23 Search Results for "Krizanc, Danny"

Document
DOI: 10.4230/LIPIcs.CPM.2026.9
Indexing and Encoding Arrays for Element Distinctness Queries

Authors: Johannes Fischer and Filippo Lari

Published in: LIPIcs, Volume 369, 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)

Abstract
We introduce the data structure variant of the well-known element distinctness problem. Given an array of n elements, the goal is to preprocess the array into a data structure that supports queries asking whether all elements within a given query range are distinct. This has applications in text indexing and possibly also in other algorithmic domains. In the indexing model (where access to the input array is allowed), we design a data structure using O((n log b)/b) bits and answering queries in the time needed to solve an online element distinctness instance of size O(b), for any b ≥ 1. As a concrete instantiation of this, there exists an index that answers queries in O(log log log n) time using O({n log²(log log log n)}/{log log log n}) bits of additional space. Moving to the encoding model (where access to the input array is not allowed), we begin by proving an information-theoretic lower bound for the space usage of 2n-O(log n) bits, and then design a matching encoding with O(1) time queries. We then consider the case in which the alphabet size σ is constant. In this setting, the lower bound can be refined to n log(r_σ) - 3 log(σ+2) + O(1) bits, where r_σ = 4cos²(π/(σ+2)). This lower bound is matched by an encoding with O(1) time queries.
Cite as

Johannes Fischer and Filippo Lari. Indexing and Encoding Arrays for Element Distinctness Queries. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{fischer_et_al:LIPIcs.CPM.2026.9,
  author =	{Fischer, Johannes and Lari, Filippo},
  title =	{{Indexing and Encoding Arrays for Element Distinctness Queries}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{9:1--9:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-420-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{369},
  editor =	{Bille, Philip and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2026.9},
  URN =		{urn:nbn:de:0030-drops-259350},
  doi =		{10.4230/LIPIcs.CPM.2026.9},
  annote =	{Keywords: element distinctness, range queries, lower bounds, succinct data structures}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2026.37
Faster Linear-Space Data Structures for Path Frequency Queries

Authors: Ovidiu Rața

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract
We present linear-space data structures for several frequency queries on trees, namely: path mode, path least frequent element, and path α-minority queries. We present the first linear-space data structures, requiring O(n √{nw}) preprocessing time, that can answer path mode and path least frequent element queries in O(√{n/w}) time. This improves upon the best previously known bound of O(log log n √{n/w}) achieved by Durocher et al. [Durocher et al., 2016] in 2016. For the path α-minority problem, where α is specified at query time, we reduce the query time of the linear-space data structure of Durocher et al. [Durocher et al., 2016] from O(α^{-1}log log n) down to O(α^{-1}) by employing a simple randomized algorithm with a success probability ≥ 1/2. We also present the first linear-space data structure supporting "Path Maximum g-value Color" queries in O(√{n/w}) time, requiring O(n √{nw}) preprocessing time. This general framework encapsulates both path mode and path least frequent element queries. For our data structures, we consider the word-RAM model with w ∈ Ω(log n), where w is the word size in bits.
Cite as

Ovidiu Rața. Faster Linear-Space Data Structures for Path Frequency Queries. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 37:1-37:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{rata:LIPIcs.SWAT.2026.37,
  author =	{Rața, Ovidiu},
  title =	{{Faster Linear-Space Data Structures for Path Frequency Queries}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{37:1--37:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.37},
  URN =		{urn:nbn:de:0030-drops-260732},
  doi =		{10.4230/LIPIcs.SWAT.2026.37},
  annote =	{Keywords: Data structure, Range query, Mode, Minority, Least frequent element, Trees, Linear-space, Path query}
}
Document
Media Exposition
DOI: 10.4230/LIPIcs.SoCG.2026.98
Interactive Uniform Floodlight Illumination and Rotating Rays Voronoi Diagrams (Media Exposition)

