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DOI: 10.4230/LIPIcs.STACS.2026.15

The Complexity of Resilience for Digraph Queries

Authors: Manuel Bodirsky and Žaneta Semanišinová

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

Abstract

We prove a complexity dichotomy for the resilience problem for unions of conjunctive digraph queries (i.e., for existential positive sentences over the signature {R} of directed graphs). Specifically, for every union μ of conjunctive digraph queries, the following problem is in P or NP-complete: given a directed multigraph G and a natural number u, can we remove u edges from G so that G ⊧ ¬ μ? In fact, we verify a more general dichotomy conjecture from [Bodirsky et al., 2024] for all resilience problems in the special case of directed graphs, and show that for such unions of queries μ there exists a countably infinite (`dual') valued structure Δ_μ which either primitively positively constructs 1-in-3-3-SAT, and hence the resilience problem for μ is NP-complete by general principles, or has a pseudo cyclic canonical fractional polymorphism, and the resilience problem for μ is in P.

Cite as

Manuel Bodirsky and Žaneta Semanišinová. The Complexity of Resilience for Digraph Queries. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 15:1-15:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bodirsky_et_al:LIPIcs.STACS.2026.15,
  author =	{Bodirsky, Manuel and Semani\v{s}inov\'{a}, \v{Z}aneta},
  title =	{{The Complexity of Resilience for Digraph Queries}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{15:1--15:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.15},
  URN =		{urn:nbn:de:0030-drops-255045},
  doi =		{10.4230/LIPIcs.STACS.2026.15},
  annote =	{Keywords: valued constraints, unions of conjunctive queries, resilience, computational complexity, pp-constructions}
}

Document

DOI: 10.4230/LIPIcs.STACS.2026.75

Effective Versions of Strong Measure Zero

Authors: Matthew Rayman

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

Abstract

Effective versions of strong measure zero sets are developed for various levels of complexity and computability. It is shown that the sets can be equivalently defined using a generalization of supermartingales called odds supermartingales, success rates on supermartingales, predictors, and coverings. We show Borel’s conjecture that a set has strong measure zero if and only if it is countable holds in the time and space bounded setting. At the level of computability this does not hold. We show the computable level contains sequences at arbitrary levels of the hyperarithmetical hierarchy. This is done by proving a correspondence principle yielding a condition for the sets of computable strong measure zero to agree with the classical sets of strong measure zero. An algorithmic version of strong measure zero using lower semicomputability is defined. We show that this notion is equivalent to the set of NCR reals studied by Reimann and Slaman, thereby giving new characterizations of this set. Effective strong packing dimension zero is investigated by requiring success with respect to the limit inferior instead of the limit superior. It is proven that every sequence in the corresponding algorithmic class is decidable. At the level of computability, the sets coincide with a notion of weak countability that we define.

Cite as

Matthew Rayman. Effective Versions of Strong Measure Zero. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 75:1-75:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{rayman:LIPIcs.STACS.2026.75,
  author =	{Rayman, Matthew},
  title =	{{Effective Versions of Strong Measure Zero}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{75:1--75:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.75},
  URN =		{urn:nbn:de:0030-drops-255648},
  doi =		{10.4230/LIPIcs.STACS.2026.75},
  annote =	{Keywords: Strong measure zero, NCR, Effective fractal dimensions, Borel’s Conjecture, Hausdorff dimension, Packing dimension}
}

Document

DOI: 10.4230/LIPIcs.DISC.2025.10

Amnesiac Flooding: Easy to Break, Hard to Escape

Authors: Henry Austin, Maximilien Gadouleau, George B. Mertzios, and Amitabh Trehan

