102 Search Results for "Serf�z�, P�ter"

Document
DOI: 10.4230/LIPIcs.ICDT.2024.17
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
DOI: 10.4230/LIPIcs.ITCS.2024.55
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
DOI: 10.4230/LIPIcs.ITCS.2024.62
On the Complexity of Algorithms with Predictions for Dynamic Graph Problems

Authors: Monika Henzinger, Barna Saha, Martin P. Seybold, and Christopher Ye

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

Abstract
Algorithms with predictions is a new research direction that leverages machine learned predictions for algorithm design. So far a plethora of recent works have incorporated predictions to improve on worst-case bounds for online problems. In this paper, we initiate the study of complexity of dynamic data structures with predictions, including dynamic graph algorithms. Unlike online algorithms, the goal in dynamic data structures is to maintain the solution efficiently with every update. We investigate three natural models of prediction: (1) δ-accurate predictions where each predicted request matches the true request with probability δ, (2) list-accurate predictions where a true request comes from a list of possible requests, and (3) bounded delay predictions where the true requests are a permutation of the predicted requests. We give general reductions among the prediction models, showing that bounded delay is the strongest prediction model, followed by list-accurate, and δ-accurate. Further, we identify two broad problem classes based on lower bounds due to the Online Matrix Vector (OMv) conjecture. Specifically, we show that locally correctable dynamic problems have strong conditional lower bounds for list-accurate predictions that are equivalent to the non-prediction setting, unless list-accurate predictions are perfect. Moreover, we show that locally reducible dynamic problems have time complexity that degrades gracefully with the quality of bounded delay predictions. We categorize problems with known OMv lower bounds accordingly and give several upper bounds in the delay model that show that our lower bounds are almost tight. We note that concurrent work by v.d.Brand et al. [SODA '24] and Liu and Srinivas [arXiv:2307.08890] independently study dynamic graph algorithms with predictions, but their work is mostly focused on showing upper bounds.
Cite as

Monika Henzinger, Barna Saha, Martin P. Seybold, and Christopher Ye. On the Complexity of Algorithms with Predictions for Dynamic Graph Problems. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 62:1-62:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{henzinger_et_al:LIPIcs.ITCS.2024.62,
  author =	{Henzinger, Monika and Saha, Barna and Seybold, Martin P. and Ye, Christopher},
  title =	{{On the Complexity of Algorithms with Predictions for Dynamic Graph Problems}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{62:1--62:25},
  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.2024.62},
  URN =		{urn:nbn:de:0030-drops-195907},
  doi =		{10.4230/LIPIcs.ITCS.2024.62},
  annote =	{Keywords: Dynamic Graph Algorithms, Algorithms with Predictions}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2023.12
Substring Complexity in Sublinear Space

Authors: Giulia Bernardini, Gabriele Fici, Paweł Gawrychowski, and Solon P. Pissis

Published in: LIPIcs, Volume 283, 34th International Symposium on Algorithms and Computation (ISAAC 2023)