Authors: Carlos Alegría, Ioannis Mantas, Marko Savić, and Martin Suderland

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
Floodlight illumination problems are art-gallery variants, where a target domain needs to be illuminated by guards, each associated with a field of view. The rotating rays Voronoi diagram is a Voronoi diagram with rays as sites under the angular distance. There is a natural connection of this Voronoi structure with the problem of finding the minimum aperture such that a given set of uniform aperture floodlights illuminates a target domain. In this work we present an interactive visualization software for such problems, supporting different angular distances, namely, oriented and unoriented versions, and for different domains, namely, the plane and simple polygons.
Cite as

Carlos Alegría, Ioannis Mantas, Marko Savić, and Martin Suderland. Interactive Uniform Floodlight Illumination and Rotating Rays Voronoi Diagrams (Media Exposition). In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 98:1-98:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{alegria_et_al:LIPIcs.SoCG.2026.98,
  author =	{Alegr{\'\i}a, Carlos and Mantas, Ioannis and Savi\'{c}, Marko and Suderland, Martin},
  title =	{{Interactive Uniform Floodlight Illumination and Rotating Rays Voronoi Diagrams}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{98:1--98:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.98},
  URN =		{urn:nbn:de:0030-drops-259048},
  doi =		{10.4230/LIPIcs.SoCG.2026.98},
  annote =	{Keywords: rotating rays Voronoi diagram, oriented angular distance, unoriented angular distance, Brocard angle, floodlight illumination, coverage problems, visualization software}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.18
Optimal Deterministic Rendezvous in Labeled Lines

Authors: Yann Bourreau, Ananth Narayanan, and Alexandre Nolin

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

Abstract
In a rendezvous task, a set of mobile agents initially dispersed in a network have to gather at an arbitrary common site. We consider the rendezvous problem on the infinite labeled line, with 2 initially asleep agents, without communication, and a synchronous notion of time. Each node on the line is labeled with a unique positive integer. The initial distance between the two agents is denoted by D. Time is divided into rounds and measured from the moment an agent first wakes up. We denote by τ the delay between the two agents' wake up times. If awake in a given round T, an agent at a node v has three options: stay at the node v, take port 0, or take port 1. If it decides to stay, the agent will still be at node v in round T+1. Otherwise, it will be at one of the two neighbors of v on the infinite line, depending on the port it chose. The agents achieve rendezvous in T rounds if they are at the same node in round T. We aim for a deterministic algorithm for this problem. The problem was recently considered by Miller and Pelc [Distributed Computing, 2025]. With 𝓁_{max} the largest label of the two starting nodes, they showed that no algorithm can guarantee rendezvous in o(D log^* 𝓁_{max}) rounds. The lower bound follows from a connection with the LOCAL model of distributed computing, and holds even if the agents are guaranteed simultaneous wake-up (τ = 0) and are told their initial distance D. Miller and Pelc also gave an algorithm of optimal matching complexity O(D log^* 𝓁_{max}) when the agents know D, but only obtained the higher bound of O(D² (log^* 𝓁_{max})³) when D is unknown to the agents. In this paper, we improve this second complexity to a tight O(D log^* 𝓁_{max}), closing the gap between the best known lower and upper bounds. In fact, our algorithm achieves rendezvous in O(D log^* 𝓁_{min}) rounds, where 𝓁_{min} is the smallest label within distance O(D) of the two starting positions. We obtain this result by having the agents compute sparse subsets of the nodes to gather at (formally, ruling sets over the line), as well as some general observations about the setting of rendezvous on labeled graphs.
Cite as

Yann Bourreau, Ananth Narayanan, and Alexandre Nolin. Optimal Deterministic Rendezvous in Labeled Lines. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 18:1-18:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bourreau_et_al:LIPIcs.STACS.2026.18,
  author =	{Bourreau, Yann and Narayanan, Ananth and Nolin, Alexandre},
  title =	{{Optimal Deterministic Rendezvous in Labeled Lines}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{18:1--18:20},
  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.2026.18},
  URN =		{urn:nbn:de:0030-drops-255071},
  doi =		{10.4230/LIPIcs.STACS.2026.18},
  annote =	{Keywords: mobile agents, rendezvous, ruling set, deterministic algorithms, labeled line}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.32
Optimal Verification of a Minimum-Weight Basis in an Uncertainty Matroid

