89 Search Results for "B�ttcher, Stefan"

Document
DOI: 10.4230/LIPIcs.STACS.2024.11
A Characterization of Efficiently Compilable Constraint Languages

Authors: Christoph Berkholz, Stefan Mengel, and Hermann Wilhelm

Published in: LIPIcs, Volume 289, 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)

Abstract
A central task in knowledge compilation is to compile a CNF-SAT instance into a succinct representation format that allows efficient operations such as testing satisfiability, counting, or enumerating all solutions. Useful representation formats studied in this area range from ordered binary decision diagrams (OBDDs) to circuits in decomposable negation normal form (DNNFs). While it is known that there exist CNF formulas that require exponential size representations, the situation is less well studied for other types of constraints than Boolean disjunctive clauses. The constraint satisfaction problem (CSP) is a powerful framework that generalizes CNF-SAT by allowing arbitrary sets of constraints over any finite domain. The main goal of our work is to understand for which type of constraints (also called the constraint language) it is possible to efficiently compute representations of polynomial size. We answer this question completely and prove two tight characterizations of efficiently compilable constraint languages, depending on whether target format is structured. We first identify the combinatorial property of "strong blockwise decomposability" and show that if a constraint language has this property, we can compute DNNF representations of linear size. For all other constraint languages we construct families of CSP-instances that provably require DNNFs of exponential size. For a subclass of "strong uniformly blockwise decomposable" constraint languages we obtain a similar dichotomy for structured DNNFs. In fact, strong (uniform) blockwise decomposability even allows efficient compilation into multi-valued analogs of OBDDs and FBDDs, respectively. Thus, we get complete characterizations for all knowledge compilation classes between O(B)DDs and DNNFs.
Cite as

Christoph Berkholz, Stefan Mengel, and Hermann Wilhelm. A Characterization of Efficiently Compilable Constraint Languages. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 11:1-11:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{berkholz_et_al:LIPIcs.STACS.2024.11,
  author =	{Berkholz, Christoph and Mengel, Stefan and Wilhelm, Hermann},
  title =	{{A Characterization of Efficiently Compilable Constraint Languages}},
  booktitle =	{41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)},
  pages =	{11:1--11:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-311-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{289},
  editor =	{Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2024.11},
  URN =		{urn:nbn:de:0030-drops-197214},
  doi =		{10.4230/LIPIcs.STACS.2024.11},
  annote =	{Keywords: constraint satisfaction, knowledge compilation, dichotomy, DNNF}
}
Document
DOI: 10.4230/LIPIcs.STACS.2024.14
A Subquadratic Bound for Online Bisection

Authors: Marcin Bienkowski and Stefan Schmid

Published in: LIPIcs, Volume 289, 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)

Abstract
The online bisection problem is a natural dynamic variant of the classic optimization problem, where one has to dynamically maintain a partition of n elements into two clusters of cardinality n/2. During runtime, an online algorithm is given a sequence of requests, each being a pair of elements: an inter-cluster request costs one unit while an intra-cluster one is free. The algorithm may change the partition, paying a unit cost for each element that changes its cluster. This natural problem admits a simple deterministic O(n²)-competitive algorithm [Avin et al., DISC 2016]. While several significant improvements over this result have been obtained since the original work, all of them either limit the generality of the input or assume some form of resource augmentation (e.g., larger clusters). Moreover, the algorithm of Avin et al. achieves the best known competitive ratio even if randomization is allowed. In this paper, we present the first randomized online algorithm that breaks this natural quadratic barrier and achieves a competitive ratio of Õ(n^{23/12}) without resource augmentation and for an arbitrary sequence of requests.
Cite as

Marcin Bienkowski and Stefan Schmid. A Subquadratic Bound for Online Bisection. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 14:1-14:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bienkowski_et_al:LIPIcs.STACS.2024.14,
  author =	{Bienkowski, Marcin and Schmid, Stefan},
  title =	{{A Subquadratic Bound for Online Bisection}},
  booktitle =	{41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)},
  pages =	{14:1--14:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-311-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{289},
  editor =	{Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2024.14},
  URN =		{urn:nbn:de:0030-drops-197247},
  doi =		{10.4230/LIPIcs.STACS.2024.14},
  annote =	{Keywords: Bisection, Graph Partitioning, online balanced Repartitioning, online Algorithms, competitive Analysis}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2023.114
Nominal Topology for Data Languages

