algorithm which simultaneously estimates many coordinates of the profile vector ϕ up to small overall error. We give an algorithm which, with constant probability, produces an estimated profile ϕˆ with the following guarantees in terms of space and estimation error: b) For any constant τ, with O(1 / ε² + log n) bits of space, ∑_{i = 1}^τ |ϕ_i - ϕˆ_i| ≤ ε D. c) With O(1/ ε²log (1/ε) + log n + log log m) bits of space, ∑_{i = 1}^m |ϕ_i - ϕˆ_i| ≤ ε m. In addition to bounding the error across multiple coordinates, our space bounds separate the terms that depend on 1/ε and those that depend on n and m. We prove matching lower bounds on space in both regimes. Application of our profile estimation algorithm gives estimates within error ± ε D of several symmetric functions of frequencies in O(1/ε² + log n) bits. This generalizes space-optimal algorithms for the distinct elements problems to other problems including estimating the Huber and Tukey losses as well as frequency cap statistics.

Cite as

Justin Y. Chen, Piotr Indyk, and David P. Woodruff. Space-Optimal Profile Estimation in Data Streams with Applications to Symmetric Functions. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 32:1-32:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{chen_et_al:LIPIcs.ITCS.2024.32,
  author =	{Chen, Justin Y. and Indyk, Piotr and Woodruff, David P.},
  title =	{{Space-Optimal Profile Estimation in Data Streams with Applications to Symmetric Functions}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{32:1--32:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.32},
  URN =		{urn:nbn:de:0030-drops-195605},
  doi =		{10.4230/LIPIcs.ITCS.2024.32},
  annote =	{Keywords: Streaming and Sketching Algorithms, Sublinear Algorithms}
}
Document
Electrical Flows for Polylogarithmic Competitive Oblivious Routing

Authors: Gramoz Goranci, Monika Henzinger, Harald Räcke, Sushant Sachdeva, and A. R. Sricharan

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)


Abstract
Oblivious routing is a well-studied paradigm that uses static precomputed routing tables for selecting routing paths within a network. Existing oblivious routing schemes with polylogarithmic competitive ratio for general networks are tree-based, in the sense that routing is performed according to a convex combination of trees. However, this restriction to trees leads to a construction that has time quadratic in the size of the network and does not parallelize well. In this paper we study oblivious routing schemes based on electrical routing. In particular, we show that general networks with n vertices and m edges admit a routing scheme that has competitive ratio O(log² n) and consists of a convex combination of only O(√m) electrical routings. This immediately leads to an improved construction algorithm with time Õ(m^{3/2}) that can also be implemented in parallel with Õ(√m) depth.

Cite as

Gramoz Goranci, Monika Henzinger, Harald Räcke, Sushant Sachdeva, and A. R. Sricharan. Electrical Flows for Polylogarithmic Competitive Oblivious Routing. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 55:1-55:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{goranci_et_al:LIPIcs.ITCS.2024.55,
  author =	{Goranci, Gramoz and Henzinger, Monika and R\"{a}cke, Harald and Sachdeva, Sushant and Sricharan, A. R.},
  title =	{{Electrical Flows for Polylogarithmic Competitive Oblivious Routing}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{55:1--55:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.55},
  URN =		{urn:nbn:de:0030-drops-195830},
  doi =		{10.4230/LIPIcs.ITCS.2024.55},
  annote =	{Keywords: oblivious routing, electrical flows}
}
Document
Training Multi-Layer Over-Parametrized Neural Network in Subquadratic Time

Authors: Zhao Song, Lichen Zhang, and Ruizhe Zhang

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)


Abstract
We consider the problem of training a multi-layer over-parametrized neural network to minimize the empirical risk induced by a loss function. In the typical setting of over-parametrization, the network width m is much larger than the data dimension d and the number of training samples n (m = poly(n,d)), which induces a prohibitive large weight matrix W ∈ ℝ^{m× m} per layer. Naively, one has to pay O(m²) time to read the weight matrix and evaluate the neural network function in both forward and backward computation. In this work, we show how to reduce the training cost per iteration. Specifically, we propose a framework that uses m² cost only in the initialization phase and achieves a truly subquadratic cost per iteration in terms of m, i.e., m^{2-Ω(1)} per iteration. Our result has implications beyond standard over-parametrization theory, as it can be viewed as designing an efficient data structure on top of a pre-trained large model to further speed up the fine-tuning process, a core procedure to deploy large language models (LLM).

