39 Search Results for "Datta, Samir"

Document
DOI: 10.4230/LIPIcs.LICS.2026.36
Dynamic Planar Graph Isomorphism Is in DynFO

Authors: Samir Datta, Asif Khan, Felix Tschirbs, Nils Vortmeier, and Thomas Zeume

Published in: LIPIcs, Volume 380, 41st Annual Symposium on Logic in Computer Science (LICS 2026)

Abstract
Consider two planar graphs which are subject to edge insertions and deletions. We show that whether the two graphs are isomorphic can be maintained with first-order logic formulas and auxiliary data of polynomial size. This places the dynamic planar graph isomorphism problem into the dynamic descriptive complexity class DynFO. As a consequence, there is a dynamic constant-time parallel algorithm with polynomial-size auxiliary data which maintains whether two dynamic planar graphs are isomorphic.
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Samir Datta, Asif Khan, Felix Tschirbs, Nils Vortmeier, and Thomas Zeume. Dynamic Planar Graph Isomorphism Is in DynFO. In 41st Annual Symposium on Logic in Computer Science (LICS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 380, pp. 36:1-36:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{datta_et_al:LIPIcs.LICS.2026.36,
  author =	{Datta, Samir and Khan, Asif and Tschirbs, Felix and Vortmeier, Nils and Zeume, Thomas},
  title =	{{Dynamic Planar Graph Isomorphism Is in DynFO}},
  booktitle =	{41st Annual Symposium on Logic in Computer Science (LICS 2026)},
  pages =	{36:1--36:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-434-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{380},
  editor =	{Faggian, Claudia and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.LICS.2026.36},
  URN =		{urn:nbn:de:0030-drops-268233},
  doi =		{10.4230/LIPIcs.LICS.2026.36},
  annote =	{Keywords: Dynamic complexity theory, parallel computation, dynamic algorithms}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.20
Longest Common Extension of a Dynamic String in Parallel Constant Time

Authors: Daniel Alexander Albert

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

Abstract
A longest common extension (LCE) query on a string computes the length of the longest common suffix or prefix at two given positions. A dynamic LCE algorithm maintains a data structure that allows efficient LCE queries on a string that can change via character insertions and deletions. A dynamic parallel constant-time algorithm is presented that can maintain LCE queries on a common CRCW PRAM with 𝒪(n^ε) work, for any ε > 0. The algorithm maintains a string synchronizing sets hierarchy, which it uses to answer substring equality queries, which it in turn uses to answer LCE queries. To achieve constant runtime, the algorithm allows parts of its information to become outdated by up to log n log^* n updates. It answers queries by combining this slightly outdated information with a list of the recent changes. Two applications of this dynamic LCE algorithm are shown. Firstly, a dynamic parallel constant-time algorithm can maintain membership in a Dyck language D_k, k > 0 with 𝒪(n^ε) work for any ε > 0. Secondly, a dynamic parallel constant-time algorithm can maintain squares with 𝒪(n^ε) work for any ε > 0.
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Daniel Alexander Albert. Longest Common Extension of a Dynamic String in Parallel Constant Time. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 20:1-20:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{albert:LIPIcs.CPM.2026.20,
  author =	{Albert, Daniel Alexander},
  title =	{{Longest Common Extension of a Dynamic String in Parallel Constant Time}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{20:1--20:21},
  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.2026.20},
  URN =		{urn:nbn:de:0030-drops-259467},
  doi =		{10.4230/LIPIcs.CPM.2026.20},
  annote =	{Keywords: Dynamic Strings, Work, Parallel Constant Time, Longest Common Extension, Longest Common Prefix}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.49
2D Minimal Graph Rigidity is in NC for One-Crossing-Minor-Free Graphs

