156 Search Results for "Bender, Michael A."

Volume

LIPIcs, Volume 144

27th Annual European Symposium on Algorithms (ESA 2019)

ESA 2019, September 9-11, 2019, Munich/Garching, Germany

Editors: Michael A. Bender, Ola Svensson, and Grzegorz Herman

Document
DOI: 10.4230/LIPIcs.STACS.2026.26
Approximate Cartesian Tree Matching with Substitutions

Authors: Panagiotis Charalampopoulos, Jonas Ellert, and Manal Mohamed

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

Abstract
The Cartesian tree of a sequence captures the relative order of the sequence’s elements. In recent years, Cartesian tree matching has attracted considerable attention, particularly due to its applications in time series analysis. Consider a text T of length n and a pattern P of length m. In the exact Cartesian tree matching problem, the task is to find all length-m fragments of T whose Cartesian tree coincides with the Cartesian tree CT(P) of the pattern. Although the exact version of the problem can be solved in linear time [Park et al., TCS 2020], it remains rather restrictive; for example, it is not robust to outliers in the pattern. To overcome this limitation, we consider the approximate setting, where the goal is to identify all fragments of T that are close to some string whose Cartesian tree matches CT(P). In this work, we quantify closeness via the widely used Hamming distance metric. For a given integer parameter k > 0, we present an algorithm that computes all fragments of T that are at Hamming distance at most k from a string whose Cartesian tree matches CT(P). Our algorithm runs in time 𝒪(n √m ⋅ k^{2.5}) for k ≤ m^{1/5} and in time 𝒪(nk⁵) for k ≥ m^{1/5}, thereby improving upon the state-of-the-art 𝒪(nmk)-time algorithm of Kim and Han [TCS 2025] in the regime k = o(m^{1/4}). On the way to our solution, we develop a toolbox of independent interest. First, we introduce a new notion of periodicity in Cartesian trees. Then, we lift multiple well-known combinatorial and algorithmic results for string matching and periodicity in strings to Cartesian tree matching and periodicity in Cartesian trees.
Cite as

Panagiotis Charalampopoulos, Jonas Ellert, and Manal Mohamed. Approximate Cartesian Tree Matching with Substitutions. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 26:1-26:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{charalampopoulos_et_al:LIPIcs.STACS.2026.26,
  author =	{Charalampopoulos, Panagiotis and Ellert, Jonas and Mohamed, Manal},
  title =	{{Approximate Cartesian Tree Matching with Substitutions}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{26:1--26:21},
  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.2026.26},
  URN =		{urn:nbn:de:0030-drops-255151},
  doi =		{10.4230/LIPIcs.STACS.2026.26},
  annote =	{Keywords: Cartesian tree, Hamming distance, approximate pattern matching}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.36
Time-Optimal Construction of String Synchronizing Sets

Authors: Jonas Ellert and Tomasz Kociumaka

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

Abstract
A powerful design principle behind many modern string algorithms is local consistency: breaking the symmetry between string positions based on their small contexts so that matching fragments are handled consistently. Among the most influential instantiations of this principle are string synchronizing sets [Kempa & Kociumaka; STOC 2019]. A τ-synchronizing set of a string of length n is a set of O(n/τ) string positions, chosen using their length-2τ contexts, such that (outside of highly periodic regions) every block of τ consecutive positions contains at least one element of the set. Synchronizing sets have found dozens of applications in diverse settings, from quantum and dynamic algorithms to fully compressed computation. In the classic word RAM model, particularly for strings over small alphabets, they enabled faster solutions to core problems in data compression, text indexing, and string similarity. In this work, we show that any string T ∈ [0 .. σ)ⁿ can be preprocessed in O(n log σ / log n) time so that, for any given integer τ ∈ [1 .. n], a τ-synchronizing set of T can be constructed in O((n log τ)/(τ log n)) time. Both bounds are optimal in the word RAM model with machine word size w = Θ(log n), matching the information-theoretic minimum for the input and output sizes, respectively. Previously, constructing a τ-synchronizing set required O(n/τ) time after an O(n)-time preprocessing [Kociumaka, Radoszewski, Rytter, and Waleń; SICOMP 2024], or, in the restricted regime of τ < 0.2 log_σ n, without any preprocessing needed [Kempa & Kociumaka; STOC 2019]. A simple instantiation of our method outputs the synchronizing set as a sorted list in O(n/τ) time, or as a bitmask in O(n/log n) time. Our optimal construction produces a compact fully indexable dictionary, supporting select queries in O(1) time and rank queries in O(log ((log τ)/(log log n))) time. The latter complexity matches known unconditional cell-probe lower bounds for τ ≤ n^{1-Ω(1)}. To achieve this, we introduce a general framework for efficiently processing sparse integer sequences via a custom variable-length encoding. We also augment the optimal variant of van Emde Boas trees [Pătraşcu & Thorup; STOC 2006] with a deterministic linear-time construction. When the set is represented as a bitmask under our sparse encoding, the same guarantees for select and rank queries hold after preprocessing in time proportional to the size of our encoding (in words).
Cite as