Abstract
Shannon’s entropy is a definitive lower bound for statistical compression. Unfortunately, no such clear measure exists for the compressibility of repetitive strings. Thus, ad hoc measures are employed to estimate the repetitiveness of strings, e.g., the size z of the Lempel–Ziv parse or the number r of equal-letter runs of the Burrows-Wheeler transform. A more recent one is the size γ of a smallest string attractor. Let T be a string of length n. A string attractor of T is a set of positions of T capturing the occurrences of all the substrings of T. Unfortunately, Kempa and Prezza [STOC 2018] showed that computing γ is NP-hard. Kociumaka et al. [LATIN 2020] considered a new measure of compressibility that is based on the function S_T(k) counting the number of distinct substrings of length k of T, also known as the substring complexity of T. This new measure is defined as δ = sup{S_T(k)/k, k ≥ 1} and lower bounds all the relevant ad hoc measures previously considered. In particular, δ ≤ γ always holds and δ can be computed in 𝒪(n) time using Θ(n) working space. Kociumaka et al. showed that one can construct an 𝒪(δ log n/(δ))-sized representation of T supporting efficient direct access and efficient pattern matching queries on T. Given that for highly compressible strings, δ is significantly smaller than n, it is natural to pose the following question: Can we compute δ efficiently using sublinear working space? It is straightforward to show that in the comparison model, any algorithm computing δ using 𝒪(b) space requires Ω(n^{2-o(1)}/b) time through a reduction from the element distinctness problem [Yao, SIAM J. Comput. 1994]. We thus wanted to investigate whether we can indeed match this lower bound. We address this algorithmic challenge by showing the following bounds to compute δ: - 𝒪((n³log b)/b²) time using 𝒪(b) space, for any b ∈ [1,n], in the comparison model. - 𝒪̃(n²/b) time using 𝒪̃(b) space, for any b ∈ [√n,n], in the word RAM model. This gives an 𝒪̃(n^{1+ε})-time and 𝒪̃(n^{1-ε})-space algorithm to compute δ, for any 0 < ε ≤ 1/2. Let us remark that our algorithms compute S_T(k), for all k, within the same complexities.
Cite as

Giulia Bernardini, Gabriele Fici, Paweł Gawrychowski, and Solon P. Pissis. Substring Complexity in Sublinear Space. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 12:1-12:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bernardini_et_al:LIPIcs.ISAAC.2023.12,
  author =	{Bernardini, Giulia and Fici, Gabriele and Gawrychowski, Pawe{\l} and Pissis, Solon P.},
  title =	{{Substring Complexity in Sublinear Space}},
  booktitle =	{34th International Symposium on Algorithms and Computation (ISAAC 2023)},
  pages =	{12:1--12:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-289-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{283},
  editor =	{Iwata, Satoru and Kakimura, Naonori},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.12},
  URN =		{urn:nbn:de:0030-drops-193143},
  doi =		{10.4230/LIPIcs.ISAAC.2023.12},
  annote =	{Keywords: sublinear-space algorithm, string algorithm, substring complexity}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2023.23
Clustering in Polygonal Domains

Authors: Mark de Berg, Leyla Biabani, Morteza Monemizadeh, and Leonidas Theocharous

Published in: LIPIcs, Volume 283, 34th International Symposium on Algorithms and Computation (ISAAC 2023)

Abstract
We study various clustering problems for a set D of n points in a polygonal domain P under the geodesic distance. We start by studying the discrete k-median problem for D in P. We develop an exact algorithm which runs in time poly(n,m) + n^O(√k), where m is the complexity of the domain. Subsequently, we show that our approach can also be applied to solve the k-center problem with z outliers in the same running time. Next, we turn our attention to approximation algorithms. In particular, we study the k-center problem in a simple polygon and show how to obtain a (1+ε)-approximation algorithm which runs in time 2^{O((k log(k))/ε)} (n log(m) + m). To obtain this, we demonstrate that a previous approach by Bădoiu et al. [Bâdoiu et al., 2002; Bâdoiu and Clarkson, 2003] that works in ℝ^d, carries over to the setting of simple polygons. Finally, we study the 1-center problem in a simple polygon in the presence of z outliers. We show that a coreset C of size O(z) exists, such that the 1-center of C is a 3-approximation of the 1-center of D, when z outliers are allowed. This result is actually more general and carries over to any metric space, which to the best of our knowledge was not known so far. By extending this approach, we show that for the 1-center problem under the Euclidean metric in ℝ², there exists an ε-coreset of size O(z/ε).
Cite as