Authors: Rohit Gurjar, Kilian Rothmund, and Thomas Thierauf

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

Abstract
Minimally rigid graphs can be decided and embedded in the plane efficiently, i.e. in polynomial time. There is also an efficient randomized parallel algorithm, i.e. in RNC. We present an NC-algorithm to decide whether one-crossing-minor-free graphs are minimally rigid. In the special case of K_{3,3}-free graphs, we also compute an infinitesimally rigid embedding in NC.
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Rohit Gurjar, Kilian Rothmund, and Thomas Thierauf. 2D Minimal Graph Rigidity is in NC for One-Crossing-Minor-Free Graphs. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 49:1-49:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{gurjar_et_al:LIPIcs.STACS.2026.49,
  author =	{Gurjar, Rohit and Rothmund, Kilian and Thierauf, Thomas},
  title =	{{2D Minimal Graph Rigidity is in NC for One-Crossing-Minor-Free Graphs}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{49:1--49:22},
  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.2026.49},
  URN =		{urn:nbn:de:0030-drops-255385},
  doi =		{10.4230/LIPIcs.STACS.2026.49},
  annote =	{Keywords: Graph Rigidity, Parallel Algorithms, Polynomial Identity Testing, Derandomization}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.4
Pseudodeterministic Algorithms for Minimum Cut Problems

Authors: Aryan Agarwala and Nithin Varma

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

Abstract
In this paper we present efficient pseudodeterministic algorithms for both the global minimum cut and minimum s-t cut problems. The running time of our algorithm for the global minimum cut problem is asymptotically better than the fastest sequential deterministic global minimum cut algorithm (Henzinger, Li, Rao, Wang; SODA 2024). Furthermore, we implement our algorithm in streaming, PRAM, and cut-query models, where no efficient deterministic global minimum cut algorithms are known.
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Aryan Agarwala and Nithin Varma. Pseudodeterministic Algorithms for Minimum Cut Problems. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 4:1-4:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{agarwala_et_al:LIPIcs.ITCS.2026.4,
  author =	{Agarwala, Aryan and Varma, Nithin},
  title =	{{Pseudodeterministic Algorithms for Minimum Cut Problems}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{4:1--4:15},
  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.2026.4},
  URN =		{urn:nbn:de:0030-drops-252917},
  doi =		{10.4230/LIPIcs.ITCS.2026.4},
  annote =	{Keywords: Minimum Cut, Pseudodeterministic Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.3
Linear Matroid Intersection Is in Catalytic Logspace

Authors: Aryan Agarwala, Yaroslav Alekseev, and Antoine Vinciguerra

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

Abstract
Linear matroid intersection is an important problem in combinatorial optimization. Given two linear matroids over the same ground set, the linear matroid intersection problem asks you to find a common independent set of maximum size. The deep interest in linear matroid intersection is due to the fact that it generalises many classical problems in theoretical computer science, such as bipartite matching, edge disjoint spanning trees, rainbow spanning tree, and many more. We study this problem in the model of catalytic computation: space-bounded machines are granted access to catalytic space, which is additional working memory that is full with arbitrary data that must be preserved at the end of its computation. Although linear matroid intersection has had a polynomial time algorithm for over 50 years, it remains an important open problem to show that linear matroid intersection belongs to any well studied subclass of {P}. We address this problem for the class catalytic logspace (CL) with a polynomial time bound (CLP). Recently, Agarwala and Mertz (2025) showed that bipartite maximum matching can be computed in the class CLP ⊆ {P}. This was the first subclass of {P} shown to contain bipartite matching, and additionally the first problem outside TC¹ shown to be contained in CL. We significantly improve the result of Agarwala and Mertz by showing that linear matroid intersection can be computed in CLP.
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Aryan Agarwala, Yaroslav Alekseev, and Antoine Vinciguerra. Linear Matroid Intersection Is in Catalytic Logspace. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 3:1-3:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{agarwala_et_al:LIPIcs.ITCS.2026.3,
  author =	{Agarwala, Aryan and Alekseev, Yaroslav and Vinciguerra, Antoine},
  title =	{{Linear Matroid Intersection Is in Catalytic Logspace}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{3:1--3:23},
  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.2026.3},
  URN =		{urn:nbn:de:0030-drops-252908},
  doi =		{10.4230/LIPIcs.ITCS.2026.3},
  annote =	{Keywords: Catalytic Computing, Computational Complexity, Matroid Theory, Algorithms}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.23
Parallel Complexity of Depth-First-Search and Maximal Path in Restricted Graph Classes