Cite as

Zhao Song, Lichen Zhang, and Ruizhe Zhang. Training Multi-Layer Over-Parametrized Neural Network in Subquadratic Time. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 93:1-93:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{song_et_al:LIPIcs.ITCS.2024.93,
  author =	{Song, Zhao and Zhang, Lichen and Zhang, Ruizhe},
  title =	{{Training Multi-Layer Over-Parametrized Neural Network in Subquadratic Time}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{93:1--93:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.93},
  URN =		{urn:nbn:de:0030-drops-196212},
  doi =		{10.4230/LIPIcs.ITCS.2024.93},
  annote =	{Keywords: Deep learning theory, Nonconvex optimization}
}
Document
A Wait-Free Deque With Polylogarithmic Step Complexity

Authors: Shalom M. Asbell and Eric Ruppert

Published in: LIPIcs, Volume 286, 27th International Conference on Principles of Distributed Systems (OPODIS 2023)


Abstract
The amortized step complexity of operations on all previous lock-free implementations of double-ended queues is linear in the number of processes. This paper presents the first concurrent double-ended queue where the amortized step complexity of each operation is polylogarithmic. Since a stack is a special case of a double-ended queue, this is also the first concurrent stack with polylogarithmic step complexity. The implementation is wait-free and the amortized step complexity is O(log² p + log q) per operation, where p is the number of processes and q is the size of the double-ended queue.

Cite as

Shalom M. Asbell and Eric Ruppert. A Wait-Free Deque With Polylogarithmic Step Complexity. In 27th International Conference on Principles of Distributed Systems (OPODIS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 286, pp. 17:1-17:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{asbell_et_al:LIPIcs.OPODIS.2023.17,
  author =	{Asbell, Shalom M. and Ruppert, Eric},
  title =	{{A Wait-Free Deque With Polylogarithmic Step Complexity}},
  booktitle =	{27th International Conference on Principles of Distributed Systems (OPODIS 2023)},
  pages =	{17:1--17:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-308-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{286},
  editor =	{Bessani, Alysson and D\'{e}fago, Xavier and Nakamura, Junya and Wada, Koichi and Yamauchi, Yukiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2023.17},
  URN =		{urn:nbn:de:0030-drops-195073},
  doi =		{10.4230/LIPIcs.OPODIS.2023.17},
  annote =	{Keywords: Lock-Free, Wait-Free, Double-Ended Queue, Deque, Stack, Space-Bounded, Polylogarithmic, Linearizable}
}
Document
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-dev.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
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-dev.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
Budgeted Matroid Maximization: a Parameterized Viewpoint

Authors: Ilan Doron-Arad, Ariel Kulik, and Hadas Shachnai

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


Abstract
We study budgeted variants of well known maximization problems with multiple matroid constraints. Given an 𝓁-matchoid ℳ on a ground set E, a profit function p:E → ℝ_{≥ 0}, a cost function c:E → ℝ_{≥ 0}, and a budget B ∈ ℝ_{≥ 0}, the goal is to find in the 𝓁-matchoid a feasible set S of maximum profit p(S) subject to the budget constraint, i.e., c(S) ≤ B. The budgeted 𝓁-matchoid (BM) problem includes as special cases budgeted 𝓁-dimensional matching and budgeted 𝓁-matroid intersection. A strong motivation for studying BM from parameterized viewpoint comes from the APX-hardness of unbudgeted 𝓁-dimensional matching (i.e., B = ∞) already for 𝓁 = 3. Nevertheless, while there are known FPT algorithms for the unbudgeted variants of the above problems, the budgeted variants are studied here for the first time through the lens of parameterized complexity. We show that BM parametrized by solution size is W[1]-hard, already with a degenerate single matroid constraint. Thus, an exact parameterized algorithm is unlikely to exist, motivating the study of FPT-approximation schemes (FPAS). Our main result is an FPAS for BM (implying an FPAS for 𝓁-dimensional matching and budgeted 𝓁-matroid intersection), relying on the notion of representative set - a small cardinality subset of elements which preserves the optimum up to a small factor. We also give a lower bound on the minimum possible size of a representative set which can be computed in polynomial time.

Cite as

Ilan Doron-Arad, Ariel Kulik, and Hadas Shachnai. Budgeted Matroid Maximization: a Parameterized Viewpoint. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{doronarad_et_al:LIPIcs.IPEC.2023.13,
  author =	{Doron-Arad, Ilan and Kulik, Ariel and Shachnai, Hadas},
  title =	{{Budgeted Matroid Maximization: a Parameterized Viewpoint}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{13:1--13:17},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.13},
  URN =		{urn:nbn:de:0030-drops-194329},
  doi =		{10.4230/LIPIcs.IPEC.2023.13},
  annote =	{Keywords: budgeted matching, budgeted matroid intersection, knapsack problems, FPT-approximation scheme}
}
Document
Computing Complexity Measures of Degenerate Graphs

Authors: Pål Grønås Drange, Patrick Greaves, Irene Muzi, and Felix Reidl

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


Abstract
We show that the VC-dimension of a graph can be computed in time n^{⌈log d+1⌉} d^{O(d)}, where d is the degeneracy of the input graph. The core idea of our algorithm is a data structure to efficiently query the number of vertices that see a specific subset of vertices inside of a (small) query set. The construction of this data structure takes time O(d2^dn), afterwards queries can be computed efficiently using fast Möbius inversion. This data structure turns out to be useful for a range of tasks, especially for finding bipartite patterns in degenerate graphs, and we outline an efficient algorithm for counting the number of times specific patterns occur in a graph. The largest factor in the running time of this algorithm is O(n^c), where c is a parameter of the pattern we call its left covering number. Concrete applications of this algorithm include counting the number of (non-induced) bicliques in linear time, the number of co-matchings in quadratic time, as well as a constant-factor approximation of the ladder index in linear time. Finally, we supplement our theoretical results with several implementations and run experiments on more than 200 real-world datasets - the largest of which has 8 million edges - where we obtain interesting insights into the VC-dimension of real-world networks.