Mark de Berg, Leyla Biabani, Morteza Monemizadeh, and Leonidas Theocharous. Clustering in Polygonal Domains. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 23:1-23:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{deberg_et_al:LIPIcs.ISAAC.2023.23,
  author =	{de Berg, Mark and Biabani, Leyla and Monemizadeh, Morteza and Theocharous, Leonidas},
  title =	{{Clustering in Polygonal Domains}},
  booktitle =	{34th International Symposium on Algorithms and Computation (ISAAC 2023)},
  pages =	{23:1--23:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-289-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{283},
  editor =	{Iwata, Satoru and Kakimura, Naonori},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.23},
  URN =		{urn:nbn:de:0030-drops-193252},
  doi =		{10.4230/LIPIcs.ISAAC.2023.23},
  annote =	{Keywords: clustering, geodesic distance, coreset, outliers}
}
Document
DOI: 10.4230/LIPIcs.AFT.2023.18
Revisiting the Nova Proof System on a Cycle of Curves

Authors: Wilson D. Nguyen, Dan Boneh, and Srinath Setty

Published in: LIPIcs, Volume 282, 5th Conference on Advances in Financial Technologies (AFT 2023)

Abstract
Nova is an efficient recursive proof system built from an elegant folding scheme for (relaxed) R1CS statements. The original Nova paper (CRYPTO'22) presented Nova using a single elliptic curve group of order p. However, for improved efficiency, the implementation of Nova alters the scheme to use a 2-cycle of elliptic curves. This altered scheme is only described in the code and has not been proven secure. In this work, we point out a soundness vulnerability in the original implementation of the 2-cycle Nova system. To demonstrate this vulnerability, we construct a convincing Nova proof for the correct evaluation of 2^{75} rounds of the Minroot VDF in only 116 milliseconds. We then present a modification of the 2-cycle Nova system and formally prove its security. The modified system also happens to be more efficient than the original implementation. In particular, the modification eliminates an R1CS instance-witness pair from the recursive proof. The implementation of Nova has now been updated to use our optimized and secure system. In addition, we show that the folding mechanism at the core of Nova is malleable: given a proof for some statement z, an adversary can construct a proof for a related statement z', at the same depth as z, without knowledge of the witness for z'.
Cite as

Wilson D. Nguyen, Dan Boneh, and Srinath Setty. Revisiting the Nova Proof System on a Cycle of Curves. In 5th Conference on Advances in Financial Technologies (AFT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 282, pp. 18:1-18:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{nguyen_et_al:LIPIcs.AFT.2023.18,
  author =	{Nguyen, Wilson D. and Boneh, Dan and Setty, Srinath},
  title =	{{Revisiting the Nova Proof System on a Cycle of Curves}},
  booktitle =	{5th Conference on Advances in Financial Technologies (AFT 2023)},
  pages =	{18:1--18:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-303-4},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{282},
  editor =	{Bonneau, Joseph and Weinberg, S. Matthew},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2023.18},
  URN =		{urn:nbn:de:0030-drops-192076},
  doi =		{10.4230/LIPIcs.AFT.2023.18},
  annote =	{Keywords: Cryptographic Protocols, Recursive Proof Systems, Folding, Vulnerability}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2023.29
Constraint Automata on Infinite Data Trees: from CTL(ℤ)/CTL^*(ℤ) to Decision Procedures

Authors: Stéphane Demri and Karin Quaas

Published in: LIPIcs, Volume 279, 34th International Conference on Concurrency Theory (CONCUR 2023)

Abstract
We introduce the class of tree constraint automata with data values in ℤ (equipped with the less than relation and equality predicates to constants), and we show that the nonemptiness problem is EXPTIME-complete. Using an automata-based approach, we establish that the satisfiability problem for CTL(ℤ) (CTL with constraints in ℤ) is EXPTIME-complete, and the satisfiability problem for CTL^*(ℤ) is 2ExpTime-complete (only decidability was known so far). By-product results with other concrete domains and other logics, are also briefly discussed.
Cite as

