28 Search Results for "Maass, Wolfgang"

Document
DOI: 10.4230/LIPIcs.STACS.2026.4
Unit Interval Selection in Random Order Streams

Authors: Cezar-Mihail Alexandru, Adithya Diddapur, Magnús M. Halldórsson, Christian Konrad, and Kheeran K. Naidu

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

Abstract
We consider the Unit Interval Selection problem in the one-pass random order streaming model. In this setting, an algorithm is presented with a sequence of n unit-length intervals on the line that arrive in uniform random order, one at a time, and the objective is to output (an approximation of) a largest set of disjoint intervals using space linear in the size of an optimal solution. Previous work only considered adversarially ordered streams and established that, within these space constraints, a (2/3)-approximation can be achieved in such streams, and this is best possible, in that going beyond such an approximation factor requires space Ω(n) [Emek et al., TALG'16]. In this work, we show that an improved expected approximation factor can be achieved if the input stream is in uniform random order, where the expectation is taken over the stream order. More specifically, we give a one-pass streaming algorithm with expected approximation factor 0.7401 that uses space O(|OPT|), where OPT denotes an optimal solution. We also show that random order algorithms with expected approximation factor above 8/9 require space Ω(n), and algorithms that compute a better than 2/3-approximation with probability above 2/3 also require Ω(n) space. On a technical level, we design an algorithm for the restricted domain [0, Δ), for some constant Δ, and use standard techniques to obtain an algorithm for unrestricted domains. For the restricted domain [0, Δ), we run O(Δ) recursive instances of our algorithm, with each instance targeting the situation where a specific interval of an optimal solution arrives first. We establish the interesting property of our algorithm that it performs worst when the input stream consists solely of a set of independent intervals. It then remains to analyse the algorithm on these simple instances. Our lower bound is proved via communication complexity arguments, similar in spirit to the robust communication lower bounds established by [Chakrabarti et al., Theory Comput. 2016].
Cite as

Cezar-Mihail Alexandru, Adithya Diddapur, Magnús M. Halldórsson, Christian Konrad, and Kheeran K. Naidu. Unit Interval Selection in Random Order Streams. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 4:1-4:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{alexandru_et_al:LIPIcs.STACS.2026.4,
  author =	{Alexandru, Cezar-Mihail and Diddapur, Adithya and Halld\'{o}rsson, Magn\'{u}s M. and Konrad, Christian and Naidu, Kheeran K.},
  title =	{{Unit Interval Selection in Random Order Streams}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{4:1--4:20},
  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.2026.4},
  URN =		{urn:nbn:de:0030-drops-254933},
  doi =		{10.4230/LIPIcs.STACS.2026.4},
  annote =	{Keywords: Random order streaming algorithms, unit interval selection}
}
Document
DOI: 10.4230/LIPIcs.CSL.2026.36
A Game for Counting Logic Formula Size and an Application to Linear Orders

Authors: Grégoire Fournier and György Turán

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract
Ehrenfeucht-Fraïssé (EF) games are a basic tool in finite model theory for proving definability lower bounds, with many applications in complexity theory and related areas. They have been applied to study various logics, giving insights on quantifier rank and other logical complexity measures. In this paper, we present an EF game to capture formula size in counting logic with a bounded number of variables. The game combines games introduced previously for counting logic quantifier rank due to Immerman and Lander, and for first-order formula size due to Adler and Immerman, and Hella and Väänänen. The game is used to prove an extension of a formula size lower bound of Grohe and Schweikardt for distinguishing linear orders, from 3-variable first-order logic to 3-variable counting logic.
Cite as

Grégoire Fournier and György Turán. A Game for Counting Logic Formula Size and an Application to Linear Orders. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 36:1-36:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{fournier_et_al:LIPIcs.CSL.2026.36,
  author =	{Fournier, Gr\'{e}goire and Tur\'{a}n, Gy\"{o}rgy},
  title =	{{A Game for Counting Logic Formula Size and an Application to Linear Orders}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{36:1--36:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.36},
  URN =		{urn:nbn:de:0030-drops-254612},
  doi =		{10.4230/LIPIcs.CSL.2026.36},
  annote =	{Keywords: Finite Model Theory, Logical Aspects of Computational Complexity}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.110
Optimal Two-Round Communication Lower Bound for Graph Connectivity via Pointer Chasing