Authors: Haya Diwan, Lisa Hellerstein, Nicole Megow, and Jens Schlöter

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

Abstract
Research in explorable uncertainty addresses combinatorial optimization problems where there is partial information about the values of numeric input parameters, and exact values of these parameters can be determined by performing costly queries. The goal is to design an adaptive query strategy that minimizes the query cost incurred in computing an optimal solution. Solving such problems generally requires that we be able to solve the associated verification problem: given the answers to all queries in advance, find a minimum-cost set of queries that certifies an optimal solution to the combinatorial optimization problem. We present a polynomial-time algorithm for verifying a minimum-weight basis of a matroid, where each weight lies in a given uncertainty area. These areas may be finite sets, real intervals, or unions of open and closed intervals, strictly generalizing previous work by Erlebach and Hoffman which only handled the special case of open intervals. Our algorithm introduces new techniques to address the resulting challenges. Verification problems are of particular importance in the area of explorable uncertainty, as the structural insights and techniques used to solve the verification problem often heavily influence work on the corresponding online problem and its stochastic variant. In our case, we use structural results from the verification problem to give a best-possible algorithm for a promise variant of the corresponding adaptive online problem. Finally, we show that our algorithms can be applied to two learning-augmented variants of the minimum-weight basis problem under explorable uncertainty.
Cite as

Haya Diwan, Lisa Hellerstein, Nicole Megow, and Jens Schlöter. Optimal Verification of a Minimum-Weight Basis in an Uncertainty Matroid. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 32:1-32:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{diwan_et_al:LIPIcs.STACS.2026.32,
  author =	{Diwan, Haya and Hellerstein, Lisa and Megow, Nicole and Schl\"{o}ter, Jens},
  title =	{{Optimal Verification of a Minimum-Weight Basis in an Uncertainty Matroid}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{32:1--32:20},
  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.2026.32},
  URN =		{urn:nbn:de:0030-drops-255216},
  doi =		{10.4230/LIPIcs.STACS.2026.32},
  annote =	{Keywords: Matroid verification, minimum-weight basis, query strategy, uncertainty matroid, explorable uncertainty}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.87
Range Longest Increasing Subsequence and Its Relatives

Authors: Karthik C. S. and Saladi Rahul

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

Abstract
Longest increasing subsequence (LIS) is a classical textbook problem which is still actively studied in various computational models. In this work, we present a few results for the range longest increasing subsequence problem (Range-LIS) and its variants. The input to Range-LIS is a sequence 𝒮 of n real numbers and a collection 𝒬 of m query ranges and for each query in 𝒬, the goal is to report the LIS of the sequence 𝒮 restricted to that query. Our two main results are for the following generalizations of the Range-LIS problem: 2D Range Queries: In this variant of the Range-LIS problem, each query is a pair of ranges, one of indices and the other of values, and we provide a randomized algorithm with running time Õ(mn^{1/2}+ n^{3/2})+O(k), where k is the cumulative length of the m output subsequences. This improves on the elementary Õ(mn) runtime algorithm when m = Ω(√n). Previously, the only known result breaking the quadratic barrier was of Tiskin [SODA'10] which could only handle 1D range queries (i.e., each query was a range of indices) and also just outputted the length of the LIS (instead of reporting the subsequence achieving that length). Subsequent to our paper, Gawrychowski, Gorbachev, and Kociumaka in a preprint have extended Tiskin’s approach to handle reporting 1D range queries in O(n(log n)³+m+k) time. Colored Sequences: In this variant of the Range-LIS problem, each element in 𝒮 is colored and for each query in 𝒬, the goal is to report a monochromatic LIS contained in the sequence 𝒮 restricted to that query. For 2D queries, we provide a randomized algorithm for this colored version with running time Õ(mn^{2/3}+ n^{5/3})+O(k). Moreover, for 1D queries, we provide an improved algorithm with running time Õ(mn^{1/2}+ n^{3/2})+O(k). Thus, we again improve on the elementary Õ(mn) runtime algorithm. Additionally, we prove that assuming the well-known Combinatorial Boolean Matrix Multiplication Hypothesis, that the runtime for 1D queries is essentially tight for combinatorial algorithms. Our algorithms combine several tools such as dynamic programming (to precompute increasing subsequences with some desirable properties), geometric data structures (to efficiently compute the dynamic programming entries), random sampling (to capture elements which are part of the LIS), classification of query ranges into large LIS and small LIS, and classification of colors into light and heavy. We believe that our techniques will be of interest to tackle other variants of LIS problem and other range-searching problems.
Cite as