Jonas Ellert and Tomasz Kociumaka. Time-Optimal Construction of String Synchronizing Sets. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 36:1-36:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ellert_et_al:LIPIcs.STACS.2026.36,
  author =	{Ellert, Jonas and Kociumaka, Tomasz},
  title =	{{Time-Optimal Construction of String Synchronizing Sets}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{36:1--36:22},
  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.2026.36},
  URN =		{urn:nbn:de:0030-drops-255258},
  doi =		{10.4230/LIPIcs.STACS.2026.36},
  annote =	{Keywords: synchronizing sets, local consistency, packed strings}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.98
Weighted Chairman Assignment and Flow-Time Scheduling

Authors: Siyue Liu and Victor Reis

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

Abstract
Given positive integers m, n, a fractional assignment x ∈ [0,1]^{m × n} and weights d ∈ ℝⁿ_{> 0}, we show that there exists an assignment y ∈ {0,1}^{m × n} so that for every i ∈ [m] and t ∈ [n], |∑_{j ∈ [t]} d_j (x_{ij} - y_{ij})| < max_{j ∈ [n]} d_j. This generalizes a result of Tijdeman (1973) on the unweighted version, known as the chairman assignment problem. This also confirms a special case of the single-source unsplittable flow conjecture with arc-wise lower and upper bounds due to Morell and Skutella (IPCO 2020). As an application, we consider a scheduling problem where jobs have release times and machines have closing times, and a job can only be scheduled on a machine if it is released before the machine closes. We give a 3-approximation algorithm for maximum flow-time minimization.
Cite as

Siyue Liu and Victor Reis. Weighted Chairman Assignment and Flow-Time Scheduling. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 98:1-98:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{liu_et_al:LIPIcs.ITCS.2026.98,
  author =	{Liu, Siyue and Reis, Victor},
  title =	{{Weighted Chairman Assignment and Flow-Time Scheduling}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{98:1--98:15},
  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.2026.98},
  URN =		{urn:nbn:de:0030-drops-253858},
  doi =		{10.4230/LIPIcs.ITCS.2026.98},
  annote =	{Keywords: prefix discrepancy, flow-time scheduling, unsplittable flow}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.88
Lower Bounds and Separations for Torus Polynomials