Authors: Fabian Birkmann, Stefan Milius, and Henning Urbat

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
We propose a novel topological perspective on data languages recognizable by orbit-finite nominal monoids. For this purpose, we introduce pro-orbit-finite nominal topological spaces. Assuming globally bounded support sizes, they coincide with nominal Stone spaces and are shown to be dually equivalent to a subcategory of nominal boolean algebras. Recognizable data languages are characterized as topologically clopen sets of pro-orbit-finite words. In addition, we explore the expressive power of pro-orbit-finite equations by establishing a nominal version of Reiterman’s pseudovariety theorem.
Cite as

Fabian Birkmann, Stefan Milius, and Henning Urbat. Nominal Topology for Data Languages. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 114:1-114:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{birkmann_et_al:LIPIcs.ICALP.2023.114,
  author =	{Birkmann, Fabian and Milius, Stefan and Urbat, Henning},
  title =	{{Nominal Topology for Data Languages}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{114:1--114:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.114},
  URN =		{urn:nbn:de:0030-drops-181662},
  doi =		{10.4230/LIPIcs.ICALP.2023.114},
  annote =	{Keywords: Nominal sets, Stone duality, Profinite space, Data languages}
}
Document
DOI: 10.4230/DagRep.12.10.143
Developmental Machine Learning: From Human Learning to Machines and Back (Dagstuhl Seminar 22422)

Authors: James M. Rehg, Pierre-Yves Oudeyer, Linda B. Smith, Sho Tsuji, Stefan Stojanov, and Ngoc Anh Thai

Published in: Dagstuhl Reports, Volume 12, Issue 10 (2023)

Abstract
This interdisciplinary seminar brought together 18 academic and industry computer science researchers in artificial intelligence, computer vision and machine learning with 19 researchers from developmental psychology, neuroscience and linguistics. The objective was to catalyze connections between these communities, through discussions on both how the use of developmental insights can spur advances in machine learning, and how computational models and data-driven learning can lead to novel tools and insights for studying child development. The seminar consisted of tutorials, working groups, and a series of talks and discussion sessions. The main outcomes of this seminar were 1) The founding of DevelopmentalAI (http://www.developmentalai.com), an online research community to serve as a venue for communication and collaboration between develpomental and machine learning researchers, as well as a place collect and organize relevant research papers and talks; 2) Working group outputs - summaries of in-depth discussions on research questions at the intersection of developmental and machine learning, including the role of information bottlenecks and multimodality, as well as proposals for novel developmentally motivated benchmarks.
Cite as

James M. Rehg, Pierre-Yves Oudeyer, Linda B. Smith, Sho Tsuji, Stefan Stojanov, and Ngoc Anh Thai. Developmental Machine Learning: From Human Learning to Machines and Back (Dagstuhl Seminar 22422). In Dagstuhl Reports, Volume 12, Issue 10, pp. 143-165, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{rehg_et_al:DagRep.12.10.143,
  author =	{Rehg, James M. and Oudeyer, Pierre-Yves and Smith, Linda B. and Tsuji, Sho and Stojanov, Stefan and Thai, Ngoc Anh},
  title =	{{Developmental Machine Learning: From Human Learning to Machines and Back (Dagstuhl Seminar 22422)}},
  pages =	{143--165},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2023},
  volume =	{12},
  number =	{10},
  editor =	{Rehg, James M. and Oudeyer, Pierre-Yves and Smith, Linda B. and Tsuji, Sho and Stojanov, Stefan and Thai, Ngoc Anh},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.12.10.143},
  URN =		{urn:nbn:de:0030-drops-178247},
  doi =		{10.4230/DagRep.12.10.143},
  annote =	{Keywords: developmental psychology, human learning, machine learning, computer vision, language learning}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.10
Efficiently Testable Circuits

Authors: Mirza Ahad Baig, Suvradip Chakraborty, Stefan Dziembowski, Małgorzata Gałązka, Tomasz Lizurej, and Krzysztof Pietrzak