Karthik C. S. and Saladi Rahul. Range Longest Increasing Subsequence and Its Relatives. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 87:1-87:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{karthikc.s._et_al:LIPIcs.ITCS.2026.87,
  author =	{Karthik C. S. and Rahul, Saladi},
  title =	{{Range Longest Increasing Subsequence and Its Relatives}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{87:1--87:20},
  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.2026.87},
  URN =		{urn:nbn:de:0030-drops-253740},
  doi =		{10.4230/LIPIcs.ITCS.2026.87},
  annote =	{Keywords: Longest Increasing Subsequence, Range Query, Fine-Grained Complexity}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.47
Dudeney’s Dissection Is Optimal

Authors: Erik D. Demaine, Tonan Kamata, and Ryuhei Uehara

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

Abstract
In 1907, Henry Ernest Dudeney posed a puzzle: "cut any equilateral triangle ... into as few pieces as possible that will fit together and form a perfect square" (without overlap, via translation and rotation). Four weeks later, Dudeney demonstrated a beautiful four-piece solution, which today remains perhaps the most famous example of dissection. In this paper (over a century later), we finally solve Dudeney’s puzzle, by proving that the equilateral triangle and square have no common dissection with three or fewer polygonal pieces. We reduce the problem to the analysis of discrete graph structures representing the correspondence between the edges and the vertices of the pieces forming each polygon.
Cite as

Erik D. Demaine, Tonan Kamata, and Ryuhei Uehara. Dudeney’s Dissection Is Optimal. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 47:1-47:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{demaine_et_al:LIPIcs.ITCS.2026.47,
  author =	{Demaine, Erik D. and Kamata, Tonan and Uehara, Ryuhei},
  title =	{{Dudeney’s Dissection Is Optimal}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{47:1--47:22},
  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.2026.47},
  URN =		{urn:nbn:de:0030-drops-253345},
  doi =		{10.4230/LIPIcs.ITCS.2026.47},
  annote =	{Keywords: Geometric Dissection, Dudeney Dissection, Dissection with Fewest Pieces}
}
Document
Invited Paper
DOI: 10.4230/OASIcs.RW.2024/2025.8
ASP Essentials: Modelling and Efficient Solving (Invited Paper)

Authors: Giuseppe Mazzotta and Francesco Ricca

Published in: OASIcs, Volume 138, Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 & RW 2025)

Abstract
Answer Set Programming (ASP) is a logic-based Knowledge Representation and Reasoning (KRR) paradigm that facilitates rapid prototyping of solutions for complex problems. It is particularly effective for tackling Deep Reasoning tasks involving exponentially large search spaces, such as combinatorial search and optimization. While getting started with ASP is relatively easy, mastering its advanced constructs and scaling solutions to real-world problem sizes can be challenging. This paper provides an introduction to ASP, guiding the reader from the fundamentals of the language to the application of programming methodologies and the computation of answer sets. Beyond the core framework, the paper also examines selected extensions of ASP that enable the modeling of complex problems, as well as compilation techniques designed to enhance solving efficiency. Furthermore, it mentions some recent tools that combine ASP with LLMs.
Cite as