Authors: Vaibhav Krishan and Sundar Vishwanathan

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

Abstract
The class ACC⁰ consists of Boolean functions that can be computed by constant-depth circuits of polynomial size with AND, NOT and MOD_m gates, where m is a natural number. At the frontier of our understanding lies a widely believed conjecture asserting that MAJORITY does not belong to ACC⁰. A few years ago, Bhrushundi, Hosseini, Lovett and Rao (ITCS 2019) introduced torus polynomial approximations as an approach towards this conjecture. Torus polynomials approximate Boolean functions when the fractional part of their value on Boolean points is close to half the value of the function. They reduced the conjecture that MAJORITY ∉ ACC⁰ to a conjecture concerning the non-existence of low degree torus polynomials that approximate MAJORITY. We reduce the non-existence problem further, to a statement about finding feasible solutions for an infinite family of linear programs. The main advantage of this statement is that it allows for incremental progress, which means finding feasible solutions for successively larger collections of these programs. As an immediate first step, we find feasible solutions for a large class of these linear programs, leaving only a finite set for further consideration. Our method is inspired by the method of dual polynomials, which is used to study the approximate degree of Boolean functions. Using our method, we also propose a way to progress further. We prove several additional key results with the same method, which include: - A lower bound on the degree of symmetric torus polynomials that approximate the AND function. As a consequence, we get a separation that symmetric torus polynomials are weaker than their asymmetric counterparts. - An error-degree trade-off for symmetric torus polynomials approximating the MAJORITY function, strengthening the corresponding result of Bhrushundi, Hosseini, Lovett and Rao (ITCS 2019). - The first lower bounds against torus polynomials approximating AND, showcasing the power of the machinery we develop. This lower bound nearly matches the corresponding upper bound. Hence, we get an almost complete characterization of the torus polynomial approximation degree of AND. - Lower bounds against asymmetric torus polynomials approximating MAJORITY, or AND, in the very low error regime. This partially answers a question posed in Bhrushundi, Hosseini, Lovett and Rao (ITCS 2019) about error-reduction for torus polynomials.
Cite as

Vaibhav Krishan and Sundar Vishwanathan. Lower Bounds and Separations for Torus Polynomials. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 88:1-88:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{krishan_et_al:LIPIcs.ITCS.2026.88,
  author =	{Krishan, Vaibhav and Vishwanathan, Sundar},
  title =	{{Lower Bounds and Separations for Torus Polynomials}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{88:1--88:20},
  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.2026.88},
  URN =		{urn:nbn:de:0030-drops-253751},
  doi =		{10.4230/LIPIcs.ITCS.2026.88},
  annote =	{Keywords: Circuit complexity, ACC, lower bounds, polynomials}
}
Document
DOI: 10.4230/DagMan.11.1.19
Conversational Agents: A Framework for Evaluation (CAFE) (Dagstuhl Perspectives Workshop 24352)

Authors: Christine Bauer, Li Chen, Nicola Ferro, Norbert Fuhr, Avishek Anand, Timo Breuer, Guglielmo Faggioli, Ophir Frieder, Hideo Joho, Jussi Karlgren, Johannes Kiesel, Bart P. Knijnenburg, Aldo Lipani, Lien Michiels, Andrea Papenmeier, Maria Soledad Pera, Mark Sanderson, Scott Sanner, Benno Stein, Johanne R. Trippas, Karin Verspoor, and Martijn C. Willemsen

Published in: Dagstuhl Manifestos, Volume 11, Issue 1 (2025)

Abstract
During the workshop, we deeply discussed what CONversational Information ACcess (CONIAC) is and its unique features, proposing a world model abstracting it, and defined the Conversational Agents Framework for Evaluation (CAFE) for the evaluation of CONIAC systems, consisting of six major components: 1) goals of the system’s stakeholders, 2) user tasks to be studied in the evaluation, 3) aspects of the users carrying out the tasks, 4) evaluation criteria to be considered, 5) evaluation methodology to be applied, and 6) measures for the quantitative criteria chosen.
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Christine Bauer, Li Chen, Nicola Ferro, Norbert Fuhr, Avishek Anand, Timo Breuer, Guglielmo Faggioli, Ophir Frieder, Hideo Joho, Jussi Karlgren, Johannes Kiesel, Bart P. Knijnenburg, Aldo Lipani, Lien Michiels, Andrea Papenmeier, Maria Soledad Pera, Mark Sanderson, Scott Sanner, Benno Stein, Johanne R. Trippas, Karin Verspoor, and Martijn C. Willemsen. Conversational Agents: A Framework for Evaluation (CAFE) (Dagstuhl Perspectives Workshop 24352). In Dagstuhl Manifestos, Volume 11, Issue 1, pp. 19-67, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@Article{bauer_et_al:DagMan.11.1.19,
  author =	{Bauer, Christine and Chen, Li and Ferro, Nicola and Fuhr, Norbert and Anand, Avishek and Breuer, Timo and Faggioli, Guglielmo and Frieder, Ophir and Joho, Hideo and Karlgren, Jussi and Kiesel, Johannes and Knijnenburg, Bart P. and Lipani, Aldo and Michiels, Lien and Papenmeier, Andrea and Pera, Maria Soledad and Sanderson, Mark and Sanner, Scott and Stein, Benno and Trippas, Johanne R. and Verspoor, Karin and Willemsen, Martijn C.},
  title =	{{Conversational Agents: A Framework for Evaluation (CAFE) (Dagstuhl Perspectives Workshop 24352)}},
  pages =	{19--67},
  journal =	{Dagstuhl Manifestos},
  ISSN =	{2193-2433},
  year =	{2025},
  volume =	{11},
  number =	{1},
  editor =	{Bauer, Christine and Chen, Li and Ferro, Nicola and Fuhr, Norbert and Anand, Avishek and Breuer, Timo and Faggioli, Guglielmo and Frieder, Ophir and Joho, Hideo and Karlgren, Jussi and Kiesel, Johannes and Knijnenburg, Bart P. and Lipani, Aldo and Michiels, Lien and Papenmeier, Andrea and Pera, Maria Soledad and Sanderson, Mark and Sanner, Scott and Stein, Benno and Trippas, Johanne R. and Verspoor, Karin and Willemsen, Martijn C.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagMan.11.1.19},
  URN =		{urn:nbn:de:0030-drops-252722},
  doi =		{10.4230/DagMan.11.1.19},
  annote =	{Keywords: Conversational Agents, Evaluation, Information Access}
}
Document
DOI: 10.4230/DagRep.15.5.1
Adaptive and Scalable Data Structures (Dagstuhl Seminar 25191)