Authors: Jaikumar Radhakrishnan, Chaitanya Reddy, and Rakesh Venkat

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

Abstract
We consider the communication complexity of the graph connectivity problem, where the edges of an n-vertex undirected graph G are distributed between two parties Alice and Bob, who are then required to communicate to determine if G is connected. We show that in any randomized protocol with two-rounds of communication, Alice and Bob must exchange Ω(nlog n) bits; such a lower bound for one-round protocols was shown by Sun and Woodruff (APPROX/RANDOM 2015). A one-round deterministic protocol, where Alice sends O(n log n) bits and Bob determines the answer, was observed by Hajnal, Maass and Turan (STOC 1988); they also showed a matching lower bound of Ω(n log n) bits for deterministic protocols with unbounded rounds of communication. For randomized protocols, a reduction from the set disjointness problem due to Babai, Frankl and Simon (FOCS 1986) implies a randomized lower bound of Ω(n) even with unbounded rounds of communication. Whether this lower bound can be improved to Ω(n log n) has been an outstanding open question, whose algorithmic implications were recently emphasized by Apers, Efron, Gawrychowski, Lee, Mukopadhyay and Nanongkai (FOCS 2022). Our lower bound for randomized two-round protocols is based on a reduction from a restricted version of the two-player pointer chasing problem originally studied by Papadimitriou and Sipser (JCSS 1984). Using this reduction, we show an ω(n) lower bounds on graph connectivity for any constant number of rounds by extending deterministic lower bounds shown by Ponzio, Radhakrishnan and Venkatesh (JCSS 2001) to the randomized setting.
Cite as

Jaikumar Radhakrishnan, Chaitanya Reddy, and Rakesh Venkat. Optimal Two-Round Communication Lower Bound for Graph Connectivity via Pointer Chasing. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 110:1-110:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{radhakrishnan_et_al:LIPIcs.ITCS.2026.110,
  author =	{Radhakrishnan, Jaikumar and Reddy, Chaitanya and Venkat, Rakesh},
  title =	{{Optimal Two-Round Communication Lower Bound for Graph Connectivity via Pointer Chasing}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{110:1--110:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.110},
  URN =		{urn:nbn:de:0030-drops-253974},
  doi =		{10.4230/LIPIcs.ITCS.2026.110},
  annote =	{Keywords: Communication complexity}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.7
Approximation and Parameterized Algorithms for Covering with Disks of Two Types of Radii

Authors: Sayan Bandyapadhyay and Eli Mitchell

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
We study the Discrete Covering with Two Types of Radii problem motivated by its application in wireless networks. In this problem, the goal is to assign either small-range high frequency or large-range low frequency to each access point, maximizing the number of users in high-frequency regions while ensuring that each user is in the range of an access point. Unlike other weighted covering problems, our problem requires satisfying two simultaneous objectives, which calls for novel approaches that leverage the underlying geometry of the problem. In our work, we present two new algorithms: the first is a polynomial-time (2.5 + ε)-approximation, and the second is an exact algorithm for sparse instances, which is fixed-parameter tractable (FPT) in the number of large-radius disks. We also prove that such an FPT algorithm is impossible for general instances lacking sparsity, assuming the Exponential Time Hypothesis. Before our work, the best-known polynomial-time approximation factor was 4 for the problem. Our approximation algorithm results from a fine-grained classification of points that can contribute to the gain of a solution. Based on this classification, we design two sub-algorithms with interdependent guarantees to recover the respective class of points as gain. Our algorithm exploits further properties of Delaunay triangulations to achieve the improved bound. The FPT algorithm is based on branching that utilizes the sparsity of the instances to limit the overall search space.
Cite as

Sayan Bandyapadhyay and Eli Mitchell. Approximation and Parameterized Algorithms for Covering with Disks of Two Types of Radii. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 7:1-7:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bandyapadhyay_et_al:LIPIcs.WADS.2025.7,
  author =	{Bandyapadhyay, Sayan and Mitchell, Eli},
  title =	{{Approximation and Parameterized Algorithms for Covering with Disks of Two Types of Radii}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{7:1--7:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.7},
  URN =		{urn:nbn:de:0030-drops-242386},
  doi =		{10.4230/LIPIcs.WADS.2025.7},
  annote =	{Keywords: Covering, Disks, Approximation, FPT}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.17
Dynamic Streaming Algorithms for Geometric Independent Set