Cite as

Pål Grønås Drange, Patrick Greaves, Irene Muzi, and Felix Reidl. Computing Complexity Measures of Degenerate Graphs. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 14:1-14:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{drange_et_al:LIPIcs.IPEC.2023.14,
  author =	{Drange, P\r{a}l Gr{\o}n\r{a}s and Greaves, Patrick and Muzi, Irene and Reidl, Felix},
  title =	{{Computing Complexity Measures of Degenerate Graphs}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{14:1--14:21},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.14},
  URN =		{urn:nbn:de:0030-drops-194333},
  doi =		{10.4230/LIPIcs.IPEC.2023.14},
  annote =	{Keywords: vc-dimension, datastructure, degeneracy, enumerating}
}
Document
Kernelization for Counting Problems on Graphs: Preserving the Number of Minimum Solutions

Authors: Bart M. P. Jansen and Bart van der Steenhoven

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


Abstract
A kernelization for a parameterized decision problem 𝒬 is a polynomial-time preprocessing algorithm that reduces any parameterized instance (x,k) into an instance (x',k') whose size is bounded by a function of k alone and which has the same yes/no answer for 𝒬. Such preprocessing algorithms cannot exist in the context of counting problems, when the answer to be preserved is the number of solutions, since this number can be arbitrarily large compared to k. However, we show that for counting minimum feedback vertex sets of size at most k, and for counting minimum dominating sets of size at most k in a planar graph, there is a polynomial-time algorithm that either outputs the answer or reduces to an instance (G',k') of size polynomial in k with the same number of minimum solutions. This shows that a meaningful theory of kernelization for counting problems is possible and opens the door for future developments. Our algorithms exploit that if the number of solutions exceeds 2^{poly(k)}, the size of the input is exponential in terms of k so that the running time of a parameterized counting algorithm can be bounded by poly(n). Otherwise, we can use gadgets that slightly increase k to represent choices among 2^{𝒪(k)} options by only poly(k) vertices.

Cite as

Bart M. P. Jansen and Bart van der Steenhoven. Kernelization for Counting Problems on Graphs: Preserving the Number of Minimum Solutions. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 27:1-27:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{jansen_et_al:LIPIcs.IPEC.2023.27,
  author =	{Jansen, Bart M. P. and van der Steenhoven, Bart},
  title =	{{Kernelization for Counting Problems on Graphs: Preserving the Number of Minimum Solutions}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{27:1--27:15},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.27},
  URN =		{urn:nbn:de:0030-drops-194466},
  doi =		{10.4230/LIPIcs.IPEC.2023.27},
  annote =	{Keywords: kernelization, counting problems, feedback vertex set, dominating set, protrusion decomposition}
}
Document
On the Parameterized Complexity of Multiway Near-Separator

Authors: Bart M. P. Jansen and Shivesh K. Roy

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


Abstract
We study a new graph separation problem called Multiway Near-Separator. Given an undirected graph G, integer k, and terminal set T ⊆ V(G), it asks whether there is a vertex set S ⊆ V(G) ⧵ T of size at most k such that in graph G-S, no pair of distinct terminals can be connected by two pairwise internally vertex-disjoint paths. Hence each terminal pair can be separated in G-S by removing at most one vertex. The problem is therefore a generalization of (Node) Multiway Cut, which asks for a vertex set for which each terminal is in a different component of G-S. We develop a fixed-parameter tractable algorithm for Multiway Near-Separator running in time 2^{𝒪(k log k)} ⋅ n^{𝒪(1)}. Our algorithm is based on a new pushing lemma for solutions with respect to important separators, along with two problem-specific ingredients. The first is a polynomial-time subroutine to reduce the number of terminals in the instance to a polynomial in the solution size k plus the size of a given suboptimal solution. The second is a polynomial-time algorithm that, given a graph G and terminal set T ⊆ V(G) along with a single vertex x ∈ V(G) that forms a multiway near-separator, computes a 14-approximation for the problem of finding a multiway near-separator not containing x.

Cite as

Bart M. P. Jansen and Shivesh K. Roy. On the Parameterized Complexity of Multiway Near-Separator. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 28:1-28:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{jansen_et_al:LIPIcs.IPEC.2023.28,
  author =	{Jansen, Bart M. P. and Roy, Shivesh K.},
  title =	{{On the Parameterized Complexity of Multiway Near-Separator}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{28:1--28:18},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.28},
  URN =		{urn:nbn:de:0030-drops-194470},
  doi =		{10.4230/LIPIcs.IPEC.2023.28},
  annote =	{Keywords: fixed-parameter tractability, multiway cut, near-separator}
}
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