Authors: Michael A. Bender, John Iacono, László Kozma, Eva Rotenberg, and Justin Dallant

Published in: Dagstuhl Reports, Volume 15, Issue 5 (2025)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 25191 "Adaptive and Scalable Data Structures". Data structures govern the organization and manipulation of data in computing systems across a broad range of applications. The efficiency and scalability of data structures has profound implications, motivating continued research on the entire spectrum from theoretical to practical. As the size and complexity of data sets increases and as the underlying computing infrastructure changes, data structures need to be continually redesigned with scalability in mind. Classical data structures also need reevaluation to better fit the requirements of modern applications. Adaptivity offers a way to design data structures that automatically take advantage of features of the underlying hardware, specific structure and biases in their usage, or side-information, and the limits of data structure adaptivity pose deep research questions. The goal of this seminar was to reflect on these complementary aspects of data structure research and to identify promising research questions. The program provides a snapshot of the current state of research and establishes possible future directions for the field.
Cite as

Michael A. Bender, John Iacono, László Kozma, Eva Rotenberg, and Justin Dallant. Adaptive and Scalable Data Structures (Dagstuhl Seminar 25191). In Dagstuhl Reports, Volume 15, Issue 5, pp. 1-20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@Article{bender_et_al:DagRep.15.5.1,
  author =	{Bender, Michael A. and Iacono, John and Kozma, L\'{a}szl\'{o} and Rotenberg, Eva and Dallant, Justin},
  title =	{{Adaptive and Scalable Data Structures (Dagstuhl Seminar 25191)}},
  pages =	{1--20},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2025},
  volume =	{15},
  number =	{5},
  editor =	{Bender, Michael A. and Iacono, John and Kozma, L\'{a}szl\'{o} and Rotenberg, Eva and Dallant, Justin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.15.5.1},
  URN =		{urn:nbn:de:0030-drops-252802},
  doi =		{10.4230/DagRep.15.5.1},
  annote =	{Keywords: Data structures, Algorithms, Big data, Computational models}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.17
Treedepth Inapproximability and Exponential ETH Lower Bound