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

Abstract
In this work, we put forward the notion of "efficiently testable circuits" and provide circuit compilers that transform any circuit into an efficiently testable one. Informally, a circuit is testable if one can detect tampering with the circuit by evaluating it on a small number of inputs from some test set. Our technical contribution is a compiler that transforms any circuit C into a testable circuit (Ĉ,𝕋̂) for which we can detect arbitrary tampering with all wires in Ĉ. The notion of a testable circuit is weaker or incomparable to existing notions of tamper-resilience, which aim to detect or even correct for errors introduced by tampering during every query, but our new notion is interesting in several settings, and we achieve security against much more general tampering classes - like tampering with all wires - with very modest overhead. Concretely, starting from a circuit C of size n and depth d, for any L (think of L as a small constant, say L = 4), we get a testable (Ĉ,𝕋̂) where Ĉ is of size ≈ 12n and depth d+log(n)+L⋅ n^{1/L}. The test set 𝕋̂ is of size 4⋅ 2^L. The number of extra input and output wires (i.e., pins) we need to add for the testing is 3+L and 2^L, respectively.
Cite as

Mirza Ahad Baig, Suvradip Chakraborty, Stefan Dziembowski, Małgorzata Gałązka, Tomasz Lizurej, and Krzysztof Pietrzak. Efficiently Testable Circuits. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 10:1-10:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{baig_et_al:LIPIcs.ITCS.2023.10,
  author =	{Baig, Mirza Ahad and Chakraborty, Suvradip and Dziembowski, Stefan and Ga{\l}\k{a}zka, Ma{\l}gorzata and Lizurej, Tomasz and Pietrzak, Krzysztof},
  title =	{{Efficiently Testable Circuits}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{10:1--10:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.10},
  URN =		{urn:nbn:de:0030-drops-175130},
  doi =		{10.4230/LIPIcs.ITCS.2023.10},
  annote =	{Keywords: circuit compilers, circuit integrity, circuit testing}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2022.28
A Sublinear Local Access Implementation for the Chinese Restaurant Process

Authors: Peter Mörters, Christian Sohler, and Stefan Walzer

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)

Abstract
The Chinese restaurant process is a stochastic process closely related to the Dirichlet process that groups sequentially arriving objects into a variable number of classes, such that within each class objects are cyclically ordered. A popular description involves a restaurant, where customers arrive one by one and either sit down next to a randomly chosen customer at one of the existing tables or open a new table. The full state of the process after n steps is given by a permutation of the n objects and cannot be represented in sublinear space. In particular, if we only need specific information about a few objects or classes it would be preferable to obtain the answers without simulating the process completely. A recent line of research [Oded Goldreich et al., 2010; Moni Naor and Asaf Nussboim, 2007; Amartya Shankha Biswas et al., 2020; Guy Even et al., 2021] attempts to provide access to huge random objects without fully instantiating them. Such local access implementations provide answers to a sequence of queries about the random object, following the same distribution as if the object was fully generated. In this paper, we provide a local access implementation for a generalization of the Chinese restaurant process described above. Our implementation can be used to answer any sequence of adaptive queries about class affiliation of objects, number and sizes of classes at any time, position of elements within a class, or founding time of a class. The running time per query is polylogarithmic in the total size of the object, with high probability. Our approach relies on some ideas from the recent local access implementation for preferential attachment trees by Even et al. [Guy Even et al., 2021]. Such trees are related to the Chinese restaurant process in the sense that both involve a "rich-get-richer" phenomenon. A novel ingredient in our implementation is to embed the process in continuous time, in which the evolution of the different classes becomes stochastically independent [Joyce and Tavaré, 1987]. This independence is used to keep the probabilistic structure manageable even if many queries have already been answered. As similar embeddings are available for a wide range of urn processes [Krishna B. Athreya and Samuel Karlin, 1968], we believe that our approach may be applicable more generally. Moreover, local access implementations for birth and death processes that we encounter along the way may be of independent interest.
Cite as

Peter Mörters, Christian Sohler, and Stefan Walzer. A Sublinear Local Access Implementation for the Chinese Restaurant Process. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 28:1-28:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{morters_et_al:LIPIcs.APPROX/RANDOM.2022.28,
  author =	{M\"{o}rters, Peter and Sohler, Christian and Walzer, Stefan},
  title =	{{A Sublinear Local Access Implementation for the Chinese Restaurant Process}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{28:1--28:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.28},
  URN =		{urn:nbn:de:0030-drops-171500},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.28},
  annote =	{Keywords: Chinese restaurant process, Dirichlet process, sublinear time algorithm, random recursive tree, random permutation, random partition, Ewens distribution, simulation, local access implementation, continuous time embedding}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.80
The Pareto Cover Problem