Authors: Archit Chauhan, Samir Datta, and M. Praveen

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

Abstract
Constructing a Depth First Search (DFS) tree is a fundamental graph problem, whose parallel complexity is still not settled. Reif showed parallel intractability of lex-first DFS. In contrast, randomized parallel algorithms (and more recently, deterministic quasipolynomial parallel algorithms) are known for constructing a DFS tree in general (di)graphs. However a deterministic parallel algorithm for DFS in general graphs remains an elusive goal. Working towards this, a series of works gave deterministic NC algorithms for DFS in planar graphs and digraphs. We further extend these results to more general graph classes, by providing NC algorithms for (di)graphs of bounded genus, and for undirected H-minor-free graphs where H is a fixed graph with at most one crossing. For the case of (di)graphs of bounded treewidth, we further improve the complexity to a Logspace bound. Constructing a maximal path is a simpler problem (that reduces to DFS) for which no deterministic parallel bounds are known for general graphs. For planar graphs a bound of O(log n) parallel time on a CRCW PRAM (thus in NC²) is known. We improve this bound to Logspace.
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Archit Chauhan, Samir Datta, and M. Praveen. Parallel Complexity of Depth-First-Search and Maximal Path in Restricted Graph Classes. 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. 23:1-23:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chauhan_et_al:LIPIcs.FSTTCS.2025.23,
  author =	{Chauhan, Archit and Datta, Samir and Praveen, M.},
  title =	{{Parallel Complexity of Depth-First-Search and Maximal Path in Restricted Graph Classes}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{23:1--23:21},
  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.2025.23},
  URN =		{urn:nbn:de:0030-drops-251041},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.23},
  annote =	{Keywords: Parallel Complexity, Graph Algorithms, Depth First Search, Maximal Path, Planar Graphs, Minor-Free, Treewidth, Logspace}
}
Document
DOI: 10.4230/LIPIcs.TQC.2025.11
Quantum Catalytic Space

Authors: Harry Buhrman, Marten Folkertsma, Ian Mertz, Florian Speelman, Sergii Strelchuk, Sathyawageeswar Subramanian, and Quinten Tupker

Published in: LIPIcs, Volume 350, 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)

Abstract
Space complexity is a key field of study in theoretical computer science. In the quantum setting there are clear motivations to understand the power of space-restricted computation, as qubits are an especially precious and limited resource. Recently, a new branch of space-bounded complexity called catalytic computing has shown that reusing space is a very powerful computational resource, especially for subroutines that incur little to no space overhead. While quantum catalysis in an information theoretic context, and the power of "dirty" qubits for quantum computation, has been studied over the years, these models are generally not suitable for use in quantum space-bounded algorithms, as they either rely on specific catalytic states or destroy the memory being borrowed. We define the notion of catalytic computing in the quantum setting and show a number of initial results about the model. First, we show that quantum catalytic logspace can always be computed quantumly in polynomial time; the classical analogue of this is the largest open question in catalytic computing. This also allows quantum catalytic space to be defined in an equivalent way with respect to circuits instead of Turing machines. We also prove that quantum catalytic logspace can simulate log-depth threshold circuits, a class which is known to contain (and believed to strictly contain) quantum logspace, thus showcasing the power of quantum catalytic space. Finally we show that both unitary quantum catalytic logspace and classical catalytic logspace can be simulated in the one-clean qubit model.
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Harry Buhrman, Marten Folkertsma, Ian Mertz, Florian Speelman, Sergii Strelchuk, Sathyawageeswar Subramanian, and Quinten Tupker. Quantum Catalytic Space. In 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 350, pp. 11:1-11:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{buhrman_et_al:LIPIcs.TQC.2025.11,
  author =	{Buhrman, Harry and Folkertsma, Marten and Mertz, Ian and Speelman, Florian and Strelchuk, Sergii and Subramanian, Sathyawageeswar and Tupker, Quinten},
  title =	{{Quantum Catalytic Space}},
  booktitle =	{20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)},
  pages =	{11:1--11:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-392-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{350},
  editor =	{Fefferman, Bill},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2025.11},
  URN =		{urn:nbn:de:0030-drops-240606},
  doi =		{10.4230/LIPIcs.TQC.2025.11},
  annote =	{Keywords: quantum computing, quantum complexity, space-bounded algorithms, catalytic computation, one clean qubit}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.6
Catalytic Computing and Register Programs Beyond Log-Depth