Authors: Édouard Bonnet, Daniel Neuen, and Marek Sokołowski

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
Treedepth is a central parameter to algorithmic graph theory. The current state-of-the-art in computing and approximating treedepth consists of a 2^{O(k²)} n-time exact algorithm and a polynomial-time O(OPT log^{3/2} OPT)-approximation algorithm, where the former algorithm returns an elimination forest of height k (witnessing that treedepth is at most k) for the n-vertex input graph G, or correctly reports that G has treedepth larger than k, and OPT is the actual value of the treedepth. On the complexity side, exactly computing treedepth is NP-complete, but the known reductions do not rule out a polynomial-time approximation scheme (PTAS), and under the Exponential Time Hypothesis (ETH) only exclude a running time of 2^o(√n) for exact algorithms. We show that 1.0003-approximating Treedepth is NP-hard, and that exactly computing the treedepth of an n-vertex graph requires time 2^Ω(n), unless the ETH fails. We further derive that there exist absolute constants δ, c > 0 such that any (1+δ)-approximation algorithm requires time 2^Ω(n/log^c n). We do so via a simple direct reduction from Satisfiability to Treedepth, inspired by a reduction recently designed for Treewidth [STOC '25].
Cite as

Édouard Bonnet, Daniel Neuen, and Marek Sokołowski. Treedepth Inapproximability and Exponential ETH Lower Bound. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 17:1-17:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bonnet_et_al:LIPIcs.IPEC.2025.17,
  author =	{Bonnet, \'{E}douard and Neuen, Daniel and Soko{\l}owski, Marek},
  title =	{{Treedepth Inapproximability and Exponential ETH Lower Bound}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{17:1--17:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.17},
  URN =		{urn:nbn:de:0030-drops-251494},
  doi =		{10.4230/LIPIcs.IPEC.2025.17},
  annote =	{Keywords: treedepth, lower bounds, approximation}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.27
Fault-Tolerant Approximate Distance Oracles with a Source Set

Authors: Dipan Dey and Telikepalli Kavitha

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
Our input is an undirected weighted graph G = (V,E) on n vertices along with a source set S ⊆ V. The problem is to preprocess G and build a compact data structure such that upon query Qu(s,v,f) where (s,v) ∈ S×V and f is any faulty edge, we can quickly find a good estimate (i.e., within a small multiplicative stretch) of the s-v distance in G-f. We use a fault-tolerant ST-distance oracle from the work of Bilò et al. (STACS 2018) to construct an S×V approximate distance oracle or sourcewise approximate distance oracle of size Õ(|S|n + n^{3/2}) with multiplicative stretch at most 5. We construct another fault-tolerant sourcewise approximate distance oracle of size Õ(|S|n + n^{4/3}) with multiplicative stretch at most 13. Both the oracles have O(1) query answering time.
Cite as

Dipan Dey and Telikepalli Kavitha. Fault-Tolerant Approximate Distance Oracles with a Source Set. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 27:1-27:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dey_et_al:LIPIcs.FSTTCS.2025.27,
  author =	{Dey, Dipan and Kavitha, Telikepalli},
  title =	{{Fault-Tolerant Approximate Distance Oracles with a Source Set}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{27:1--27:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.27},
  URN =		{urn:nbn:de:0030-drops-251081},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.27},
  annote =	{Keywords: Weighted graphs, approximate distances, fault-tolerant data structures}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.36
Streaming Periodicity with Mismatches, Wildcards, and Edits

Authors: Taha El Ghazi and Tatiana Starikovskaya

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

Abstract
In this work, we study the problem of detecting periodic trends in strings. While detecting exact periodicity has been studied extensively, real-world data is often noisy, where small deviations or mismatches occur between repetitions. This work focuses on a generalized approach to period detection that efficiently handles noise. Given a string S of length n, the task is to identify integers p such that the prefix and the suffix of S, each of length n-p+1, are similar under a given distance measure. Ergün et al. [APPROX-RANDOM 2017] were the first to study this problem in the streaming model under the Hamming distance. In this work, we combine, in a non-trivial way, the Hamming distance sketch of Clifford et al. [SODA 2019] and the structural description of the k-mismatch occurrences of a pattern in a text by Charalampopoulos et al. [FOCS 2020] to present a more efficient streaming algorithm for period detection under the Hamming distance. As a corollary, we derive a streaming algorithm for detecting periods of strings which may contain wildcards, a special symbol that match any character of the alphabet. Our algorithm is not only more efficient than that of Ergün et al. [TCS 2020], but it also operates without their assumption that the string must be free of wildcards in its final characters. Additionally, we introduce the first two-pass streaming algorithm for computing periods under the edit distance by leveraging and extending the Bhattacharya-Koucký’s grammar decomposition technique [STOC 2023].
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Taha El Ghazi and Tatiana Starikovskaya. Streaming Periodicity with Mismatches, Wildcards, and Edits. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 36:1-36:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{elghazi_et_al:LIPIcs.ISAAC.2025.36,
  author =	{El Ghazi, Taha and Starikovskaya, Tatiana},
  title =	{{Streaming Periodicity with Mismatches, Wildcards, and Edits}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{36:1--36:20},
  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.2025.36},
  URN =		{urn:nbn:de:0030-drops-249446},
  doi =		{10.4230/LIPIcs.ISAAC.2025.36},
  annote =	{Keywords: approximate periods, pattern matching, streaming algorithms}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.6
A Dimension-Reducing Fréchet Simplification Oracle