Authors: Bento Natura, Meike Neuwohner, and Stefan Weltge

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

Abstract
We introduce the problem of finding a set B of k points in [0,1]ⁿ such that the expected cost of the cheapest point in B that dominates a random point from [0,1]ⁿ is minimized. We study the case where the coordinates of the random points are independently distributed and the cost function is linear. This problem arises naturally in various application areas where customers' requests are satisfied based on predefined products, each corresponding to a subset of features. We show that the problem is NP-hard already for k = 2 when each coordinate is drawn from {0,1}, and obtain an FPTAS for general fixed k under mild assumptions on the distributions.
Cite as

Bento Natura, Meike Neuwohner, and Stefan Weltge. The Pareto Cover Problem. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 80:1-80:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{natura_et_al:LIPIcs.ESA.2022.80,
  author =	{Natura, Bento and Neuwohner, Meike and Weltge, Stefan},
  title =	{{The Pareto Cover Problem}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{80:1--80:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.80},
  URN =		{urn:nbn:de:0030-drops-170186},
  doi =		{10.4230/LIPIcs.ESA.2022.80},
  annote =	{Keywords: Pareto, Covering, Optimization, Approximation Algorithm}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2022.14
On the Role of the High-Low Partition in Realizing a Degree Sequence by a Bipartite Graph

Authors: Amotz Bar-Noy, Toni Böhnlein, David Peleg, and Dror Rawitz

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

Abstract
We consider the problem of characterizing degree sequences that can be realized by a bipartite graph. If a partition of the sequence into the two sides of the bipartite graph is given as part of the input, then a complete characterization has been established over 60 years ago. However, the general question, in which a partition and a realizing graph need to be determined, is still open. We investigate the role of an important class of special partitions, called High-Low partitions, which separate the degrees of a sequence into two groups, the high degrees and the low degrees. We show that when the High-Low partition exists and satisfies some natural properties, analysing the High-Low partition resolves the bigraphic realization problem. For sequences that are known to be not realizable by a bipartite graph or that are undecided, we provide approximate realizations based on the High-Low partition.
Cite as

Amotz Bar-Noy, Toni Böhnlein, David Peleg, and Dror Rawitz. On the Role of the High-Low Partition in Realizing a Degree Sequence by a Bipartite Graph. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 14:1-14:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{barnoy_et_al:LIPIcs.MFCS.2022.14,
  author =	{Bar-Noy, Amotz and B\"{o}hnlein, Toni and Peleg, David and Rawitz, Dror},
  title =	{{On the Role of the High-Low Partition in Realizing a Degree Sequence by a Bipartite Graph}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{14:1--14:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.14},
  URN =		{urn:nbn:de:0030-drops-168121},
  doi =		{10.4230/LIPIcs.MFCS.2022.14},
  annote =	{Keywords: Graph Realization, Bipartite Graphs, Degree Sequences, Graphic Sequences, Bigraphic Sequences, Approximate Realization, Multigraph Realization}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2022.22
Tree Exploration in Dual-Memory Model

Authors: Dominik Bojko, Karol Gotfryd, Dariusz R. Kowalski, and Dominik Pająk

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

Abstract
We study the problem of online tree exploration by a deterministic mobile agent. Our main objective is to establish what features of the model of the mobile agent and the environment allow linear exploration time. We study agents that, upon entering a node, do not receive as input the edge via which they entered. In such model, deterministic memoryless exploration is infeasible, hence the agent needs to be allowed to use some memory. The memory can be located at the agent or at each node. The existing lower bounds show that if the memory is either only at the agent or only at the nodes, then the exploration needs superlinear time. We show that tree exploration in dual-memory model, with constant memory at the agent and logarithmic in the degree at each node is possible in linear time when one of the two additional features is present: fixed initial state of the memory at each node (so called clean memory) or a single movable token. We present two algorithms working in linear time for arbitrary trees in these two models. On the other hand, in our lower bound we show that if the agent has a single bit of memory and one bit is present at each node, then the exploration may require quadratic time even on paths, if the initial memory at nodes could be set arbitrarily (so called dirty memory). This shows that having clean node memory or a token allows linear time exploration of trees in the dual-memory model, but having neither of those features may lead to quadratic exploration time even on a simple path.
Cite as