Authors: Timothy M. Chan and Yuancheng Yu

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
We present the first space-efficient, fully dynamic streaming algorithm for computing a constant-factor approximation of the maximum independent set size of n axis-aligned rectangles in two dimensions. For an arbitrarily small constant δ > 0, our algorithm obtains an O((1/δ)²) approximation and requires O(U^δ polylog n) space and update time with high probability, assuming that coordinates are integers bounded by U. We also obtain a similar result for fat objects in any constant dimension. This extends recent non-streaming algorithms by Bhore and Chan from SODA'25, and also greatly extends previous streaming results, which were limited to special types of geometric objects such as one-dimensional intervals and unit disks.
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Timothy M. Chan and Yuancheng Yu. Dynamic Streaming Algorithms for Geometric Independent Set. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 17:1-17:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chan_et_al:LIPIcs.WADS.2025.17,
  author =	{Chan, Timothy M. and Yu, Yuancheng},
  title =	{{Dynamic Streaming Algorithms for Geometric Independent Set}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{17:1--17:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.17},
  URN =		{urn:nbn:de:0030-drops-242481},
  doi =		{10.4230/LIPIcs.WADS.2025.17},
  annote =	{Keywords: Geometric Independent Set, Dynamic Streaming Algorithms}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.27
A QPTAS for Facility Location on Unit Disk Graphs

Authors: Zachary Friggstad, Mohsen Rezapour, Mohammad R. Salavatipour, and Hao Sun

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
We study the classic (Uncapacitated) Facility Location problem on Unit Disk Graphs (UDGs). For a given point set P in the plane, the unit disk graph UDG(P) on P has vertex set P and an edge between two distinct points p, q ∈ P if and only if their Euclidean distance |pq| is at most 1. The weight of the edge pq is equal to their distance |pq|. An instance of {Facility Location} on UDG(P) consists of a set C ⊆ P of clients and a set F ⊆ P of facilities, each having an opening cost f_i. The goal is to pick a subset F' ⊆ F to open while minimizing ∑_{i ∈ F'} f_i + ∑_{v ∈ C} d(v,F'), where d(v,F') is the distance of v to nearest facility in F' through UDG(P). In this paper, we present the first Quasi-Polynomial Time Approximation Schemes (QPTAS) for the problem. While approximation schemes are well-established for facility location problems on sparse geometric graphs (such as planar graphs), there is a lack of such results for dense graphs. Specifically, prior to this study, to the best of our knowledge, there was no approximation scheme for any facility location problem on UDGs in the general setting.
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Zachary Friggstad, Mohsen Rezapour, Mohammad R. Salavatipour, and Hao Sun. A QPTAS for Facility Location on Unit Disk Graphs. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 27:1-27:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{friggstad_et_al:LIPIcs.WADS.2025.27,
  author =	{Friggstad, Zachary and Rezapour, Mohsen and Salavatipour, Mohammad R. and Sun, Hao},
  title =	{{A QPTAS for Facility Location on Unit Disk Graphs}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{27:1--27:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.27},
  URN =		{urn:nbn:de:0030-drops-242586},
  doi =		{10.4230/LIPIcs.WADS.2025.27},
  annote =	{Keywords: Facility Location, Unit Disk Graphs, Approximation Algorithms}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.21
Structure and Independence in Hyperbolic Uniform Disk Graphs

Authors: Thomas Bläsius, Jean-Pierre von der Heydt, Sándor Kisfaludi-Bak, Marcus Wilhelm, and Geert van Wordragen