Authors: Boris Aronov, Tsuri Farhana, Matthew J. Katz, and Indu Ramesh

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

Abstract
Let P be a polygonal curve with n vertices in the plane. We construct a data structure of size O(n log n) suited for simplification queries of the following kind. Given a query line 𝓁 and an integer k ≥ 1, find a curve Q on 𝓁 with at most k vertices that minimizes the discrete Fréchet distance to P, among all such curves. Using our data structure, a query can be handled in O(k² log³ n + k log⁴n) time. More generally, a geometric tree T on n vertices in the plane can be preprocessed into a near-linear-size structure so that, given a pair u, v of its vertices, a line 𝓁, and an integer k ≥ 1, one can find a curve Q on 𝓁 with at most k vertices that minimizes the discrete Fréchet distance to the path from u to v in T, in time O(k² polylog n). For the general dimension-reduction problem, where P is a curve in ℝ^d (d ≥ 3), 0 < ε₀ < 1 is a real parameter, and a query specifies a g-flat h (1 ≤ g ≤ d-1) and an integer k ≥ 1, we construct a data structure of size O(nlog n + f(ε₀) n), where f(ε₀) = (1+1/ε₀)^{(d-1)/2}, that allows us to find a curve Q on h with at most k vertices, whose discrete Fréchet distance to P is at most 1+ε₀ times the distance of Q^* to P, where Q^* is such a curve that minimizes the distance to P. The query handling time is O(f(ε₀) k² log² n).
Cite as

Boris Aronov, Tsuri Farhana, Matthew J. Katz, and Indu Ramesh. A Dimension-Reducing Fréchet Simplification Oracle. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 6:1-6:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{aronov_et_al:LIPIcs.ISAAC.2025.6,
  author =	{Aronov, Boris and Farhana, Tsuri and Katz, Matthew J. and Ramesh, Indu},
  title =	{{A Dimension-Reducing Fr\'{e}chet Simplification Oracle}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{6:1--6:20},
  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.2025.6},
  URN =		{urn:nbn:de:0030-drops-249149},
  doi =		{10.4230/LIPIcs.ISAAC.2025.6},
  annote =	{Keywords: Computational geometry, discrete Fr\'{e}chet distance, curve simplification oracle, restricted minimum enclosing disk queries}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.3
Circle-Segment Intersection Queries in Connected Geometric Graphs

Authors: Peyman Afshani, Yannick Bosch, and Sabine Storandt

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

Abstract
In this paper, we study the problem of efficiently reporting all intersections between a given set of line segments in the plane and a query circle, focusing on the case where the segments form the edges of a connected geometric graph. While previous data structures for circle-segment intersection queries on general segment sets incur high space or query time costs, we exploit the connectivity of the input to obtain significantly improved performance. In fact, we propose a new circle-segment intersection data structure that can be constructed in 𝒪((n + C) log³ n) time and space on connected graphs with n edges and C edge crossings. It answers intersection queries in 𝒪(k log³ n) time, where k denotes the output size. Our method relies on the construction of efficient circle-graph intersection oracles as well as a novel linear-time algorithm to partition the edges of the graph into balanced, connected components, which might be of independent interest. In a proof-of-concept experimental study on real-world road networks, we show that our novel data structure also performs well in practice. Even on networks with millions of edges, the construction time is within minutes and queries are answered in a few milliseconds.
Cite as