Dominik Bojko, Karol Gotfryd, Dariusz R. Kowalski, and Dominik Pająk. Tree Exploration in Dual-Memory Model. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 22:1-22:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bojko_et_al:LIPIcs.MFCS.2022.22,
  author =	{Bojko, Dominik and Gotfryd, Karol and Kowalski, Dariusz R. and Paj\k{a}k, Dominik},
  title =	{{Tree Exploration in Dual-Memory Model}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{22:1--22:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.22},
  URN =		{urn:nbn:de:0030-drops-168207},
  doi =		{10.4230/LIPIcs.MFCS.2022.22},
  annote =	{Keywords: Graph exploration, agent, memory, tree, deterministic algorithms, lower bound}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2022.34
On Dynamic α + 1 Arboricity Decomposition and Out-Orientation

Authors: Aleksander B. G. Christiansen, Jacob Holm, Eva Rotenberg, and Carsten Thomassen

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

Abstract
A graph has arboricity α if its edges can be partitioned into α forests. The dynamic arboricity decomposition problem is to update a partitioning of the graph’s edges into forests, as a graph undergoes insertions and deletions of edges. We present an algorithm for maintaining partitioning into α+1 forests, provided the arboricity of the dynamic graph never exceeds α. Our algorithm has an update time of Õ(n^{3/4}) when α is at most polylogarithmic in n. Similarly, the dynamic bounded out-orientation problem is to orient the edges of the graph such that the out-degree of each vertex is at all times bounded. For this problem, we give an algorithm that orients the edges such that the out-degree is at all times bounded by α+1, with an update time of Õ(n^{5/7}), when α is at most polylogarithmic in n. Here, the choice of α+1 should be viewed in the light of the well-known lower bound by Brodal and Fagerberg which establishes that, for general graphs, maintaining only α out-edges would require linear update time. However, the lower bound by Brodal and Fagerberg is non-planar. In this paper, we give a lower bound showing that even for planar graphs, linear update time is needed in order to maintain an explicit three-out-orientation. For planar graphs, we show that the dynamic four forest decomposition and four-out-orientations, can be updated in Õ(n^{1/2}) time.
Cite as

Aleksander B. G. Christiansen, Jacob Holm, Eva Rotenberg, and Carsten Thomassen. On Dynamic α + 1 Arboricity Decomposition and Out-Orientation. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 34:1-34:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{christiansen_et_al:LIPIcs.MFCS.2022.34,
  author =	{Christiansen, Aleksander B. G. and Holm, Jacob and Rotenberg, Eva and Thomassen, Carsten},
  title =	{{On Dynamic \alpha + 1 Arboricity Decomposition and Out-Orientation}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{34:1--34:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.34},
  URN =		{urn:nbn:de:0030-drops-168320},
  doi =		{10.4230/LIPIcs.MFCS.2022.34},
  annote =	{Keywords: Dynamic graphs, bounded arboricity, data structures}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2022.42
Constant-Factor Approximation Algorithm for Binary Search in Trees with Monotonic Query Times

Authors: Dariusz Dereniowski and Izajasz Wrosz

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

Abstract
We consider a generalization of binary search in linear orders to the domain of weighted trees. The goal is to design an adaptive search strategy whose aim is to locate an unknown target vertex of a given tree. Each query to a vertex v incurs a non-negative cost ω(v) (that can be interpreted as the duration of the query) and returns a feedback that either v is the target or the edge incident to v is given that is on the path towards the target. The goal of the algorithm is to find a strategy that minimizes the worst-case total cost. We propose a constant-factor approximation algorithm for trees with a monotonic cost function. Such function is defined as follows: there exists a vertex r such that for any two vertices u,v on any path connecting r with a leaf it holds that if u is closer to r than v, then ω(u) ≥ ω(v). The best known approximation algorithm for general weight functions has the ratio of O{√{log n}} [Dereniowski et al. ICALP 2017] and it remains as a challenging open question whether constant-factor approximation is achievable in such case. This gives our first motivation towards considering monotonic cost functions and the second one lies in the potential applications.
Cite as