Stéphane Demri and Karin Quaas. Constraint Automata on Infinite Data Trees: from CTL(ℤ)/CTL^*(ℤ) to Decision Procedures. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 29:1-29:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{demri_et_al:LIPIcs.CONCUR.2023.29,
  author =	{Demri, St\'{e}phane and Quaas, Karin},
  title =	{{Constraint Automata on Infinite Data Trees: from CTL(\mathbb{Z})/CTL^*(\mathbb{Z}) to Decision Procedures}},
  booktitle =	{34th International Conference on Concurrency Theory (CONCUR 2023)},
  pages =	{29:1--29:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-299-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{279},
  editor =	{P\'{e}rez, Guillermo A. and Raskin, Jean-Fran\c{c}ois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2023.29},
  URN =		{urn:nbn:de:0030-drops-190238},
  doi =		{10.4230/LIPIcs.CONCUR.2023.29},
  annote =	{Keywords: Constraints, Constraint Automata, Temporal Logics, Infinite Data Trees}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.ESA.2023.1
On Hashing by (Random) Equations (Invited Talk)

Authors: Martin Dietzfelbinger

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
The talk will consider aspects of the following setup: Assume for each (key) x from a set 𝒰 (the universe) a vector a_x = (a_{x,0},… ,a_{x,{m-1}}) has been chosen. Given a list Z = (z_i)_{i ∈ [m]} of vectors in {0,1}^r we obtain a mapping φ_Z: 𝒰 → {0,1}^r, x ↦ ⟨a_x,Z⟩ := ⨁_{i ∈ [m]} a_{x,i} ⋅ z_i, where ⨁ is bitwise XOR. The simplest way for creating a data structure for calculating φ_Z is to store Z in an array Z[0..m-1] and answer a query for x by returning ⟨ a_x,Z⟩. The length m of the array should be (1+ε)n for some small ε, and calculating this inner product should be fast. In the focus of the talk is the case where for all or for most of the sets S ⊆ 𝒰 of a certain size n the vectors a_x, x ∈ S, are linearly independent. Choosing Z at random will lead to hash families of various degrees of independence. We will be mostly interested in the case where a_x, x ∈ 𝒰 are chosen independently at random from {0,1}^m, according to some distribution 𝒟. We wish to construct (static) retrieval data structures, which means that S ⊂ 𝒰 and some mapping f: S → {0,1}^r are given, and the task is to find Z such that the restriction of φ_Z to S is f. For creating such a data structure it is necessary to solve the linear system (a_x)_{x ∈ S} ⋅ Z = (f(x))_{x ∈ S} for Z. Two problems are central: Under what conditions on m and 𝒟 can we expect the vectors a_x, x ∈ S to be linearly independent, and how can we arrange things so that in this case the system can be solved fast, in particular in time close to linear (in n, assuming a reasonable machine model)? Solutions to these problems, some classical and others that have emerged only in recent years, will be discussed.
Cite as

Martin Dietzfelbinger. On Hashing by (Random) Equations (Invited Talk). In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, p. 1:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{dietzfelbinger:LIPIcs.ESA.2023.1,
  author =	{Dietzfelbinger, Martin},
  title =	{{On Hashing by (Random) Equations}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{1:1--1:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.1},
  URN =		{urn:nbn:de:0030-drops-186545},
  doi =		{10.4230/LIPIcs.ESA.2023.1},
  annote =	{Keywords: Hashing, Retrieval, Linear equations, Randomness}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.13
On Computing Homological Hitting Sets

Authors: Ulrich Bauer, Abhishek Rathod, and Meirav Zehavi

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract
Cut problems form one of the most fundamental classes of problems in algorithmic graph theory. In this paper, we initiate the algorithmic study of a high-dimensional cut problem. The problem we study, namely, Homological Hitting Set (HHS), is defined as follows: Given a nontrivial r-cycle z in a simplicial complex, find a set 𝒮 of r-dimensional simplices of minimum cardinality so that 𝒮 meets every cycle homologous to z. Our first result is that HHS admits a polynomial-time solution on triangulations of closed surfaces. Interestingly, the minimal solution is given in terms of the cocycles of the surface. Next, we provide an example of a 2-complex for which the (unique) minimal hitting set is not a cocycle. Furthermore, for general complexes, we show that HHS is W[1]-hard with respect to the solution size p. In contrast, on the positive side, we show that HHS admits an FPT algorithm with respect to p+Δ, where Δ is the maximum degree of the Hasse graph of the complex 𝖪.
Cite as