Giuseppe Mazzotta and Francesco Ricca. ASP Essentials: Modelling and Efficient Solving (Invited Paper). In Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 & RW 2025). Open Access Series in Informatics (OASIcs), Volume 138, pp. 8:1-8:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mazzotta_et_al:OASIcs.RW.2024/2025.8,
  author =	{Mazzotta, Giuseppe and Ricca, Francesco},
  title =	{{ASP Essentials: Modelling and Efficient Solving}},
  booktitle =	{Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 \& RW 2025)},
  pages =	{8:1--8:21},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-405-5},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{138},
  editor =	{Artale, Alessandro and Bienvenu, Meghyn and Garc{\'\i}a, Yazm{\'\i}n Ib\'{a}\~{n}ez and Murlak, Filip},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.RW.2024/2025.8},
  URN =		{urn:nbn:de:0030-drops-250539},
  doi =		{10.4230/OASIcs.RW.2024/2025.8},
  annote =	{Keywords: Answer Set Programming, ASP with Quantifiers, Grounding Bottleneck, Compilation-based ASP solving, Neurosymbolic AI, LLMs}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.34
Deterministic Local Problems in Radio Networks: On the Impact of Local Domination and a Bit of Advice

Authors: Pawel Garncarek, Tomasz Jurdzinski, Dariusz R. Kowalski, Shay Kutten, and Miguel A. Mosteiro

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
Radio Networks (RN) is one of the fundamental models for network communication where nodes can broadcast messages locally but their simultaneous transmissions can interfere with each other at their shared neighbors. This work focuses on performing the very fundamental primitive of Local Broadcast, in spite of the interferences. We investigate to what extent local knowledge, called advice, relating to the 2-local domination number γ₂ may speed up Local Broadcast. Specifically for each node and some dominating set, knowledge about some neighboring dominating node and the local number among the neighbors of that dominating node. We show that such advice is sufficient to build an efficient oblivious transmission schedule. Along those lines, we present three algorithms trading the level of adaptiveness (from oblivious to adaptive) for bits of advice per node (from O(log (Δγ₂)) to 1). All our algorithms complete Local Broadcast in Õ(Δγ₂²) rounds, where Δ is the maximum degree of the network. On the side of lower bounds, we show that, for each quasi-adaptive deterministic Local Broadcast algorithm, there is some RN that requires Ω(min{(min{Δ,γ₂}/log n)²,n}) communication rounds, where n is the number of network nodes. In quasi-adaptive protocols nodes may stop executing once its computational task is completed. To the best of our knowledge, this is the first (nearly) quadratic Local Broadcast (same message for all neighbors) lower bound in the RN model. Our lower bound is stronger than previous works in multiple ways: i) it is nearly quadratically better than the best known general lower bound for this class of algorithms, ii) it applies to a wider class of algorithms than previous work for fully oblivious, iii) it achieves similar time lower bound than previous work proved for a much more demanding Local Broadcast where each node sends a possibly different message to each neighbor, and iv) it takes into account the local domination parameter γ₂.
Cite as

Pawel Garncarek, Tomasz Jurdzinski, Dariusz R. Kowalski, Shay Kutten, and Miguel A. Mosteiro. Deterministic Local Problems in Radio Networks: On the Impact of Local Domination and a Bit of Advice. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 34:1-34:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{garncarek_et_al:LIPIcs.ISAAC.2025.34,
  author =	{Garncarek, Pawel and Jurdzinski, Tomasz and Kowalski, Dariusz R. and Kutten, Shay and Mosteiro, Miguel A.},
  title =	{{Deterministic Local Problems in Radio Networks: On the Impact of Local Domination and a Bit of Advice}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{34:1--34:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.34},
  URN =		{urn:nbn:de:0030-drops-249426},
  doi =		{10.4230/LIPIcs.ISAAC.2025.34},
  annote =	{Keywords: Radio Networks, Local Broadcast, Distributed Deterministic Algorithms, Lower Bounds, Graph algorithms, Advice, Labeling Schemes, Local Domination}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.25
Instance-Optimal Imprecise Convex Hull

Authors: Sarita de Berg, Ivor van der Hoog, Eva Rotenberg, Daniel Rutschmann, and Sampson Wong