Authors: Yaroslav Alekseev, Yuval Filmus, Ian Mertz, Alexander Smal, and Antoine Vinciguerra

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

Abstract
In a seminal work, Buhrman et al. (STOC 2014) defined the class CSPACE(s,c) of problems solvable in space s with an additional catalytic tape of size c, which is a tape whose initial content must be restored at the end of the computation. They showed that uniform TC¹ circuits are computable in catalytic logspace, i.e., CL = CSPACE(O(log{n}), 2^{O(log{n})}), thus giving strong evidence that catalytic space gives L strict additional power. Their study focuses on an arithmetic model called register programs, which has been a focal point in development since then. Understanding CL remains a major open problem, as TC¹ remains the most powerful containment to date. In this work, we study the power of catalytic space and register programs to compute circuits of larger depth. Using register programs, we show that for every ε > 0, SAC² ⊆ CSPACE (O((log²n)/(log log n)), 2^{O(log^{1+ε} n)}) . On the other hand, we know that SAC² ⊆ TC² ⊆ CSPACE(O(log²{n}) , 2^{O(log{n})}). Our result thus shows an O(log log n) factor improvement on the free space needed to compute SAC², at the expense of a nearly-polynomial-sized catalytic tape. We also exhibit non-trivial register programs for matrix powering, which is a further step towards showing NC² ⊆ CL.
Cite as

Yaroslav Alekseev, Yuval Filmus, Ian Mertz, Alexander Smal, and Antoine Vinciguerra. Catalytic Computing and Register Programs Beyond Log-Depth. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 6:1-6:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{alekseev_et_al:LIPIcs.MFCS.2025.6,
  author =	{Alekseev, Yaroslav and Filmus, Yuval and Mertz, Ian and Smal, Alexander and Vinciguerra, Antoine},
  title =	{{Catalytic Computing and Register Programs Beyond Log-Depth}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{6:1--6:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.6},
  URN =		{urn:nbn:de:0030-drops-241136},
  doi =		{10.4230/LIPIcs.MFCS.2025.6},
  annote =	{Keywords: catalytic computing, circuit classes, polynomial method}
}
Document
DOI: 10.4230/LIPIcs.SAND.2025.13
Self-Stabilizing Weakly Byzantine Perpetual Gathering of Mobile Agents

Authors: Jion Hirose, Ryota Eguchi, and Yuichi Sudo

Published in: LIPIcs, Volume 330, 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)