Ulrich Bauer, Abhishek Rathod, and Meirav Zehavi. On Computing Homological Hitting Sets. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 13:1-13:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bauer_et_al:LIPIcs.ITCS.2023.13,
  author =	{Bauer, Ulrich and Rathod, Abhishek and Zehavi, Meirav},
  title =	{{On Computing Homological Hitting Sets}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{13:1--13:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.13},
  URN =		{urn:nbn:de:0030-drops-175169},
  doi =		{10.4230/LIPIcs.ITCS.2023.13},
  annote =	{Keywords: Algorithmic topology, Cut problems, Surfaces, Parameterized complexity}
}
Document
DOI: 10.4230/LIPIcs.CSL.2023.33
Parity Games of Bounded Tree-Depth

Authors: Konrad Staniszewski

Published in: LIPIcs, Volume 252, 31st EACSL Annual Conference on Computer Science Logic (CSL 2023)

Abstract
The exact complexity of solving parity games is a major open problem. Several authors have searched for efficient algorithms over specific classes of graphs. In particular, Obdržálek showed that for graphs of bounded tree-width or clique-width, the problem is in P, which was later improved by Ganardi, who showed that it is even in LOGCFL (with an additional assumption for clique-width case). Here we extend this line of research by showing that for graphs of bounded tree-depth the problem of solving parity games is in logspace uniform AC⁰. We achieve this by first considering a parameter that we obtain from a modification of clique-width, which we call shallow clique-width. We subsequently provide a suitable reduction.
Cite as

Konrad Staniszewski. Parity Games of Bounded Tree-Depth. In 31st EACSL Annual Conference on Computer Science Logic (CSL 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 252, pp. 33:1-33:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{staniszewski:LIPIcs.CSL.2023.33,
  author =	{Staniszewski, Konrad},
  title =	{{Parity Games of Bounded Tree-Depth}},
  booktitle =	{31st EACSL Annual Conference on Computer Science Logic (CSL 2023)},
  pages =	{33:1--33:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-264-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{252},
  editor =	{Klin, Bartek and Pimentel, Elaine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2023.33},
  URN =		{urn:nbn:de:0030-drops-174942},
  doi =		{10.4230/LIPIcs.CSL.2023.33},
  annote =	{Keywords: Parity Games, Circuits, Tree-Depth, Clique-Width}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2022.30
List Locally Surjective Homomorphisms in Hereditary Graph Classes

Authors: Pavel Dvořák, Tomáš Masařík, Jana Novotná, Monika Krawczyk, Paweł Rzążewski, and Aneta Żuk

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

Abstract
A locally surjective homomorphism from a graph G to a graph H is an edge-preserving mapping from V(G) to V(H) that is surjective in the neighborhood of each vertex in G. In the list locally surjective homomorphism problem, denoted by LLSHom(H), the graph H is fixed and the instance consists of a graph G whose every vertex is equipped with a subset of V(H), called list. We ask for the existence of a locally surjective homomorphism from G to H, where every vertex of G is mapped to a vertex from its list. In this paper, we study the complexity of the LLSHom(H) problem in F-free graphs, i.e., graphs that exclude a fixed graph F as an induced subgraph. We aim to understand for which pairs (H,F) the problem can be solved in subexponential time. We show that for all graphs H, for which the problem is NP-hard in general graphs, it cannot be solved in subexponential time in F-free graphs for F being a bounded-degree forest, unless the ETH fails. The initial study reveals that a natural subfamily of bounded-degree forests F, that might lead to some tractability results, is the family 𝒮 consisting of forests whose every component has at most three leaves. In this case, we exhibit the following dichotomy theorem: besides the cases that are polynomial-time solvable in general graphs, the graphs H ∈ {P₃,C₄} are the only connected ones that allow for a subexponential-time algorithm in F-free graphs for every F ∈ 𝒮 (unless the ETH fails).
Cite as