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

Abstract

Broadcast is a central problem in distributed computing. Recently, Hussak and Trehan [PODC'19/ STACS'20/DC'23] proposed a stateless broadcasting protocol (Amnesiac Flooding), which was surprisingly proven to terminate in asymptotically optimal time (linear in the diameter of the network). However, it remains unclear: (i) Are there other stateless terminating broadcast algorithms with the desirable properties of Amnesiac Flooding, (ii) How robust is Amnesiac Flooding with respect to faults? In this paper we make progress on both of these fronts. Under a reasonable restriction (obliviousness to message content) additional to the fault-free synchronous model, we prove that Amnesiac Flooding is the only strictly stateless deterministic protocol that can achieve terminating broadcast. We achieve this by identifying four natural properties of a terminating broadcast protocol that Amnesiac Flooding uniquely satisfies. In contrast, we prove that even minor relaxations of any of these four criteria allow the construction of other terminating broadcast protocols. On the other hand, we prove that Amnesiac Flooding can become non-terminating or non-broadcasting, even if we allow just one node to drop a single message on a single edge in a single round. As a tool for proving this, we focus on the set of all configurations of transmissions between nodes in the network, and obtain a dichotomy characterizing the configurations, starting from which, Amnesiac Flooding terminates. Additionally, we characterise the structure of sets of Byzantine agents capable of forcing non-termination or non-broadcast of the protocol on arbitrary networks.

Cite as

Henry Austin, Maximilien Gadouleau, George B. Mertzios, and Amitabh Trehan. Amnesiac Flooding: Easy to Break, Hard to Escape. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 10:1-10:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{austin_et_al:LIPIcs.DISC.2025.10,
  author =	{Austin, Henry and Gadouleau, Maximilien and Mertzios, George B. and Trehan, Amitabh},
  title =	{{Amnesiac Flooding: Easy to Break, Hard to Escape}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{10:1--10:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.10},
  URN =		{urn:nbn:de:0030-drops-248273},
  doi =		{10.4230/LIPIcs.DISC.2025.10},
  annote =	{Keywords: Amnesiac flooding, Terminating protocol, Algorithm state, Stateless protocol, Flooding algorithm, Network algorithms, Graph theory, Termination, Communication, Broadcast}
}

Document

DOI: 10.4230/LIPIcs.ESA.2025.62

Polynomial-Time Constant-Approximation for Fair Sum-Of-Radii Clustering

Authors: Sina Bagheri Nezhad, Sayan Bandyapadhyay, and Tianzhi Chen

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract

In a seminal work, Chierichetti et al. [Chierichetti et al., 2017] introduced the (t,k)-fair clustering problem: Given a set of red points and a set of blue points in a metric space, a clustering is called fair if the number of red points in each cluster is at most t times and at least 1/t times the number of blue points in that cluster. The goal is to compute a fair clustering with at most k clusters that optimizes certain objective function. Considering this problem, they designed a polynomial-time O(1)- and O(t)-approximation for the k-center and the k-median objective, respectively. Recently, Carta et al. [Carta et al., 2024] studied this problem with the sum-of-radii objective and obtained a (6+ε)-approximation with running time O((k log_{1+ε}(k/ε))^k n^O(1)), i.e., fixed-parameter tractable in k. Here n is the input size. In this work, we design the first polynomial-time O(1)-approximation for (t,k)-fair clustering with the sum-of-radii objective, improving the result of Carta et al. Our result places sum-of-radii in the same group of objectives as k-center, that admit polynomial-time O(1)-approximations. This result also implies a polynomial-time O(1)-approximation for the Euclidean version of the problem, for which an f(k)⋅n^O(1)-time (1+ε)-approximation was known due to Drexler et al. [Drexler et al., 2023]. Here f is an exponential function of k. We are also able to extend our result to any arbitrary 𝓁 ≥ 2 number of colors when t = 1. This matches known results for the k-center and k-median objectives in this case. The significant disparity of sum-of-radii compared to k-center and k-median presents several complex challenges, all of which we successfully overcome in our work. Our main contribution is a novel cluster-merging-based analysis technique for sum-of-radii that helps us achieve the constant-approximation bounds.