Dariusz Dereniowski and Izajasz Wrosz. Constant-Factor Approximation Algorithm for Binary Search in Trees with Monotonic Query Times. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 42:1-42:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{dereniowski_et_al:LIPIcs.MFCS.2022.42,
  author =	{Dereniowski, Dariusz and Wrosz, Izajasz},
  title =	{{Constant-Factor Approximation Algorithm for Binary Search in Trees with Monotonic Query Times}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{42:1--42:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.42},
  URN =		{urn:nbn:de:0030-drops-168405},
  doi =		{10.4230/LIPIcs.MFCS.2022.42},
  annote =	{Keywords: binary search, graph search, approximation algorithm, query complexity}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2022.55
Dispersing Obnoxious Facilities on Graphs by Rounding Distances

Authors: Tim A. Hartmann and Stefan Lendl

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

Abstract
We continue the study of δ-dispersion, a continuous facility location problem on a graph where all edges have unit length and where the facilities may also be positioned in the interior of the edges. The goal is to position as many facilities as possible subject to the condition that every two facilities have distance at least δ from each other. Our main technical contribution is an efficient procedure to "round-up" distance δ. It transforms a δ-dispersed set S into a δ^⋆-dispersed set S^⋆ of same size where distance δ^⋆ is a potentially slightly larger rational a/b with a numerator a upper bounded by the longest (not-induced) path in the input graph. Based on this rounding procedure and connections to the distance-d independent set problem we derive a number of algorithmic results. When parameterized by treewidth, the problem is in XP. When parameterized by treedepth the problem is FPT and has a matching lower bound on its time complexity under ETH. Moreover, we can also settle the parameterized complexity with the solution size as parameter using our rounding technique: δ-Dispersion is FPT for every δ ≤ 2 and W[1]-hard for every δ > 2. Further, we show that δ-dispersion is NP-complete for every fixed irrational distance δ, which was left open in a previous work.
Cite as

Tim A. Hartmann and Stefan Lendl. Dispersing Obnoxious Facilities on Graphs by Rounding Distances. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 55:1-55:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{hartmann_et_al:LIPIcs.MFCS.2022.55,
  author =	{Hartmann, Tim A. and Lendl, Stefan},
  title =	{{Dispersing Obnoxious Facilities on Graphs by Rounding Distances}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{55:1--55:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.55},
  URN =		{urn:nbn:de:0030-drops-168536},
  doi =		{10.4230/LIPIcs.MFCS.2022.55},
  annote =	{Keywords: facility location, parameterized complexity, packing}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2022.57
Gaps, Ambiguity, and Establishing Complexity-Class Containments via Iterative Constant-Setting

Authors: Lane A. Hemaspaandra, Mandar Juvekar, Arian Nadjimzadah, and Patrick A. Phillips

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

Abstract
Cai and Hemachandra used iterative constant-setting to prove that Few ⊆ ⊕ P (and thus that FewP ⊆ ⊕ P). In this paper, we note that there is a tension between the nondeterministic ambiguity of the class one is seeking to capture, and the density (or, to be more precise, the needed "nongappy"-ness) of the easy-to-find "targets" used in iterative constant-setting. In particular, we show that even less restrictive gap-size upper bounds regarding the targets allow one to capture ambiguity-limited classes. Through a flexible, metatheorem-based approach, we do so for a wide range of classes including the logarithmic-ambiguity version of Valiant’s unambiguous nondeterminism class UP. Our work lowers the bar for what advances regarding the existence of infinite, P-printable sets of primes would suffice to show that restricted counting classes based on the primes have the power to accept superconstant-ambiguity analogues of UP. As an application of our work, we prove that the Lenstra-Pomerance-Wagstaff Conjecture implies that all O(log log n)-ambiguity NP sets are in the restricted counting class RC_PRIMES.
Cite as

Lane A. Hemaspaandra, Mandar Juvekar, Arian Nadjimzadah, and Patrick A. Phillips. Gaps, Ambiguity, and Establishing Complexity-Class Containments via Iterative Constant-Setting. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 57:1-57:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{hemaspaandra_et_al:LIPIcs.MFCS.2022.57,
  author =	{Hemaspaandra, Lane A. and Juvekar, Mandar and Nadjimzadah, Arian and Phillips, Patrick A.},
  title =	{{Gaps, Ambiguity, and Establishing Complexity-Class Containments via Iterative Constant-Setting}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{57:1--57:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.57},
  URN =		{urn:nbn:de:0030-drops-168552},
  doi =		{10.4230/LIPIcs.MFCS.2022.57},
  annote =	{Keywords: structural complexity theory, computational complexity theory, ambiguity-limited NP, counting classes, P-printable sets}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2022.62
The Complexity of Computing Optimum Labelings for Temporal Connectivity