Pavel Dvořák, Tomáš Masařík, Jana Novotná, Monika Krawczyk, Paweł Rzążewski, and Aneta Żuk. List Locally Surjective Homomorphisms in Hereditary Graph Classes. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 30:1-30:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{dvorak_et_al:LIPIcs.ISAAC.2022.30,
  author =	{Dvo\v{r}\'{a}k, Pavel and Masa\v{r}{\'\i}k, Tom\'{a}\v{s} and Novotn\'{a}, Jana and Krawczyk, Monika and Rz\k{a}\.{z}ewski, Pawe{\l} and \.{Z}uk, Aneta},
  title =	{{List Locally Surjective Homomorphisms in Hereditary Graph Classes}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{30:1--30:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.30},
  URN =		{urn:nbn:de:0030-drops-173154},
  doi =		{10.4230/LIPIcs.ISAAC.2022.30},
  annote =	{Keywords: Homomorphism, Hereditary graphs, Subexponential-time algorithms}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2022.56
Pursuit-Evasion in Graphs: Zombies, Lazy Zombies and a Survivor

Authors: Prosenjit Bose, Jean-Lou De Carufel, and Thomas Shermer

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

Abstract
We study zombies and survivor, a variant of the game of cops and robber on graphs. In this variant, the single survivor plays the role of the robber and attempts to escape from the zombies that play the role of the cops. The zombies are restricted, on their turn, to always follow an edge of a shortest path towards the survivor. Let z(G) be the smallest number of zombies required to catch the survivor on a graph G with n vertices. We show that there exist outerplanar graphs and visibility graphs of simple polygons such that z(G) = Θ(n). We also show that there exist maximum-degree-3 outerplanar graphs such that z(G) = Ω(n/log(n)). Let z_L(G) be the smallest number of lazy zombies (zombies that can stay still on their turn) required to catch the survivor on a graph G. We show that lazy zombies are more powerful than normal zombies but less powerful than cops. We prove that z_L(G) ≤ 2 for connected outerplanar graphs and this bound is tight in the worst case. We show that z_L(G) ≤ k for connected graphs with treedepth k. This result implies that z_L(G) is at most (k+1)log n for connected graphs with treewidth k, O(√n) for connected planar graphs, O(√{gn}) for connected graphs with genus g and O(h√{hn}) for connected graphs with any excluded h-vertex minor. Our results on lazy zombies still hold when an adversary chooses the initial positions of the zombies.
Cite as

Prosenjit Bose, Jean-Lou De Carufel, and Thomas Shermer. Pursuit-Evasion in Graphs: Zombies, Lazy Zombies and a Survivor. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 56:1-56:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bose_et_al:LIPIcs.ISAAC.2022.56,
  author =	{Bose, Prosenjit and De Carufel, Jean-Lou and Shermer, Thomas},
  title =	{{Pursuit-Evasion in Graphs: Zombies, Lazy Zombies and a Survivor}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{56:1--56:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.56},
  URN =		{urn:nbn:de:0030-drops-173418},
  doi =		{10.4230/LIPIcs.ISAAC.2022.56},
  annote =	{Keywords: Pursuit-evasion games, Outerplanar, Graphs, Treedepth, Treewidth}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.51
Intersection Searching Amid Tetrahedra in 4-Space and Efficient Continuous Collision Detection