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Sina Bagheri Nezhad, Sayan Bandyapadhyay, and Tianzhi Chen. Polynomial-Time Constant-Approximation for Fair Sum-Of-Radii Clustering. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 62:1-62:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bagherinezhad_et_al:LIPIcs.ESA.2025.62,
  author =	{Bagheri Nezhad, Sina and Bandyapadhyay, Sayan and Chen, Tianzhi},
  title =	{{Polynomial-Time Constant-Approximation for Fair Sum-Of-Radii Clustering}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{62:1--62:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.62},
  URN =		{urn:nbn:de:0030-drops-245309},
  doi =		{10.4230/LIPIcs.ESA.2025.62},
  annote =	{Keywords: fair clustering, sum-of-radii clustering, approximation algorithms}
}

Document

DOI: 10.4230/LIPIcs.MFCS.2025.24

Temporal Valued Constraint Satisfaction Problems

Authors: Manuel Bodirsky, Édouard Bonnet, and Žaneta Semanišinová

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract

We study the computational complexity of the valued constraint satisfaction problem (VCSP) for every valued structure over ℚ that is preserved by all order-preserving bijections. Such VCSPs will be called temporal, in analogy to the (classical) constraint satisfaction problem: a relational structure is preserved by all order-preserving bijections if and only if all its relations have a first-order definition in (ℚ; <), and the CSPs for such structures are called temporal CSPs. Many optimization problems that have been studied intensively in the literature can be phrased as a temporal VCSP. We prove that a temporal VCSP is in P, or NP-complete. Our analysis uses the concept of fractional polymorphisms. This is the first dichotomy result for VCSPs over infinite domains which is complete in the sense that it treats all valued structures that contain a given automorphism group.

Cite as

Manuel Bodirsky, Édouard Bonnet, and Žaneta Semanišinová. Temporal Valued Constraint Satisfaction Problems. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 24:1-24:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bodirsky_et_al:LIPIcs.MFCS.2025.24,
  author =	{Bodirsky, Manuel and Bonnet, \'{E}douard and Semani\v{s}inov\'{a}, \v{Z}aneta},
  title =	{{Temporal Valued Constraint Satisfaction Problems}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{24:1--24:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.24},
  URN =		{urn:nbn:de:0030-drops-241311},
  doi =		{10.4230/LIPIcs.MFCS.2025.24},
  annote =	{Keywords: Constraint Satisfaction Problems, valued CSPs, temporal CSPs, fractional polymorphisms, complexity dichotomy, min CSPs}
}

Document

DOI: 10.4230/LIPIcs.CALCO.2025.13

Expressivity of Bisimulation Pseudometrics over Analytic State Spaces

Authors: Daniel Luckhardt, Harsh Beohar, and Clemens Kupke

Published in: LIPIcs, Volume 342, 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)

Abstract

A Markov decision process (MDP) is a state-based dynamical system capable of describing probabilistic behaviour with rewards. In this paper, we view MDPs as coalgebras living in the category of analytic spaces, a very general class of measurable spaces. Note that analytic spaces were already studied in the literature on labelled Markov processes and bisimulation relations. Our results are twofold. First, we define bisimulation pseudometrics over such coalgebras using the framework of fibrations. Second, we develop a quantitative modal logic for such coalgebras and prove a quantitative form of Hennessy-Milner theorem in this new setting stating that the bisimulation pseudometric corresponds to the logical distance induced by modal formulae.