Abstract
We study the Byzantine gathering problem involving k mobile agents with unique identifiers (IDs), f of which are Byzantine. These agents start the execution of a common algorithm from (possibly different) nodes in an n-node network, potentially starting at different times. Once started, the agents operate in synchronous rounds. We focus on weakly Byzantine environments, where Byzantine agents can behave arbitrarily but cannot falsify their IDs. The goal is for all non-Byzantine agents to eventually terminate at a single node simultaneously. In this paper, we first prove two impossibility results: (1) for any number of non-Byzantine agents, no algorithm can solve this problem without global knowledge of the network size or the number of agents, and (2) no self-stabilizing algorithm exists if k ≤ 2f even with n, k, f, and the length Λ_g of the largest ID among IDs of non-Byzantine agents, where the self-stabilizing algorithm enables agents to gather starting from arbitrary (inconsistent) initial states. Next, based on these results, we introduce a perpetual gathering problem and propose a self-stabilizing algorithm for this problem. This problem requires that all non-Byzantine agents always be co-located from a certain time onwards. If the agents know Λ_g and upper bounds N, K, F on n, k, f, the proposed algorithm works in O(K⋅ F⋅ Λ_g⋅ X(N)) rounds, where X(n) is the time required to visit all nodes in a n-nodes network. Our results indicate that while no algorithm can solve the original self-stabilizing gathering problem for any k and f even with exact global knowledge of the network size and the number of agents, the self-stabilizing perpetual gathering problem can always be solved with just upper bounds on this knowledge.
Cite as

Jion Hirose, Ryota Eguchi, and Yuichi Sudo. Self-Stabilizing Weakly Byzantine Perpetual Gathering of Mobile Agents. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 13:1-13:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hirose_et_al:LIPIcs.SAND.2025.13,
  author =	{Hirose, Jion and Eguchi, Ryota and Sudo, Yuichi},
  title =	{{Self-Stabilizing Weakly Byzantine Perpetual Gathering of Mobile Agents}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{13:1--13:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-368-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{330},
  editor =	{Meeks, Kitty and Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.13},
  URN =		{urn:nbn:de:0030-drops-230662},
  doi =		{10.4230/LIPIcs.SAND.2025.13},
  annote =	{Keywords: Distributed algorithms, Byzantine environments, Gathering}
}
Document
DOI: 10.4230/LIPIcs.ICDT.2025.12
Tractable Conjunctive Queries over Static and Dynamic Relations

Authors: Ahmet Kara, Zheng Luo, Milos Nikolic, Dan Olteanu, and Haozhe Zhang

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

Abstract
We investigate the evaluation of conjunctive queries over static and dynamic relations. While static relations are given as input and do not change, dynamic relations are subject to inserts and deletes. We characterise syntactically three classes of queries that admit constant update time and constant enumeration delay. We call such queries tractable. Depending on the class, the preprocessing time is linear, polynomial, or exponential (under data complexity, so the query size is constant). To decide whether a query is tractable, it does not suffice to analyse separately the sub-queries over the static relations and over the dynamic relations, respectively. Instead, we need to take the interaction between the static and the dynamic relations into account. Even when the sub-query over the dynamic relations is not tractable, the overall query can become tractable if the dynamic relations are sufficiently constrained by the static ones.
Cite as

Ahmet Kara, Zheng Luo, Milos Nikolic, Dan Olteanu, and Haozhe Zhang. Tractable Conjunctive Queries over Static and Dynamic Relations. In 28th International Conference on Database Theory (ICDT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 328, pp. 12:1-12:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kara_et_al:LIPIcs.ICDT.2025.12,
  author =	{Kara, Ahmet and Luo, Zheng and Nikolic, Milos and Olteanu, Dan and Zhang, Haozhe},
  title =	{{Tractable Conjunctive Queries over Static and Dynamic Relations}},
  booktitle =	{28th International Conference on Database Theory (ICDT 2025)},
  pages =	{12:1--12:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-364-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{328},
  editor =	{Roy, Sudeepa and Kara, Ahmet},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2025.12},
  URN =		{urn:nbn:de:0030-drops-229534},
  doi =		{10.4230/LIPIcs.ICDT.2025.12},
  annote =	{Keywords: fully dynamic algorithm, constant enumeration delay, constant update time}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.5
Edge-Minimum Walk of Modular Length in Polynomial Time