Authors: Esther Ezra and Micha Sharir

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Abstract
We develop data structures for intersection detection queries in four dimensions that involve segments, triangles and tetrahedra. Specifically, we study two main problems: (i) Preprocess a set of n tetrahedra in {ℝ}⁴ into a data structure for answering segment-intersection queries amid the given tetrahedra (referred to as segment-tetrahedron intersection queries), and (ii) Preprocess a set of n triangles in {ℝ}⁴ into a data structure that supports triangle-intersection queries amid the input triangles (referred to as triangle-triangle intersection queries). As far as we can tell, these problems have not been previously studied. For problem (i), we first present a "standard" solution which, for any prespecified value n ≤ s ≤ n⁶ of a so-called storage parameter s, yields a data structure with O^*(s) storage and expected preprocessing, which answers an intersection query in O^*(n/s^{1/6}) time (here and in what follows, the O^*(⋅) notation hides subpolynomial factors). For problem (ii), using similar arguments, we present a solution that has the same asymptotic performance bounds. We then improve the solution for problem (i), and present a more intricate data structure that uses O^*(n²) storage and expected preprocessing, and answers a segment-tetrahedron intersection query in O^*(n^{1/2}) time. Using the parametric search technique of Agarwal and Matoušek [P. K. Agarwal and J. Matoušek, 1993], we can obtain data structures with similar performance bounds for the ray-shooting problem amid tetrahedra in {ℝ}⁴. Unfortunately, so far we do not know how to obtain a similar improvement for problem (ii). Our algorithms are based on a primal-dual technique for range searching with semi-algebraic sets, based on recent advances in this area [P. K. Agarwal et al., 2021; J. Matoušek and Z. Patáková, 2015]. As this is a result of independent interest, we spell out the details of this technique. As an application, we present a solution to the problem of "continuous collision detection" amid moving tetrahedra in 3-space. That is, the workspace consists of n tetrahedra, each moving at its own fixed velocity, and the goal is to detect a collision between some pair of moving tetrahedra. Using our solutions to problems (i) and (ii), we obtain an algorithm that detects a collision in O^*(n^{12/7}) expected time. We also present further applications, including an output-sensitive algorithm for constructing the arrangement of n tetrahedra in ℝ⁴ and an output-sensitive algorithm for constructing the intersection or union of two or several nonconvex polyhedra in ℝ⁴.
Cite as

Esther Ezra and Micha Sharir. Intersection Searching Amid Tetrahedra in 4-Space and Efficient Continuous Collision Detection. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 51:1-51:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{ezra_et_al:LIPIcs.ESA.2022.51,
  author =	{Ezra, Esther and Sharir, Micha},
  title =	{{Intersection Searching Amid Tetrahedra in 4-Space and Efficient Continuous Collision Detection}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{51:1--51:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.51},
  URN =		{urn:nbn:de:0030-drops-169895},
  doi =		{10.4230/LIPIcs.ESA.2022.51},
  annote =	{Keywords: Computational geometry, Ray shooting, Tetrahedra in \{\mathbb{R}\}⁴, Intersection queries in \{\mathbb{R}\}⁴, Polynomial partitioning, Range searching, Semi-algebraic sets, Tradeoff}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.58
Taming Graphs with No Large Creatures and Skinny Ladders

Authors: Jakub Gajarský, Lars Jaffke, Paloma T. Lima, Jana Novotná, Marcin Pilipczuk, Paweł Rzążewski, and Uéverton S. Souza

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Abstract
We confirm a conjecture of Gartland and Lokshtanov [arXiv:2007.08761]: if for a hereditary graph class 𝒢 there exists a constant k such that no member of 𝒢 contains a k-creature as an induced subgraph or a k-skinny-ladder as an induced minor, then there exists a polynomial p such that every G ∈ 𝒢 contains at most p(|V(G)|) minimal separators. By a result of Fomin, Todinca, and Villanger [SIAM J. Comput. 2015] the latter entails the existence of polynomial-time algorithms for Maximum Weight Independent Set, Feedback Vertex Set and many other problems, when restricted to an input graph from 𝒢. Furthermore, as shown by Gartland and Lokshtanov, our result implies a full dichotomy of hereditary graph classes defined by a finite set of forbidden induced subgraphs into tame (admitting a polynomial bound of the number of minimal separators) and feral (containing infinitely many graphs with exponential number of minimal separators).
Cite as