Cite as

Daniel Luckhardt, Harsh Beohar, and Clemens Kupke. Expressivity of Bisimulation Pseudometrics over Analytic State Spaces. In 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 342, pp. 13:1-13:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{luckhardt_et_al:LIPIcs.CALCO.2025.13,
  author =	{Luckhardt, Daniel and Beohar, Harsh and Kupke, Clemens},
  title =	{{Expressivity of Bisimulation Pseudometrics over Analytic State Spaces}},
  booktitle =	{11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)},
  pages =	{13:1--13:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-383-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{342},
  editor =	{C\^{i}rstea, Corina and Knapp, Alexander},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2025.13},
  URN =		{urn:nbn:de:0030-drops-235727},
  doi =		{10.4230/LIPIcs.CALCO.2025.13},
  annote =	{Keywords: Markov decision process, quantitative Hennessy-Milner theorem}
}

Document

DOI: 10.4230/LIPIcs.SoCG.2025.75

Levels in Arrangements: Linear Relations, the g-Matrix, and Applications to Crossing Numbers

Authors: Elizaveta Streltsova and Uli Wagner

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract

A long-standing conjecture of Eckhoff, Linhart, and Welzl, which would generalize McMullen’s Upper Bound Theorem for polytopes and refine asymptotic bounds due to Clarkson, asserts that for k ⩽ ⌊(n-d-2)/2⌋, the complexity of the (⩽ k)-level in a simple arrangement of n hemispheres in S^d is maximized for arrangements that are polar duals of neighborly d-polytopes. We prove this conjecture in the case n = d+4. By Gale duality, this implies the following result about crossing numbers: In every spherical arc drawing of K_n in S² (given by a set V ⊂ S² of n unit vectors connected by spherical arcs), the number of crossings is at least 1/4 ⌊n/2⌋ ⌊(n-1)/2⌋ ⌊(n-2)/2⌋ ⌊(n-3)/2⌋. This lower bound is attained if every open linear halfspace contains at least ⌊(n-2)/2⌋ of the vectors in V. Moreover, we determine the space of all linear and affine relations that hold between the face numbers of levels in simple arrangements of n hemispheres in S^d. This completes a long line of research on such relations, answers a question posed by Andrzejak and Welzl in 2003, and generalizes the classical fact that the Dehn-Sommerville relations generate all linear relations between the face numbers of simple polytopes (which correspond to the 0-level). To prove these results, we introduce the notion of the g-matrix, which encodes the face numbers of levels in an arrangement and generalizes the classical g-vector of a polytope.

Cite as

Elizaveta Streltsova and Uli Wagner. Levels in Arrangements: Linear Relations, the g-Matrix, and Applications to Crossing Numbers. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 75:1-75:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{streltsova_et_al:LIPIcs.SoCG.2025.75,
  author =	{Streltsova, Elizaveta and Wagner, Uli},
  title =	{{Levels in Arrangements: Linear Relations, the g-Matrix, and Applications to Crossing Numbers}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{75:1--75:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.75},
  URN =		{urn:nbn:de:0030-drops-232276},
  doi =		{10.4230/LIPIcs.SoCG.2025.75},
  annote =	{Keywords: Levels in arrangements, k-sets, k-facets, convex polytopes, f-vector, h-vector, g-vector, Dehn-Sommerville relations, Radon partitions, Gale duality, g-matrix}
}

Document

DOI: 10.4230/LIPIcs.ICDT.2025.31

On Deciding the Data Complexity of Answering Linear Monadic Datalog Queries with LTL Operators

Authors: Alessandro Artale, Anton Gnatenko, Vladislav Ryzhikov, and Michael Zakharyaschev

Published in: LIPIcs, Volume 328, 28th International Conference on Database Theory (ICDT 2025)

Abstract

Our concern is the data complexity of answering linear monadic datalog queries whose atoms in the rule bodies can be prefixed by operators of linear temporal logic LTL. We first observe that, for data complexity, answering any connected query with operators ○/○- (at the next/previous moment) is either in AC⁰, or in ACC⁰\AC⁰, or NC¹-complete, or L-hard and in NL. Then we show that the problem of deciding L-hardness of answering such queries is PSpace-complete, while checking membership in the classes AC⁰ and ACC⁰ as well as NC¹-completeness can be done in ExpSpace. Finally, we prove that membership in AC⁰ or in ACC⁰, NC¹-completeness, and L-hardness are undecidable for queries with operators ◇/◇- (sometime in the future/past) provided that NC¹ ≠ NL and L ≠ NL.