Authors: Antoine Amarilli, Benoît Groz, and Nicole Wein

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

Abstract
We study the problem of finding, in a directed graph, an st-walk of length r od q which is edge-minimum, i.e., uses the smallest number of distinct edges. Despite the vast literature on paths and cycles with modularity constraints, to the best of our knowledge we are the first to study this problem. Our main result is a polynomial-time algorithm that solves this task when r and q are constants. We also show how our proof technique gives an algorithm to solve a generalization of the well-known Directed Steiner Network problem, in which connections between endpoint pairs are required to satisfy modularity constraints on their length. Our algorithm is polynomial when the number of endpoint pairs and the modularity constraints on the pairs are constants. In this version of the article, proofs and examples are omitted because of space constraints. Detailed proofs are available in the full version [Antoine Amarilli et al., 2024].
Cite as

Antoine Amarilli, Benoît Groz, and Nicole Wein. Edge-Minimum Walk of Modular Length in Polynomial Time. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 5:1-5:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{amarilli_et_al:LIPIcs.ITCS.2025.5,
  author =	{Amarilli, Antoine and Groz, Beno\^{i}t and Wein, Nicole},
  title =	{{Edge-Minimum Walk of Modular Length in Polynomial Time}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{5:1--5:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.5},
  URN =		{urn:nbn:de:0030-drops-226330},
  doi =		{10.4230/LIPIcs.ITCS.2025.5},
  annote =	{Keywords: Directed Steiner Network, Modularity}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.96
Formulations and Constructions of Remote State Preparation with Verifiability, with Applications

Authors: Jiayu Zhang

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

Abstract
Remote state preparation with verifiability (RSPV) is an important quantum cryptographic primitive [Alexandru Gheorghiu and Thomas Vidick, 2019; Jiayu Zhang, 2022]. In this primitive, a client would like to prepare a quantum state (sampled or chosen from a state family) on the server side, such that ideally the client knows its full description, while the server holds and only holds the state itself. In this work we make several contributions on its formulations, constructions and applications. In more detail: - We first work on the definitions and abstract properties of the RSPV problem. We select and compare different variants of definitions [Bennett et al., 2001; Alexandru Gheorghiu and Thomas Vidick, 2019; Jiayu Zhang, 2022; Alexandru Gheorghiu et al., 2022], and study their basic properties (like composability and amplification). - We also study a closely related question of how to certify the server’s operations (instead of solely the states). We introduce a new notion named remote operator application with verifiability (ROAV). We compare this notion with related existing definitions [Summers and Werner, 1987; Dominic Mayers and Andrew Chi-Chih Yao, 2004; Zhengfeng Ji et al., 2021; Tony Metger and Thomas Vidick, 2021; Anand Natarajan and Tina Zhang, 2023], study its abstract properties and leave its concrete constructions for further works. - Building on the abstract properties and existing results [Zvika Brakerski et al., 2023], we construct a series of new RSPV protocols. Our constructions not only simplify existing results [Alexandru Gheorghiu and Thomas Vidick, 2019] but also cover new state families, for example, states in the form of 1/√2 (|0⟩ + |x_0⟩ + |1⟩ |x_1⟩). All these constructions rely only on the existence of weak NTCF [Zvika Brakerski et al., 2020; Navid Alamati et al., 2022], without additional requirements like the adaptive hardcore bit property [Zvika Brakerski et al., 2018; Navid Alamati et al., 2022]. - As a further application, we show that the classical verification of quantum computations (CVQC) problem [Dorit Aharonov et al., 2010; Urmila Mahadev, 2018] could be constructed from assumptions on group actions [Navid Alamati et al., 2020]. This is achieved by combining our results on RSPV with group-action-based instantiation of weak NTCF [Navid Alamati et al., 2022], and then with the quantum-gadget-assisted quantum verification protocol [Ferracin et al., 2018].
Cite as