Peyman Afshani, Yannick Bosch, and Sabine Storandt. Circle-Segment Intersection Queries in Connected Geometric Graphs. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 3:1-3:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{afshani_et_al:LIPIcs.ISAAC.2025.3,
  author =	{Afshani, Peyman and Bosch, Yannick and Storandt, Sabine},
  title =	{{Circle-Segment Intersection Queries in Connected Geometric Graphs}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{3:1--3:16},
  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.2025.3},
  URN =		{urn:nbn:de:0030-drops-249114},
  doi =		{10.4230/LIPIcs.ISAAC.2025.3},
  annote =	{Keywords: Intersection data structure, Graph partitioning, Dobkin-Kirkpatrick hierarchy}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.44
Approximation Schemes for k-Subset Sum Ratio and k-Way Number Partitioning Ratio

Authors: Sotiris Kanellopoulos, Giorgos Mitropoulos, Antonis Antonopoulos, Nikos Leonardos, Aris Pagourtzis, Christos Pergaminelis, Stavros Petsalakis, and Kanellos Tsitouras

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

Abstract
The Subset Sum Ratio problem (SSR) asks, given a multiset A of positive integers, to find two disjoint subsets of A such that the largest-to-smallest ratio of their sums is minimized. In this paper we study the k-version of SSR, namely k-Subset Sum Ratio (k-SSR), which asks to minimize the largest-to-smallest ratio of sums of k disjoint subsets of A. We develop an approximation scheme for k-SSR running in O(n^{2k}/ε^{k-1}) time, where n = |A| and ε is the error parameter. To the best of our knowledge, this is the first FPTAS for k-SSR for fixed k > 2. We also study the k-way Number Partitioning Ratio (k-PART) problem, which differs from k-SSR in that the k subsets must constitute a partition of A; this problem in fact corresponds to the objective of minimizing the largest-to-smallest sum ratio in the family of Multiway Number Partitioning problems. We present a more involved FPTAS for k-PART, also achieving O(n^{2k}/ε^{k-1}) time complexity. Notably, k-PART is also equivalent to the Minimum Envy-Ratio problem with identical valuation functions, which has been studied in the context of fair division of indivisible goods. Thus, for the case of identical valuations, our FPTAS represents a significant improvement over the O(n^{4k²+1}/ε^{2k²}) bound obtained by Nguyen and Rothe’s FPTAS [Trung Thanh Nguyen and Jörg Rothe, 2014] for Minimum Envy-Ratio with general additive valuations. Lastly, we propose a second FPTAS for k-SSR, which employs carefully designed calls to the first one; the new scheme has a time complexity of Õ(n/ε^{3k-1}), thus being much faster when n≫ 1/ ε.
Cite as

Sotiris Kanellopoulos, Giorgos Mitropoulos, Antonis Antonopoulos, Nikos Leonardos, Aris Pagourtzis, Christos Pergaminelis, Stavros Petsalakis, and Kanellos Tsitouras. Approximation Schemes for k-Subset Sum Ratio and k-Way Number Partitioning Ratio. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 44:1-44:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kanellopoulos_et_al:LIPIcs.ISAAC.2025.44,
  author =	{Kanellopoulos, Sotiris and Mitropoulos, Giorgos and Antonopoulos, Antonis and Leonardos, Nikos and Pagourtzis, Aris and Pergaminelis, Christos and Petsalakis, Stavros and Tsitouras, Kanellos},
  title =	{{Approximation Schemes for k-Subset Sum Ratio and k-Way Number Partitioning Ratio}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{44:1--44:22},
  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.2025.44},
  URN =		{urn:nbn:de:0030-drops-249521},
  doi =		{10.4230/LIPIcs.ISAAC.2025.44},
  annote =	{Keywords: Fully polynomial-time approximation schemes, Subset Sum Ratio, Number Partitioning, Fair division, Envy minimization, Pseudo-polynomial time algorithms}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.15
Parameterized Complexity of Directed Traveling Salesman Problem

Authors: Václav Blažej, Andreas Emil Feldmann, Foivos Fioravantes, Paweł Rzążewski, and Ondřej Suchý