Cite as

Alessandro Artale, Anton Gnatenko, Vladislav Ryzhikov, and Michael Zakharyaschev. On Deciding the Data Complexity of Answering Linear Monadic Datalog Queries with LTL Operators. In 28th International Conference on Database Theory (ICDT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 328, pp. 31:1-31:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{artale_et_al:LIPIcs.ICDT.2025.31,
  author =	{Artale, Alessandro and Gnatenko, Anton and Ryzhikov, Vladislav and Zakharyaschev, Michael},
  title =	{{On Deciding the Data Complexity of Answering Linear Monadic Datalog Queries with LTL Operators}},
  booktitle =	{28th International Conference on Database Theory (ICDT 2025)},
  pages =	{31:1--31:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-364-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{328},
  editor =	{Roy, Sudeepa and Kara, Ahmet},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2025.31},
  URN =		{urn:nbn:de:0030-drops-229723},
  doi =		{10.4230/LIPIcs.ICDT.2025.31},
  annote =	{Keywords: Linear monadic datalog, linear temporal logic, data complexity}
}

Document

Position

DOI: 10.4230/TGDK.1.1.5

Knowledge Graphs for the Life Sciences: Recent Developments, Challenges and Opportunities

Authors: Jiaoyan Chen, Hang Dong, Janna Hastings, Ernesto Jiménez-Ruiz, Vanessa López, Pierre Monnin, Catia Pesquita, Petr Škoda, and Valentina Tamma

Published in: TGDK, Volume 1, Issue 1 (2023): Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge, Volume 1, Issue 1

Abstract

The term life sciences refers to the disciplines that study living organisms and life processes, and include chemistry, biology, medicine, and a range of other related disciplines. Research efforts in life sciences are heavily data-driven, as they produce and consume vast amounts of scientific data, much of which is intrinsically relational and graph-structured. The volume of data and the complexity of scientific concepts and relations referred to therein promote the application of advanced knowledge-driven technologies for managing and interpreting data, with the ultimate aim to advance scientific discovery. In this survey and position paper, we discuss recent developments and advances in the use of graph-based technologies in life sciences and set out a vision for how these technologies will impact these fields into the future. We focus on three broad topics: the construction and management of Knowledge Graphs (KGs), the use of KGs and associated technologies in the discovery of new knowledge, and the use of KGs in artificial intelligence applications to support explanations (explainable AI). We select a few exemplary use cases for each topic, discuss the challenges and open research questions within these topics, and conclude with a perspective and outlook that summarizes the overarching challenges and their potential solutions as a guide for future research.

Cite as

Jiaoyan Chen, Hang Dong, Janna Hastings, Ernesto Jiménez-Ruiz, Vanessa López, Pierre Monnin, Catia Pesquita, Petr Škoda, and Valentina Tamma. Knowledge Graphs for the Life Sciences: Recent Developments, Challenges and Opportunities. In Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge (TGDK), Volume 1, Issue 1, pp. 5:1-5:33, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{chen_et_al:TGDK.1.1.5,
  author =	{Chen, Jiaoyan and Dong, Hang and Hastings, Janna and Jim\'{e}nez-Ruiz, Ernesto and L\'{o}pez, Vanessa and Monnin, Pierre and Pesquita, Catia and \v{S}koda, Petr and Tamma, Valentina},
  title =	{{Knowledge Graphs for the Life Sciences: Recent Developments, Challenges and Opportunities}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{5:1--5:33},
  year =	{2023},
  volume =	{1},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.1.1.5},
  URN =		{urn:nbn:de:0030-drops-194791},
  doi =		{10.4230/TGDK.1.1.5},
  annote =	{Keywords: Knowledge graphs, Life science, Knowledge discovery, Explainable AI}
}

Document

DOI: 10.4230/LITES.8.1.2

Micro- and Macroscopic Road Traffic Analysis using Drone Image Data

Authors: Friedrich Kruber, Eduardo Sánchez Morales, Robin Egolf, Jonas Wurst, Samarjit Chakraborty, and Michael Botsch