Jiayu Zhang. Formulations and Constructions of Remote State Preparation with Verifiability, with Applications. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 96:1-96:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{zhang:LIPIcs.ITCS.2025.96,
  author =	{Zhang, Jiayu},
  title =	{{Formulations and Constructions of Remote State Preparation with Verifiability, with Applications}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{96:1--96:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.96},
  URN =		{urn:nbn:de:0030-drops-227245},
  doi =		{10.4230/LIPIcs.ITCS.2025.96},
  annote =	{Keywords: Quantum Cryptography, Remote State Preparation, Self-testing, Verification of Quantum Computations}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.50
Fully Characterizing Lossy Catalytic Computation

Authors: Marten Folkertsma, Ian Mertz, Florian Speelman, and Quinten Tupker

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

Abstract
A catalytic machine is a model of computation where a traditional space-bounded machine is augmented with an additional, significantly larger, "catalytic" tape, which, while being available as a work tape, has the caveat of being initialized with an arbitrary string, which must be preserved at the end of the computation. Despite this restriction, catalytic machines have been shown to have surprising additional power; a logspace machine with a polynomial length catalytic tape, known as catalytic logspace (CL), can compute problems which are believed to be impossible for L. A fundamental question of the model is whether the catalytic condition, of leaving the catalytic tape in its exact original configuration, is robust to minor deviations. This study was initialized by Gupta et al. (2024), who defined lossy catalytic logspace (LCL[e]) as a variant of CL where we allow up to e errors when resetting the catalytic tape. They showed that LCL[e] = CL for any e = O(1), which remains the frontier of our understanding. In this work we completely characterize lossy catalytic space (LCSPACE[s,c,e]) in terms of ordinary catalytic space (CSPACE[s,c]). We show that LCSPACE[s,c,e] = CSPACE[Θ(s + e log c), Θ(c)] In other words, allowing e errors on a catalytic tape of length c is equivalent, up to a constant stretch, to an equivalent errorless catalytic machine with an additional e log c bits of ordinary working memory. As a consequence, we show that for any e, LCL[e] = CL implies SPACE[e log n] ⊆ ZPP, thus giving a barrier to any improvement beyond LCL[O(1)] = CL. We also show equivalent results for non-deterministic and randomized catalytic space.
Cite as

Marten Folkertsma, Ian Mertz, Florian Speelman, and Quinten Tupker. Fully Characterizing Lossy Catalytic Computation. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 50:1-50:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{folkertsma_et_al:LIPIcs.ITCS.2025.50,
  author =	{Folkertsma, Marten and Mertz, Ian and Speelman, Florian and Tupker, Quinten},
  title =	{{Fully Characterizing Lossy Catalytic Computation}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{50:1--50:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.50},
  URN =		{urn:nbn:de:0030-drops-226786},
  doi =		{10.4230/LIPIcs.ITCS.2025.50},
  annote =	{Keywords: Space complexity, catalytic computation, error-correcting codes}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.14
Finite Variable Counting Logics with Restricted Requantification

Authors: Simon Raßmann, Georg Schindling, and Pascal Schweitzer

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract
Counting logics with a bounded number of variables form one of the central concepts in descriptive complexity theory. Although they restrict the number of variables that a formula can contain, the variables can be nested within scopes of quantified occurrences of themselves. In other words, the variables can be requantified. We study the fragments obtained from counting logics by restricting requantification for some but not necessarily all the variables. Similar to the logics without limitation on requantification, we develop tools to investigate the restricted variants. Specifically, we introduce a bijective pebble game in which certain pebbles can only be placed once and for all, and a corresponding two-parametric family of Weisfeiler-Leman algorithms. We show close correspondences between the three concepts. By using a suitable cops-and-robber game and adaptations of the Cai-Fürer-Immerman construction, we completely clarify the relative expressive power of the new logics. We show that the restriction of requantification has beneficial algorithmic implications in terms of graph identification. Indeed, we argue that with regard to space complexity, non-requantifiable variables only incur an additive polynomial factor when testing for equivalence. In contrast, for all we know, requantifiable variables incur a multiplicative linear factor. Finally, we observe that graphs of bounded tree-depth and 3-connected planar graphs can be identified using no, respectively, only a very limited number of requantifiable variables.
Cite as