Authors: Nina Klobas, George B. Mertzios, Hendrik Molter, and Paul G. Spirakis

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

Abstract
A graph is temporally connected if there exists a strict temporal path, i.e., a path whose edges have strictly increasing labels, from every vertex u to every other vertex v. In this paper we study temporal design problems for undirected temporally connected graphs. The basic setting of these optimization problems is as follows: given a connected undirected graph G, what is the smallest number |λ| of time-labels that we need to add to the edges of G such that the resulting temporal graph (G,λ) is temporally connected? As it turns out, this basic problem, called Minimum Labeling (ML), can be optimally solved in polynomial time. However, exploiting the temporal dimension, the problem becomes more interesting and meaningful in its following variations, which we investigate in this paper. First we consider the problem Min. Aged Labeling (MAL) of temporally connecting the graph when we are given an upper-bound on the allowed age (i.e., maximum label) of the obtained temporal graph (G,λ). Second we consider the problem Min. Steiner Labeling (MSL), where the aim is now to have a temporal path between any pair of "important" vertices which lie in a subset R ⊆ V, which we call the terminals. This relaxed problem resembles the problem Steiner Tree in static (i.e., non-temporal) graphs. However, due to the requirement of strictly increasing labels in a temporal path, Steiner Tree is not a special case of MSL. Finally we consider the age-restricted version of MSL, namely Min. Aged Steiner Labeling (MASL). Our main results are threefold: we prove that (i) MAL becomes NP-complete on undirected graphs, while (ii) MASL becomes W[1]-hard with respect to the number |R| of terminals. On the other hand we prove that (iii) although the age-unrestricted problem MSL remains NP-hard, it is in FPT with respect to the number |R| of terminals. That is, adding the age restriction, makes the above problems strictly harder (unless P=NP or W[1]=FPT).
Cite as

Nina Klobas, George B. Mertzios, Hendrik Molter, and Paul G. Spirakis. The Complexity of Computing Optimum Labelings for Temporal Connectivity. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 62:1-62:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{klobas_et_al:LIPIcs.MFCS.2022.62,
  author =	{Klobas, Nina and Mertzios, George B. and Molter, Hendrik and Spirakis, Paul G.},
  title =	{{The Complexity of Computing Optimum Labelings for Temporal Connectivity}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{62:1--62:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.62},
  URN =		{urn:nbn:de:0030-drops-168603},
  doi =		{10.4230/LIPIcs.MFCS.2022.62},
  annote =	{Keywords: Temporal graph, graph labeling, foremost temporal path, temporal connectivity, Steiner Tree}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2022.64
Countdown μ-Calculus

Authors: Jędrzej Kołodziejski and Bartek Klin

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

Abstract
We introduce the countdown μ-calculus, an extension of the modal μ-calculus with ordinal approximations of fixpoint operators. In addition to properties definable in the classical calculus, it can express (un)boundedness properties such as the existence of arbitrarily long sequences of specific actions. The standard correspondence with parity games and automata extends to suitably defined countdown games and automata. However, unlike in the classical setting, the scalar fragment is provably weaker than the full vectorial calculus and corresponds to automata satisfying a simple syntactic condition. We establish some facts, in particular decidability of the model checking problem and strictness of the hierarchy induced by the maximal allowed nesting of our new operators.
Cite as

Jędrzej Kołodziejski and Bartek Klin. Countdown μ-Calculus. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 64:1-64:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{kolodziejski_et_al:LIPIcs.MFCS.2022.64,
  author =	{Ko{\l}odziejski, J\k{e}drzej and Klin, Bartek},
  title =	{{Countdown \mu-Calculus}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{64:1--64:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.64},
  URN =		{urn:nbn:de:0030-drops-168624},
  doi =		{10.4230/LIPIcs.MFCS.2022.64},
  annote =	{Keywords: countdown \mu-calculus, games, automata}
}
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