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

Abstract
Imprecise measurements of a point set P = (p₁, …, p_n) can be modelled by a family of regions F = (R₁, …, R_n), where each imprecise region R_i ∈ F contains a unique point p_i ∈ P. A retrieval models an accurate measurement by replacing an imprecise region R_i with its corresponding point p_i. We construct the convex hull of an imprecise point set in the plane, by determining the cyclic ordering of the convex hull vertices of P as efficiently as possible. Efficiency is interpreted in two ways: (i) minimising the number of retrievals, and (ii) the computation time to determine the set of regions that must be retrieved. Previous works focused on only one of these two aspects: either minimising retrievals or optimising algorithmic runtime. Our contribution is the first to simultaneously achieve both. Let r(F, P) denote the minimal number of retrievals required by any algorithm to determine the convex hull of P for a given instance (F, P). For a family F of n constant-complexity polygons, our main result is a reconstruction algorithm that performs Θ(r(F, P)) retrievals in O(r(F, P) log³ n) time. Compared to previous approaches that achieve optimal retrieval counts, we improve the runtime per retrieval from polynomial to polylogarithmic. We extend the generality of previous results to simple k-gons, to pairwise disjoint disks with radii in [1,k], and to unit disks where at most k disks overlap in a single point. Our runtime scales linearly with k.
Cite as

Sarita de Berg, Ivor van der Hoog, Eva Rotenberg, Daniel Rutschmann, and Sampson Wong. Instance-Optimal Imprecise Convex Hull. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 25:1-25:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{deberg_et_al:LIPIcs.ESA.2025.25,
  author =	{de Berg, Sarita and van der Hoog, Ivor and Rotenberg, Eva and Rutschmann, Daniel and Wong, Sampson},
  title =	{{Instance-Optimal Imprecise Convex Hull}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{25:1--25:15},
  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.2025.25},
  URN =		{urn:nbn:de:0030-drops-244932},
  doi =		{10.4230/LIPIcs.ESA.2025.25},
  annote =	{Keywords: convex hull, imprecise geometry preprocessing model, partial information}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.41
What Is the Minimum Number of Random Bits Required for Computability and Efficiency in Anonymous Networks?

Authors: Dariusz R. Kowalski, Piotr Krysta, and Shay Kutten

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
Angluin (STOC'80) and Yamashita and Kameda (PODC'88) show that some useful distributed tasks are impossible (for deterministic algorithms) in a general network if nodes do not possess unique identifiers. However, any task decidable in the non-distributed context, can be solved deterministically if the network has a unique leader. Alternatively, much research has been devoted to randomized distributed algorithms in anonymous networks. We present tight upper and lower bounds for the fundamental question: How much randomness is necessary and sufficient to solve Leader Election (LE) in anonymous networks, i.e., to transform an anonymous network into a non-anonymous one? We prove that at least one random bit per node is required in some cases. Surprisingly, a single random bit is also enough, for a total of n bits, where n is the number of nodes. However, the time complexity of our (total of) n random bits algorithm for general networks turned out to be impractically high. Hence, we also developed time-efficient algorithms for the very symmetric graphs of cliques and cycles, paying only an additional cost of o(n) random bits. The primary steps of our algorithms are of independent interest. At first glance, it seems that using one random bit per node, any algorithm can distinguish only two sets of nodes: those with 0 and those with 1. Our algorithms manage to partition the nodes into more than two sets with high probability. In some sense, they perform the task of a "distributed pseudorandom generator", for example, one of our algorithms turns n bits, one per node, into n unique (with high probability) numbers. Even though a complete graph looks very symmetric, the algorithms explore interesting asymmetries inherent in any n permutations (of n values each), if each describes the assignment (by the adversary) of ports in a node to edges leading to neighbors. Finally, we show how to transform any randomized algorithm that generates xn+o(n) random bits in total to one where each node generates at most x+1 bits. Our results apply to both synchronous and asynchronous networks.
Cite as