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

Abstract
We consider intersection graphs of disks of radius r in the hyperbolic plane. Unlike the Euclidean setting, these graph classes are different for different values of r, where very small r corresponds to an almost-Euclidean setting and r ∈ Ω(log n) corresponds to a firmly hyperbolic setting. We observe that larger values of r create simpler graph classes, at least in terms of separators and the computational complexity of the Independent Set problem. First, we show that intersection graphs of disks of radius r in the hyperbolic plane can be separated with 𝒪((1+1/r)log n) cliques in a balanced manner. Our second structural insight concerns Delaunay complexes in the hyperbolic plane and may be of independent interest. We show that for any set S of n points with pairwise distance at least 2r in the hyperbolic plane, the corresponding Delaunay complex has outerplanarity 1+𝒪((log n)/r), which implies a similar bound on the balanced separators and treewidth of such Delaunay complexes. Using this outerplanarity (and treewidth) bound we prove that Independent Set can be solved in n^𝒪(1+(log n)/r) time. The algorithm is based on dynamic programming on some unknown sphere cut decomposition that is based on the solution. The resulting algorithm is a far-reaching generalization of a result of Kisfaludi-Bak (SODA 2020), and it is tight under the Exponential Time Hypothesis. In particular, Independent Set is polynomial-time solvable in the firmly hyperbolic setting of r ∈ Ω(log n). Finally, in the case when the disks have ply (depth) at most 𝓁, we give a PTAS for Maximum Independent Set that has only quasi-polynomial dependence on 1/ε and 𝓁. Our PTAS is a further generalization of our exact algorithm.
Cite as

Thomas Bläsius, Jean-Pierre von der Heydt, Sándor Kisfaludi-Bak, Marcus Wilhelm, and Geert van Wordragen. Structure and Independence in Hyperbolic Uniform Disk Graphs. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 21:1-21:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{blasius_et_al:LIPIcs.SoCG.2025.21,
  author =	{Bl\"{a}sius, Thomas and von der Heydt, Jean-Pierre and Kisfaludi-Bak, S\'{a}ndor and Wilhelm, Marcus and van Wordragen, Geert},
  title =	{{Structure and Independence in Hyperbolic Uniform Disk Graphs}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{21:1--21:16},
  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.2025.21},
  URN =		{urn:nbn:de:0030-drops-231731},
  doi =		{10.4230/LIPIcs.SoCG.2025.21},
  annote =	{Keywords: hyperbolic geometry, unit disk graphs, independent set, treewidth}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.35
Dimension-Free Parameterized Approximation Schemes for Hybrid Clustering

Authors: Ameet Gadekar and Tanmay Inamdar

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
Hybrid k-Clustering is a model of clustering that generalizes two of the most widely studied clustering objectives: k-Center and k-Median. In this model, given a set of n points P, the goal is to find k centers such that the sum of the r-distances of each point to its nearest center is minimized. The r-distance between two points p and q is defined as max{dist(p, q)-r, 0} - this represents the distance of p to the boundary of the r-radius ball around q if p is outside the ball, and 0 otherwise. This problem was recently introduced by Fomin et al. [APPROX 2024], who designed a (1+ε, 1+ε)-bicrtieria approximation that runs in time 2^{(kd/ε)^{O(1)}} ⋅ n^{O(1)} for inputs in ℝ^d; such a bicriteria solution uses balls of radius (1+ε)r instead of r, and has a cost at most 1+ε times the cost of an optimal solution using balls of radius r. In this paper we significantly improve upon this result by designing an approximation algorithm with the same bicriteria guarantee, but with running time that is FPT only in k and ε - crucially, removing the exponential dependence on the dimension d. This resolves an open question posed in their paper. Our results extend further in several directions. First, our approximation scheme works in a broader class of metric spaces, including doubling spaces, minor-free, and bounded treewidth metrics. Secondly, our techniques yield a similar bicriteria FPT-approximation schemes for other variants of Hybrid k-Clustering, e.g., when the objective features the sum of z-th power of the r-distances. Finally, we also design a coreset for Hybrid k-Clustering in doubling spaces, answering another open question from the work of Fomin et al.
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Ameet Gadekar and Tanmay Inamdar. Dimension-Free Parameterized Approximation Schemes for Hybrid Clustering. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 35:1-35:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gadekar_et_al:LIPIcs.STACS.2025.35,
  author =	{Gadekar, Ameet and Inamdar, Tanmay},
  title =	{{Dimension-Free Parameterized Approximation Schemes for Hybrid Clustering}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{35:1--35:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine 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.2025.35},
  URN =		{urn:nbn:de:0030-drops-228615},
  doi =		{10.4230/LIPIcs.STACS.2025.35},
  annote =	{Keywords: Clustering, Parameterized algorithms, FPT approximation, k-Median, k-Center}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.42
Nearest Neighbor Complexity and Boolean Circuits