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

Abstract
The Directed Traveling Salesman Problem (DTSP) is a variant of the classical Traveling Salesman Problem in which the edges in the graph are directed and a vertex and edge can be visited multiple times. The goal is to find a directed closed walk of minimum length (or total weight) that visits every vertex of the given graph at least once. In a yet more general version, Directed Waypoint Routing Problem (DWRP), some vertices are marked as terminals and we are only required to visit all terminals. Furthermore, each edge has its capacity bounding the number of times this edge can be used by a solution. While both problems (and many other variants of TSP) were extensively investigated, mostly from the approximation point of view, there are surprisingly few results concerning the parameterized complexity. Our starting point is the result of Marx et al. [APPROX/RANDOM 2016] who proved that DTSP is W[1]-hard parameterized by distance to pathwidth 3. In this paper we aim to initiate the systematic complexity study of variants of Directed Traveling Salesman Problem with respect to various, mostly structural, parameters. We show that DWRP is FPT parameterized by the solution size, the feedback edge number and the vertex integrity of the underlying undirected graph. Furthermore, the problem is XP parameterized by treewidth. On the complexity side, we show that the problem is W[1]-hard parameterized by the distance to constant treedepth.
Cite as

Václav Blažej, Andreas Emil Feldmann, Foivos Fioravantes, Paweł Rzążewski, and Ondřej Suchý. Parameterized Complexity of Directed Traveling Salesman Problem. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{blazej_et_al:LIPIcs.ISAAC.2025.15,
  author =	{Bla\v{z}ej, V\'{a}clav and Feldmann, Andreas Emil and Fioravantes, Foivos and Rz\k{a}\.{z}ewski, Pawe{\l} and Such\'{y}, Ond\v{r}ej},
  title =	{{Parameterized Complexity of Directed Traveling Salesman Problem}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{15:1--15:18},
  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.2025.15},
  URN =		{urn:nbn:de:0030-drops-249231},
  doi =		{10.4230/LIPIcs.ISAAC.2025.15},
  annote =	{Keywords: Directed TSP, parameterized complexity, vertex integrity, treedepth}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.25
Structural Parameterizations of Simultaneous Planarity

Authors: Thomas Depian, Simon D. Fink, Alexander Firbas, Robert Ganian, Matthias Pfretzschner, and Ignaz Rutter

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

Abstract
Given a set of graphs on the same vertex set, the problem Simultaneous Embedding With Fixed Edges (SEFE) asks, whether there exist planar drawings of all input graphs, such that every pair of drawings coincides on their shared subgraph. It is known that SEFE is NP-complete [Elisabeth Gassner et al., 2006], even in the so-called sunflower case, where all pairs of input graphs have the same shared graph G_∩ [Marcus Schaefer, 2012]. Fink, Pfretzschner, and Rutter [Simon D. Fink et al., 2023] recently initiated the study of the parameterized complexity of SEFE in the sunflower case, mainly focusing on structural parameters of G_∩. In this work, we shift the focus towards parameters of the union graph G_∪ that contains the edges of all input graphs. On the positive side, we establish fixed-parameter tractability for the problem with respect to the feedback edge set number of G_∪. We complement this result by showing that it, surprisingly, remains NP-complete even if G_∪ has constant vertex cover number. These results settle two open questions posed by Fink et al. [Simon D. Fink et al., 2023].
Cite as

Thomas Depian, Simon D. Fink, Alexander Firbas, Robert Ganian, Matthias Pfretzschner, and Ignaz Rutter. Structural Parameterizations of Simultaneous Planarity. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 25:1-25:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{depian_et_al:LIPIcs.ISAAC.2025.25,
  author =	{Depian, Thomas and Fink, Simon D. and Firbas, Alexander and Ganian, Robert and Pfretzschner, Matthias and Rutter, Ignaz},
  title =	{{Structural Parameterizations of Simultaneous Planarity}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{25:1--25:17},
  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.2025.25},
  URN =		{urn:nbn:de:0030-drops-249332},
  doi =		{10.4230/LIPIcs.ISAAC.2025.25},
  annote =	{Keywords: SEFE, Simultaneous Planarity, Fixed-Parameter Tractability, NP-hardness}
}
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