Published in: LITES, Volume 8, Issue 1 (2022): Special Issue on Embedded Systems for Computer Vision. Leibniz Transactions on Embedded Systems, Volume 8, Issue 1

Abstract

The current development in the drone technology, alongside with machine learning based image processing, open new possibilities for various applications. Thus, the market volume is expected to grow rapidly over the next years. The goal of this paper is to demonstrate the capabilities and limitations of drone based image data processing for the purpose of road traffic analysis. In the first part a method for generating microscopic traffic data is proposed. More precisely, the state of vehicles and the resulting trajectories are estimated. The method is validated by conducting experiments with reference sensors and proofs to achieve precise vehicle state estimation results. It is also shown, how the computational effort can be reduced by incorporating the tracking information into a neural network. A discussion on current limitations supplements the findings. By collecting a large number of vehicle trajectories, macroscopic statistics, such as traffic flow and density can be obtained from the data. In the second part, a publicly available drone based data set is analyzed to evaluate the suitability for macroscopic traffic modeling. The results show that the method is well suited for gaining detailed information about macroscopic statistics, such as traffic flow dependent time headway or lane change occurrences. In conclusion, this paper presents methods to exploit the remarkable opportunities of drone based image processing for joint macro- and microscopic traffic analysis.

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Friedrich Kruber, Eduardo Sánchez Morales, Robin Egolf, Jonas Wurst, Samarjit Chakraborty, and Michael Botsch. Micro- and Macroscopic Road Traffic Analysis using Drone Image Data. In LITES, Volume 8, Issue 1 (2022): Special Issue on Embedded Systems for Computer Vision. Leibniz Transactions on Embedded Systems, Volume 8, Issue 1, pp. 02:1-02:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@Article{kruber_et_al:LITES.8.1.2,
  author =	{Kruber, Friedrich and S\'{a}nchez Morales, Eduardo and Egolf, Robin and Wurst, Jonas and Chakraborty, Samarjit and Botsch, Michael},
  title =	{{Micro- and Macroscopic Road Traffic Analysis using Drone Image Data}},
  journal =	{Leibniz Transactions on Embedded Systems},
  pages =	{02:1--02:27},
  ISSN =	{2199-2002},
  year =	{2022},
  volume =	{8},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LITES.8.1.2},
  URN =		{urn:nbn:de:0030-drops-192898},
  doi =		{10.4230/LITES.8.1.2},
  annote =	{Keywords: traffic data analysis, trajectory data, drone image data}
}

Document

DOI: 10.4230/LIPIcs.STACS.2022.48

Extending the Reach of the Point-To-Set Principle

Authors: Jack H. Lutz, Neil Lutz, and Elvira Mayordomo

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

Abstract

The point-to-set principle of J. Lutz and N. Lutz (2018) has recently enabled the theory of computing to be used to answer open questions about fractal geometry in Euclidean spaces ℝⁿ. These are classical questions, meaning that their statements do not involve computation or related aspects of logic. In this paper we extend the reach of the point-to-set principle from Euclidean spaces to arbitrary separable metric spaces X. We first extend two fractal dimensions - computability-theoretic versions of classical Hausdorff and packing dimensions that assign dimensions dim(x) and Dim(x) to individual points x ∈ X - to arbitrary separable metric spaces and to arbitrary gauge families. Our first two main results then extend the point-to-set principle to arbitrary separable metric spaces and to a large class of gauge families. We demonstrate the power of our extended point-to-set principle by using it to prove new theorems about classical fractal dimensions in hyperspaces. (For a concrete computational example, the stages E₀, E₁, E₂, … used to construct a self-similar fractal E in the plane are elements of the hyperspace of the plane, and they converge to E in the hyperspace.) Our third main result, proven via our extended point-to-set principle, states that, under a wide variety of gauge families, the classical packing dimension agrees with the classical upper Minkowski dimension on all hyperspaces of compact sets. We use this theorem to give, for all sets E that are analytic, i.e., Σ¹₁, a tight bound on the packing dimension of the hyperspace of E in terms of the packing dimension of E itself.