Authors: Mason DiCicco, Vladimir Podolskii, and Daniel Reichman

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
A nearest neighbor representation of a Boolean function f is a set of vectors (anchors) labeled by 0 or 1 such that f(x) = 1 if and only if the closest anchor to x is labeled by 1. This model was introduced by Hajnal, Liu and Turán [2022], who studied bounds on the minimum number of anchors required to represent Boolean functions under different choices of anchors (real vs. Boolean vectors) as well as the analogous model of k-nearest neighbors representations. We initiate a systematic study of the representational power of nearest and k-nearest neighbors through Boolean circuit complexity. To this end, we establish a close connection between Boolean functions with polynomial nearest neighbor complexity and those that can be efficiently represented by classes based on linear inequalities - min-plus polynomial threshold functions - previously studied in relation to threshold circuits. This extends an observation of Hajnal et al. [2022]. Next, we further extend the connection between nearest neighbor representations and circuits to the k-nearest neighbors case. As an outcome of these connections we obtain exponential lower bounds on the k-nearest neighbors complexity of explicit n-variate functions, assuming k ≤ n^{1-ε}. Previously, no superlinear lower bound was known for any k > 1. At the same time, we show that proving superpolynomial lower bounds for the k-nearest neighbors complexity of an explicit function for arbitrary k would require a breakthrough in circuit complexity. In addition, we prove an exponential separation between the nearest neighbor and k-nearest neighbors complexity (for unrestricted k) of an explicit function. These results address questions raised by [Hajnal et al., 2022] of proving strong lower bounds for k-nearest neighbors and understanding the role of the parameter k. Finally, we devise new bounds on the nearest neighbor complexity for several families of Boolean functions.
Cite as

Mason DiCicco, Vladimir Podolskii, and Daniel Reichman. Nearest Neighbor Complexity and Boolean Circuits. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 42:1-42:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dicicco_et_al:LIPIcs.ITCS.2025.42,
  author =	{DiCicco, Mason and Podolskii, Vladimir and Reichman, Daniel},
  title =	{{Nearest Neighbor Complexity and Boolean Circuits}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{42:1--42:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.42},
  URN =		{urn:nbn:de:0030-drops-226704},
  doi =		{10.4230/LIPIcs.ITCS.2025.42},
  annote =	{Keywords: Complexity, Nearest Neighbors, Circuits}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.51
Parameterized Geometric Graph Modification with Disk Scaling

Authors: Fedor V. Fomin, Petr A. Golovach, Tanmay Inamdar, Saket Saurabh, and Meirav Zehavi

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
The parameterized analysis of graph modification problems represents the most extensively studied area within Parameterized Complexity. Given a graph G and an integer k ∈ ℕ as input, the goal is to determine whether we can perform at most k operations on G to transform it into a graph belonging to a specified graph class ℱ. Typical operations are combinatorial and include vertex deletions and edge deletions, insertions, and contractions. However, in many real-world scenarios, when the input graph is constrained to be a geometric intersection graph, the modification of the graph is influenced by changes in the geometric properties of the underlying objects themselves, rather than by combinatorial modifications. It raises the question of whether vertex deletions or adjacency modifications are necessarily the most appropriate modification operations for studying modifications of geometric graphs. We propose the study of the disk intersection graph modification through the scaling of disks. This operation is typical in the realm of topology control but has not yet been explored in the context of Parameterized Complexity. We design parameterized algorithms and kernels for modifying to the most basic graph classes: edgeless, connected, and acyclic. Our technical contributions encompass a novel combination of linear programming, branching, and kernelization techniques, along with a fresh application of bidimensionality theory to analyze the area covered by disks, which may have broader applicability.
Cite as

Fedor V. Fomin, Petr A. Golovach, Tanmay Inamdar, Saket Saurabh, and Meirav Zehavi. Parameterized Geometric Graph Modification with Disk Scaling. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 51:1-51:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fomin_et_al:LIPIcs.ITCS.2025.51,
  author =	{Fomin, Fedor V. and Golovach, Petr A. and Inamdar, Tanmay and Saurabh, Saket and Zehavi, Meirav},
  title =	{{Parameterized Geometric Graph Modification with Disk Scaling}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{51:1--51:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.51},
  URN =		{urn:nbn:de:0030-drops-226795},
  doi =		{10.4230/LIPIcs.ITCS.2025.51},
  annote =	{Keywords: parameterized algorithms, kernelization, spreading points, distant representatives, unit disk packing}
}
Document
Survey
DOI: 10.4230/TGDK.2.1.4
Logics for Conceptual Data Modelling: A Review