Dariusz R. Kowalski, Piotr Krysta, and Shay Kutten. What Is the Minimum Number of Random Bits Required for Computability and Efficiency in Anonymous Networks?. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 41:1-41:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kowalski_et_al:LIPIcs.APPROX/RANDOM.2025.41,
  author =	{Kowalski, Dariusz R. and Krysta, Piotr and Kutten, Shay},
  title =	{{What Is the Minimum Number of Random Bits Required for Computability and Efficiency in Anonymous Networks?}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{41:1--41:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.41},
  URN =		{urn:nbn:de:0030-drops-244071},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.41},
  annote =	{Keywords: Distributed computability, Anonymous Networks, Randomness, Leader Election}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.48
Sharp Thresholds for the Overlap Gap Property: Ising p-Spin Glass and Random k-SAT

Authors: Eren C. Kızıldağ

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
The Ising p-spin glass and random k-SAT are two canonical examples of disordered systems that play a central role in understanding the link between geometric features of optimization landscapes and computational tractability. Both models exhibit hard regimes where all known polynomial-time algorithms fail and possess the multi Overlap Gap Property (m-OGP), an intricate geometrical property that rigorously rules out a broad class of algorithms exhibiting input stability. We establish that, in both models, the symmetric m-OGP undergoes a sharp phase transition, and we pinpoint its exact threshold. For the Ising p-spin glass, our results hold for all sufficiently large p; for the random k-SAT, they apply to all k growing mildly with the number of Boolean variables. Notably, our findings yield qualitative insights into the power of OGP-based arguments. A particular consequence for the Ising p-spin glass is that the strength of the m-OGP in establishing algorithmic hardness grows without bound as m increases. These are the first sharp threshold results for the m-OGP. Our analysis hinges on a judicious application of the second moment method, enhanced by concentration. While a direct second moment calculation fails, we overcome this via a refined approach that leverages an argument of Frieze [Frieze, 1990] and exploiting concentration properties of carefully constructed random variables.
Cite as

Eren C. Kızıldağ. Sharp Thresholds for the Overlap Gap Property: Ising p-Spin Glass and Random k-SAT. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 48:1-48:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kizildag:LIPIcs.APPROX/RANDOM.2025.48,
  author =	{K{\i}z{\i}lda\u{g}, Eren C.},
  title =	{{Sharp Thresholds for the Overlap Gap Property: Ising p-Spin Glass and Random k-SAT}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{48:1--48:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.48},
  URN =		{urn:nbn:de:0030-drops-244147},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.48},
  annote =	{Keywords: spin glasses, p-spin model, random constraint satisfaction problems, overlap gap property, phase transitions, computational complexity}
}
Document
Research
DOI: 10.4230/OASIcs.Grossi.12
Encoding Data Structures for Range Queries on Arrays

Authors: Seungbum Jo and Srinivasa Rao Satti

Published in: OASIcs, Volume 132, From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday (2025)

Abstract
Efficiently processing range queries on arrays is a fundamental problem in computer science, with applications spanning diverse domains such as database management, computational biology, and geographic information systems. A range query retrieves information about a specific segment of an array, such as the sum, minimum, maximum, or median of elements within a given range. The challenge lies in designing data structures that allow such queries to be answered quickly, often in constant or logarithmic time, while keeping space overhead (and preprocessing time) small. Encoding data structures for range queries has emerged as a pivotal area of research due to the increasing demand for high-performance systems handling massive datasets. These structures consider the data together with the queries and aim to store only as much information about the data as is needed to answer the queries. The data structure does not need to access the original data to answer the queries. Encoding-based solutions often leverage techniques from succinct data structures, bit manipulation, and combinatorial optimization to achieve both space and time efficiency. By encoding the array in a manner that preserves critical information, these methods strike a balance between query time and space usage. In this survey article, we explore the landscape of encoding data structures for range queries on arrays, providing a comprehensive overview of some important results on space-efficient encodings for various types of range query.
Cite as