Cite as

Jack H. Lutz, Neil Lutz, and Elvira Mayordomo. Extending the Reach of the Point-To-Set Principle. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 48:1-48:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{lutz_et_al:LIPIcs.STACS.2022.48,
  author =	{Lutz, Jack H. and Lutz, Neil and Mayordomo, Elvira},
  title =	{{Extending the Reach of the Point-To-Set Principle}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{48:1--48:14},
  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.2022.48},
  URN =		{urn:nbn:de:0030-drops-158585},
  doi =		{10.4230/LIPIcs.STACS.2022.48},
  annote =	{Keywords: algorithmic dimensions, geometric measure theory, hyperspace, point-to-set principle}
}

Document

DOI: 10.4230/LIPIcs.DNA.2020.5

Population-Induced Phase Transitions and the Verification of Chemical Reaction Networks

Authors: James I. Lathrop, Jack H. Lutz, Robyn R. Lutz, Hugh D. Potter, and Matthew R. Riley

Published in: LIPIcs, Volume 174, 26th International Conference on DNA Computing and Molecular Programming (DNA 26) (2020)

Abstract

We show that very simple molecular systems, modeled as chemical reaction networks, can have behaviors that exhibit dramatic phase transitions at certain population thresholds. Moreover, the magnitudes of these thresholds can thwart attempts to use simulation, model checking, or approximation by differential equations to formally verify the behaviors of such systems at realistic populations. We show how formal theorem provers can successfully verify some such systems at populations where other verification methods fail.

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James I. Lathrop, Jack H. Lutz, Robyn R. Lutz, Hugh D. Potter, and Matthew R. Riley. Population-Induced Phase Transitions and the Verification of Chemical Reaction Networks. In 26th International Conference on DNA Computing and Molecular Programming (DNA 26). Leibniz International Proceedings in Informatics (LIPIcs), Volume 174, pp. 5:1-5:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{lathrop_et_al:LIPIcs.DNA.2020.5,
  author =	{Lathrop, James I. and Lutz, Jack H. and Lutz, Robyn R. and Potter, Hugh D. and Riley, Matthew R.},
  title =	{{Population-Induced Phase Transitions and the Verification of Chemical Reaction Networks}},
  booktitle =	{26th International Conference on DNA Computing and Molecular Programming (DNA 26)},
  pages =	{5:1--5:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-163-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{174},
  editor =	{Geary, Cody and Patitz, Matthew J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.2020.5},
  URN =		{urn:nbn:de:0030-drops-129583},
  doi =		{10.4230/LIPIcs.DNA.2020.5},
  annote =	{Keywords: chemical reaction networks, molecular programming, phase transitions, population protocols, verification}
}

Document

DOI: 10.4230/LIPIcs.FORC.2020.5

Service in Your Neighborhood: Fairness in Center Location

Authors: Christopher Jung, Sampath Kannan, and Neil Lutz

Published in: LIPIcs, Volume 156, 1st Symposium on Foundations of Responsible Computing (FORC 2020)

Abstract

When selecting locations for a set of centers, standard clustering algorithms may place unfair burden on some individuals and neighborhoods. We formulate a fairness concept that takes local population densities into account. In particular, given k centers to locate and a population of size n, we define the "neighborhood radius" of an individual i as the minimum radius of a ball centered at i that contains at least n/k individuals. Our objective is to ensure that each individual has a center that is within at most a small constant factor of her neighborhood radius. We present several theoretical results: We show that optimizing this factor is NP-hard; we give an approximation algorithm that guarantees a factor of at most 2 in all metric spaces; and we prove matching lower bounds in some metric spaces. We apply a variant of this algorithm to real-world address data, showing that it is quite different from standard clustering algorithms and outperforms them on our objective function and balances the load between centers more evenly.