Jakub Gajarský, Lars Jaffke, Paloma T. Lima, Jana Novotná, Marcin Pilipczuk, Paweł Rzążewski, and Uéverton S. Souza. Taming Graphs with No Large Creatures and Skinny Ladders. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 58:1-58:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{gajarsky_et_al:LIPIcs.ESA.2022.58,
  author =	{Gajarsk\'{y}, Jakub and Jaffke, Lars and Lima, Paloma T. and Novotn\'{a}, Jana and Pilipczuk, Marcin and Rz\k{a}\.{z}ewski, Pawe{\l} and Souza, U\'{e}verton S.},
  title =	{{Taming Graphs with No Large Creatures and Skinny Ladders}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{58:1--58:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.58},
  URN =		{urn:nbn:de:0030-drops-169969},
  doi =		{10.4230/LIPIcs.ESA.2022.58},
  annote =	{Keywords: Minimal separator, hereditary graph class}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.92
Optimal Coding Theorems in Time-Bounded Kolmogorov Complexity

Authors: Zhenjian Lu, Igor C. Oliveira, and Marius Zimand

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
The classical coding theorem in Kolmogorov complexity states that if an n-bit string x is sampled with probability δ by an algorithm with prefix-free domain then 𝖪(x) ≤ log(1/δ) + O(1). In a recent work, Lu and Oliveira [Zhenjian Lu and Igor C. Oliveira, 2021] established an unconditional time-bounded version of this result, by showing that if x can be efficiently sampled with probability δ then rKt(x) = O(log(1/δ)) + O(log n), where rKt denotes the randomized analogue of Levin’s Kt complexity. Unfortunately, this result is often insufficient when transferring applications of the classical coding theorem to the time-bounded setting, as it achieves a O(log(1/δ)) bound instead of the information-theoretic optimal log(1/δ). Motivated by this discrepancy, we investigate optimal coding theorems in the time-bounded setting. Our main contributions can be summarised as follows. • Efficient coding theorem for rKt with a factor of 2. Addressing a question from [Zhenjian Lu and Igor C. Oliveira, 2021], we show that if x can be efficiently sampled with probability at least δ then rKt(x) ≤ (2 + o(1)) ⋅ log(1/δ) + O(log n). As in previous work, our coding theorem is efficient in the sense that it provides a polynomial-time probabilistic algorithm that, when given x, the code of the sampler, and δ, it outputs, with probability ≥ 0.99, a probabilistic representation of x that certifies this rKt complexity bound. • Optimality under a cryptographic assumption. Under a hypothesis about the security of cryptographic pseudorandom generators, we show that no efficient coding theorem can achieve a bound of the form rKt(x) ≤ (2 - o(1)) ⋅ log(1/δ) + poly(log n). Under a weaker assumption, we exhibit a gap between efficient coding theorems and existential coding theorems with near-optimal parameters. • Optimal coding theorem for pK^t and unconditional Antunes-Fortnow. We consider pK^t complexity [Halley Goldberg et al., 2022], a variant of rKt where the randomness is public and the time bound is fixed. We observe the existence of an optimal coding theorem for pK^t, and employ this result to establish an unconditional version of a theorem of Antunes and Fortnow [Luis Filipe Coelho Antunes and Lance Fortnow, 2009] which characterizes the worst-case running times of languages that are in average polynomial-time over all 𝖯-samplable distributions.
Cite as

Zhenjian Lu, Igor C. Oliveira, and Marius Zimand. Optimal Coding Theorems in Time-Bounded Kolmogorov Complexity. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 92:1-92:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{lu_et_al:LIPIcs.ICALP.2022.92,
  author =	{Lu, Zhenjian and Oliveira, Igor C. and Zimand, Marius},
  title =	{{Optimal Coding Theorems in Time-Bounded Kolmogorov Complexity}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{92:1--92:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.92},
  URN =		{urn:nbn:de:0030-drops-164331},
  doi =		{10.4230/LIPIcs.ICALP.2022.92},
  annote =	{Keywords: computational complexity, randomized algorithms, Kolmogorov complexity}
}
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