Seungbum Jo and Srinivasa Rao Satti. Encoding Data Structures for Range Queries on Arrays. In From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 132, pp. 12:1-12:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jo_et_al:OASIcs.Grossi.12,
  author =	{Jo, Seungbum and Satti, Srinivasa Rao},
  title =	{{Encoding Data Structures for Range Queries on Arrays}},
  booktitle =	{From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday},
  pages =	{12:1--12:12},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-391-1},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{132},
  editor =	{Conte, Alessio and Marino, Andrea and Rosone, Giovanna and Vitter, Jeffrey Scott},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Grossi.12},
  URN =		{urn:nbn:de:0030-drops-238116},
  doi =		{10.4230/OASIcs.Grossi.12},
  annote =	{Keywords: range queries, RMQ, Cartesian tree, top-k queries, range median, range mode}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.8
Identifying Approximate Minimizers Under Stochastic Uncertainity

Authors: Hessa Al-Thani and Viswanath Nagarajan

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We study a fundamental stochastic selection problem involving n independent random variables, each of which can be queried at some cost. Given a tolerance level δ, the goal is to find a δ-approximately minimum (or maximum) value over all the random variables, at minimum expected cost. A solution to this problem is an adaptive sequence of queries, where the choice of the next query may depend on previously-observed values. Two variants arise, depending on whether the goal is to find a δ-minimum value or a δ-minimizer. When all query costs are uniform, we provide a 4-approximation algorithm for both variants. When query costs are non-uniform, we provide a 5.83-approximation algorithm for the δ-minimum value and a 7.47-approximation for the δ-minimizer. All our algorithms rely on non-adaptive policies (that perform a fixed sequence of queries), so we also upper bound the corresponding "adaptivity" gaps. Our analysis relates the stopping probabilities in the algorithm and optimal policies, where a key step is in proving and using certain stochastic dominance properties.
Cite as

Hessa Al-Thani and Viswanath Nagarajan. Identifying Approximate Minimizers Under Stochastic Uncertainity. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{althani_et_al:LIPIcs.ICALP.2025.8,
  author =	{Al-Thani, Hessa and Nagarajan, Viswanath},
  title =	{{Identifying Approximate Minimizers Under Stochastic Uncertainity}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{8:1--8:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.8},
  URN =		{urn:nbn:de:0030-drops-233854},
  doi =		{10.4230/LIPIcs.ICALP.2025.8},
  annote =	{Keywords: Approximation algorithms, stochastic optimization, selection problem}
}
Document
DOI: 10.4230/LIPIcs.CPM.2025.25
Encodings for Range Minimum Queries over Bounded Alphabets

Authors: Seungbum Jo and Srinivasa Rao Satti

Published in: LIPIcs, Volume 331, 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)

Abstract
Range minimum queries (RMQs) are fundamental operations with widespread applications in database management, text indexing and computational biology. While many space-efficient data structures have been designed for RMQs on arrays with arbitrary elements, there has not been any results developed for the case when the alphabet size is small, which is the case in many practical scenarios where RMQ structures are used. In this paper, we investigate the encoding complexity of RMQs on arrays over bounded alphabet. We consider both one-dimensional (1D) and two-dimensional (2D) arrays. For the 1D case, we present a near-optimal space encoding. For constant-sized alphabets, this also supports the queries in constant time. For the 2D case, we systematically analyze the 1-sided, 2-sided, 3-sided and 4-sided queries and derive lower bounds for encoding space, and also matching upper bounds that support efficient queries in most cases. Our results demonstrate that, even with the bounded alphabet restriction, the space requirements remain close to those for the general alphabet case.
Cite as

Seungbum Jo and Srinivasa Rao Satti. Encodings for Range Minimum Queries over Bounded Alphabets. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 25:1-25:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jo_et_al:LIPIcs.CPM.2025.25,
  author =	{Jo, Seungbum and Satti, Srinivasa Rao},
  title =	{{Encodings for Range Minimum Queries over Bounded Alphabets}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{25:1--25:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-369-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{331},
  editor =	{Bonizzoni, Paola and M\"{a}kinen, Veli},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2025.25},
  URN =		{urn:nbn:de:0030-drops-231198},
  doi =		{10.4230/LIPIcs.CPM.2025.25},
  annote =	{Keywords: Range minimum queries, Encoding data structures, Cartesian trees}
}
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