Authors: Pablo R. Fillottrani and C. Maria Keet

Published in: TGDK, Volume 2, Issue 1 (2024): Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge, Volume 2, Issue 1

Abstract
Information modelling for databases and object-oriented information systems avails of conceptual data modelling languages such as EER and UML Class Diagrams. Many attempts exist to add logical rigour to them, for various reasons and with disparate strengths. In this paper we aim to provide a structured overview of the many efforts. We focus on aims, approaches to the formalisation, including key dimensions of choice points, popular logics used, and the main relevant reasoning services. We close with current challenges and research directions.
Cite as

Pablo R. Fillottrani and C. Maria Keet. Logics for Conceptual Data Modelling: A Review. In Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge (TGDK), Volume 2, Issue 1, pp. 4:1-4:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{fillottrani_et_al:TGDK.2.1.4,
  author =	{Fillottrani, Pablo R. and Keet, C. Maria},
  title =	{{Logics for Conceptual Data Modelling: A Review}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{4:1--4:30},
  ISSN =	{2942-7517},
  year =	{2024},
  volume =	{2},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.2.1.4},
  URN =		{urn:nbn:de:0030-drops-198616},
  doi =		{10.4230/TGDK.2.1.4},
  annote =	{Keywords: Conceptual Data Modelling, EER, UML, Description Logics, OWL}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2018.57
Long Term Memory and the Densest K-Subgraph Problem

Authors: Robert Legenstein, Wolfgang Maass, Christos H. Papadimitriou, and Santosh S. Vempala

Published in: LIPIcs, Volume 94, 9th Innovations in Theoretical Computer Science Conference (ITCS 2018)

Abstract
In a recent experiment, a cell in the human medial temporal lobe (MTL) encoding one sensory stimulus starts to also respond to a second stimulus following a combined experience associating the two. We develop a theoretical model predicting that an assembly of cells with exceptionally high synaptic intraconnectivity can emerge, in response to a particular sensory experience, to encode and abstract that experience. We also show that two such assemblies are modified to increase their intersection after a sensory event that associates the two corresponding stimuli. The main technical tools employed are random graph theory, and Bernoulli approximations. Assembly creation must overcome a computational challenge akin to the Densest K-Subgraph problem, namely selecting, from a large population of randomly and sparsely interconnected cells, a subset with exceptionally high density of interconnections. We identify three mechanisms that help achieve this feat in our model: (1) a simple two-stage randomized algorithm, and (2) the "triangle completion bias" in synaptic connectivity and a "birthday paradox", while (3) the strength of these connections is enhanced through Hebbian plasticity.
Cite as

Robert Legenstein, Wolfgang Maass, Christos H. Papadimitriou, and Santosh S. Vempala. Long Term Memory and the Densest K-Subgraph Problem. In 9th Innovations in Theoretical Computer Science Conference (ITCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 94, pp. 57:1-57:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{legenstein_et_al:LIPIcs.ITCS.2018.57,
  author =	{Legenstein, Robert and Maass, Wolfgang and Papadimitriou, Christos H. and Vempala, Santosh S.},
  title =	{{Long Term Memory and the Densest K-Subgraph Problem}},
  booktitle =	{9th Innovations in Theoretical Computer Science Conference (ITCS 2018)},
  pages =	{57:1--57:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-060-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{94},
  editor =	{Karlin, Anna R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2018.57},
  URN =		{urn:nbn:de:0030-drops-83593},
  doi =		{10.4230/LIPIcs.ITCS.2018.57},
  annote =	{Keywords: Brain computation, long term memory, assemblies, association}
}
Document
DOI: 10.4230/DagSemProc.10302.1
10302 Abstracts Collection – Learning paradigms in dynamic environments

Authors: Barbara Hammer, Pascal Hitzler, Wolfgang Maass, and Marc Toussaint

Published in: Dagstuhl Seminar Proceedings, Volume 10302, Learning paradigms in dynamic environments (2010)