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Christopher Jung, Sampath Kannan, and Neil Lutz. Service in Your Neighborhood: Fairness in Center Location. In 1st Symposium on Foundations of Responsible Computing (FORC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 156, pp. 5:1-5:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{jung_et_al:LIPIcs.FORC.2020.5,
  author =	{Jung, Christopher and Kannan, Sampath and Lutz, Neil},
  title =	{{Service in Your Neighborhood: Fairness in Center Location}},
  booktitle =	{1st Symposium on Foundations of Responsible Computing (FORC 2020)},
  pages =	{5:1--5:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-142-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{156},
  editor =	{Roth, Aaron},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2020.5},
  URN =		{urn:nbn:de:0030-drops-120215},
  doi =		{10.4230/LIPIcs.FORC.2020.5},
  annote =	{Keywords: Fairness, Clustering, Facility Location}
}

Document

DOI: 10.4230/LIPIcs.MFCS.2018.71

Projection Theorems Using Effective Dimension

Authors: Neil Lutz and Donald M. Stull

Published in: LIPIcs, Volume 117, 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)

Abstract

In this paper we use the theory of computing to study fractal dimensions of projections in Euclidean spaces. A fundamental result in fractal geometry is Marstrand's projection theorem, which shows that for every analytic set E, for almost every line L, the Hausdorff dimension of the orthogonal projection of E onto L is maximal. We use Kolmogorov complexity to give two new results on the Hausdorff and packing dimensions of orthogonal projections onto lines. The first shows that the conclusion of Marstrand's theorem holds whenever the Hausdorff and packing dimensions agree on the set E, even if E is not analytic. Our second result gives a lower bound on the packing dimension of projections of arbitrary sets. Finally, we give a new proof of Marstrand's theorem using the theory of computing.

Cite as

Neil Lutz and Donald M. Stull. Projection Theorems Using Effective Dimension. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 71:1-71:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{lutz_et_al:LIPIcs.MFCS.2018.71,
  author =	{Lutz, Neil and Stull, Donald M.},
  title =	{{Projection Theorems Using Effective Dimension}},
  booktitle =	{43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
  pages =	{71:1--71:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Potapov, Igor and Spirakis, Paul and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.71},
  URN =		{urn:nbn:de:0030-drops-96532},
  doi =		{10.4230/LIPIcs.MFCS.2018.71},
  annote =	{Keywords: algorithmic randomness, geometric measure theory, Hausdorff dimension, Kolmogorov complexity}
}

Document

DOI: 10.4230/LIPIcs.MFCS.2017.58

Fractal Intersections and Products via Algorithmic Dimension

Authors: Neil Lutz

Published in: LIPIcs, Volume 83, 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)

Abstract

Algorithmic dimensions quantify the algorithmic information density of individual points and may be defined in terms of Kolmogorov complexity. This work uses these dimensions to bound the classical Hausdorff and packing dimensions of intersections and Cartesian products of fractals in Euclidean spaces. This approach shows that a known intersection formula for Borel sets holds for arbitrary sets, and it significantly simplifies the proof of a known product formula. Both of these formulas are prominent, fundamental results in fractal geometry that are taught in typical undergraduate courses on the subject.

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Neil Lutz. Fractal Intersections and Products via Algorithmic Dimension. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 58:1-58:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{lutz:LIPIcs.MFCS.2017.58,
  author =	{Lutz, Neil},
  title =	{{Fractal Intersections and Products via Algorithmic Dimension}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{58:1--58:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-046-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{83},
  editor =	{Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean-Francois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.58},
  URN =		{urn:nbn:de:0030-drops-80875},
  doi =		{10.4230/LIPIcs.MFCS.2017.58},
  annote =	{Keywords: algorithmic randomness, geometric measure theory, Hausdorff dimension, Kolmogorov complexity}
}

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