Simon Raßmann, Georg Schindling, and Pascal Schweitzer. Finite Variable Counting Logics with Restricted Requantification. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 14:1-14:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ramann_et_al:LIPIcs.CSL.2025.14,
  author =	{Ra{\ss}mann, Simon and Schindling, Georg and Schweitzer, Pascal},
  title =	{{Finite Variable Counting Logics with Restricted Requantification}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{14:1--14:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.14},
  URN =		{urn:nbn:de:0030-drops-227716},
  doi =		{10.4230/LIPIcs.CSL.2025.14},
  annote =	{Keywords: Requantification, Finite variable counting logics, Weisfeiler-Leman algorithm}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2024.4
The Parallel Dynamic Complexity of the Abelian Cayley Group Membership Problem

Authors: V. Arvind, Samir Datta, Asif Khan, Shivdutt Sharma, Yadu Vasudev, and Shankar Ram Vasudevan

Published in: LIPIcs, Volume 323, 44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024)

Abstract
Let G be a finite group given as input by its multiplication table. For a subset S ⊆ G and an element g ∈ G the Cayley Group Membership Problem (CGM) is to check if g belongs to the subgroup generated by S. While this problem is easily seen to be in polynomial time, pinpointing its parallel complexity has been of research interest over the years. Barrington et al [Barrington et al., 2001] have shown that for abelian groups the CGM problem can be solved in O(log log |G|) parallel time. In this paper we further explore the parallel complexity of the abelian CGM problem, with focus on the dynamic setting: the generating set S changes with insertions and deletions and the goal is to maintain a data structure that supports efficient membership queries to the subgroup ⟨S⟩. Though the static version of the CGM problem can be easily reduced to digraph reachability, the reduction does not carry over to the dynamic setting. We obtain the following results: 1) First, we consider the more general problem of Monoid Membership, where G is a monoid input by its multiplication table. When G is a commutative monoid we show there is a deterministic dynamic AC⁰ algorithm for membership testing that supports O(1) insertions and deletions in each step. 2) Building on the previous result we show that there is a dynamic randomized AC⁰ algorithm for abelian CGM that supports polylog(|G|) insertions/deletions to S in each step. 3) If the number of insertions/deletions is at most O(log n/log log n) then we obtain a deterministic dynamic AC⁰ algorithm for abelian CGM. 4) Applying these algorithms we obtain analogous results for the dynamic abelian Group Isomorphism. We can also handle sub-linearly many changes to the multiplication table for G, utilizing the hamming distance between multiplication tables of any two distinct groups.
Cite as

V. Arvind, Samir Datta, Asif Khan, Shivdutt Sharma, Yadu Vasudev, and Shankar Ram Vasudevan. The Parallel Dynamic Complexity of the Abelian Cayley Group Membership Problem. In 44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 323, pp. 4:1-4:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{arvind_et_al:LIPIcs.FSTTCS.2024.4,
  author =	{Arvind, V. and Datta, Samir and Khan, Asif and Sharma, Shivdutt and Vasudev, Yadu and Vasudevan, Shankar Ram},
  title =	{{The Parallel Dynamic Complexity of the Abelian Cayley Group Membership Problem}},
  booktitle =	{44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024)},
  pages =	{4:1--4:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-355-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{323},
  editor =	{Barman, Siddharth and Lasota, S{\l}awomir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2024.4},
  URN =		{urn:nbn:de:0030-drops-221939},
  doi =		{10.4230/LIPIcs.FSTTCS.2024.4},
  annote =	{Keywords: Dynamic Complexity, Group Theory, Cayley Group Membership, Abelian Group Isomorphism}
}
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