Abstract
From 25.07. to 30.07.2010, the Dagstuhl Seminar 10302 ``Learning paradigms in dynamic environments '' was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.
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Barbara Hammer, Pascal Hitzler, Wolfgang Maass, and Marc Toussaint. 10302 Abstracts Collection – Learning paradigms in dynamic environments. In Learning paradigms in dynamic environments. Dagstuhl Seminar Proceedings, Volume 10302, pp. 1-15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{hammer_et_al:DagSemProc.10302.1,
  author =	{Hammer, Barbara and Hitzler, Pascal and Maass, Wolfgang and Toussaint, Marc},
  title =	{{10302 Abstracts Collection – Learning paradigms in dynamic environments}},
  booktitle =	{Learning paradigms in dynamic environments},
  pages =	{1--15},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10302},
  editor =	{Barbara Hammer and Pascal Hitzler and Wolfgang Maass and Marc Toussaint},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.10302.1},
  URN =		{urn:nbn:de:0030-drops-28048},
  doi =		{10.4230/DagSemProc.10302.1},
  annote =	{Keywords: Recurrent neural networks, Dynamic systems, Speech processing, Neurobiology, Neural-symbolic integration, Autonomous learning}
}
Document
DOI: 10.4230/DagSemProc.10302.2
10302 Summary – Learning paradigms in dynamic environments

Authors: Barbara Hammer, Pascal Hitzler, Wolfgang Maass, and Marc Toussaint

Published in: Dagstuhl Seminar Proceedings, Volume 10302, Learning paradigms in dynamic environments (2010)

Abstract
The seminar centered around problems which arise in the context of machine learning in dynamic environments. Particular emphasis was put on a couple of specific questions in this context: how to represent and abstract knowledge appropriately to shape the problem of learning in a partially unknown and complex environment and how to combine statistical inference and abstract symbolic representations; how to infer from few data and how to deal with non i.i.d. data, model revision and life-long learning; how to come up with efficient strategies to control realistic environments for which exploration is costly, the dimensionality is high and data are sparse; how to deal with very large settings; and how to apply these models in challenging application areas such as robotics, computer vision, or the web.
Cite as

Barbara Hammer, Pascal Hitzler, Wolfgang Maass, and Marc Toussaint. 10302 Summary – Learning paradigms in dynamic environments. In Learning paradigms in dynamic environments. Dagstuhl Seminar Proceedings, Volume 10302, pp. 1-4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{hammer_et_al:DagSemProc.10302.2,
  author =	{Hammer, Barbara and Hitzler, Pascal and Maass, Wolfgang and Toussaint, Marc},
  title =	{{10302 Summary – Learning paradigms in dynamic environments}},
  booktitle =	{Learning paradigms in dynamic environments},
  pages =	{1--4},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10302},
  editor =	{Barbara Hammer and Pascal Hitzler and Wolfgang Maass and Marc Toussaint},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.10302.2},
  URN =		{urn:nbn:de:0030-drops-28027},
  doi =		{10.4230/DagSemProc.10302.2},
  annote =	{Keywords: Summary}
}
Document
DOI: 10.4230/DagSemProc.10302.3
Neurons and Symbols: A Manifesto

Authors: Artur S. d'Avila Garcez

Published in: Dagstuhl Seminar Proceedings, Volume 10302, Learning paradigms in dynamic environments (2010)

Abstract
We discuss the purpose of neural-symbolic integration including its principles, mechanisms and applications. We outline a cognitive computational model for neural-symbolic integration, position the model in the broader context of multi-agent systems, machine learning and automated reasoning, and list some of the challenges for the area of neural-symbolic computation to achieve the promise of effective integration of robust learning and expressive reasoning under uncertainty.
Cite as

Artur S. d'Avila Garcez. Neurons and Symbols: A Manifesto. In Learning paradigms in dynamic environments. Dagstuhl Seminar Proceedings, Volume 10302, pp. 1-16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{davilagarcez:DagSemProc.10302.3,
  author =	{d'Avila Garcez, Artur S.},
  title =	{{Neurons and Symbols: A Manifesto}},
  booktitle =	{Learning paradigms in dynamic environments},
  pages =	{1--16},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10302},
  editor =	{Barbara Hammer and Pascal Hitzler and Wolfgang Maass and Marc Toussaint},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.10302.3},
  URN =		{urn:nbn:de:0030-drops-28005},
  doi =		{10.4230/DagSemProc.10302.3},
  annote =	{Keywords: Neuro-symbolic systems, cognitive models, machine learning}
}
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