52 Search Results for "Wagner, Christian"

Document
DOI: 10.4230/LIPIcs.STACS.2026.66
Computational Hardness of Estimating Quantum Entropies via Binary Entropy Bounds

Authors: Yupan Liu

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

Abstract
We investigate the computational hardness of estimating the quantum α-Rényi entropy S^𝚁_α(ρ) = (ln Tr(ρ^α))/(1-α) and the quantum q-Tsallis entropy S^𝚃_q(ρ) = (1-Tr(ρ^q))/(q-1), both converging to the von Neumann entropy as the order approaches 1. The promise problems Quantum α-Rényi Entropy Approximation (RényiQEA_α) and Quantum q-Tsallis Entropy Approximation (TsallisQEA_q) ask whether S^𝚁_α(ρ) or S^𝚃_q(ρ), respectively, is at least τ_Y or at most τ_N, where τ_Y - τ_N is typically a positive constant. Previous hardness results cover only the von Neumann entropy (order 1) and some cases of the quantum q-Tsallis entropy, while existing approaches do not readily extend to other orders. We establish that for all positive real orders, the rank-2 variants Rank2RényiQEA_α and Rank2TsallisQEA_q are BQP-hard. Combined with prior (rank-dependent) quantum query algorithms in Wang, Guan, Liu, Zhang, and Ying (TIT 2024), Wang, Zhang, and Li (TIT 2024), and Liu and Wang (SODA 2025), our results imply: - For all real order α > 0 and 0 < q ≤ 1, LowRankRényiQEA_α and LowRankTsallisQEA_q are BQP-complete, where both are restricted versions of RényiQEA_α and TsallisQEA_q with ρ of polynomial rank. - For all real order q > 1, TsallisQEA_q is BQP-complete. Our hardness results stem from reductions based on new inequalities relating the α-Rényi or q-Tsallis binary entropies of different orders, where the reductions differ substantially from previous approaches, and the inequalities are also of independent interest.
Cite as

Yupan Liu. Computational Hardness of Estimating Quantum Entropies via Binary Entropy Bounds. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 66:1-66:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{liu:LIPIcs.STACS.2026.66,
  author =	{Liu, Yupan},
  title =	{{Computational Hardness of Estimating Quantum Entropies via Binary Entropy Bounds}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{66:1--66:23},
  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.2026.66},
  URN =		{urn:nbn:de:0030-drops-255550},
  doi =		{10.4230/LIPIcs.STACS.2026.66},
  annote =	{Keywords: computational hardness, quantum state testing, quantum R\'{e}nyi entropy, quantum Tsallis entropy, von Neumann entropy}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.54
Testable Algorithms for Approximately Counting Edges and Triangles in Sublinear Time and Space

Authors: Talya Eden, Ronitt Rubinfeld, and Arsen Vasilyan

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

Abstract
We consider the fundamental problems of approximately counting the numbers of edges and triangles in a graph in sublinear time. Previous algorithms for these tasks are significantly more efficient under a promise that the arboricity of the graph is bounded by some parameter ̅α. However, when this promise is violated, the estimates given by these algorithms are no longer guaranteed to be correct. For the triangle counting task, we give an algorithm that requires no promise on the input graph G, and computes a (1±ε)-approximation for the number of triangles t in G in time O^*((m⋅ α(G))/t + m/(t^{2/3)}), where α(G) is the arboricity of the graph. The algorithm can be used on any graph G (no prior knowledge of the arboricity α(G) is required), and the algorithm adapts its run-time on the fly based on the graph G. We accomplish this by trying a sequence of candidate values α̃ for α(G) and using a novel algorithm in the framework of testable algorithms. This ensures that wrong candidates α̃ cannot lead to wrong estimates: if the advice is incorrect, the algorithm either succeeds despite this or detects this and continues with a new candidate. Once the algorithm accepts the candidate, its output is guaranteed to be correct with high probability. We prove that this approach preserves - up to an additive overhead - the dramatic efficiency gains obtainable when good arboricity bounds are known in advance, while ensuring robustness against misleading advice. We further complement this result with a lower bound, showing that such an overhead is unavoidable whenever the advice may be faulty. We further demonstrate implications of our results for triangle counting in the streaming model.
Cite as

Talya Eden, Ronitt Rubinfeld, and Arsen Vasilyan. Testable Algorithms for Approximately Counting Edges and Triangles in Sublinear Time and Space. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 54:1-54:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{eden_et_al:LIPIcs.ITCS.2026.54,
  author =	{Eden, Talya and Rubinfeld, Ronitt and Vasilyan, Arsen},
  title =	{{Testable Algorithms for Approximately Counting Edges and Triangles in Sublinear Time and Space}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{54:1--54:24},
  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.2026.54},
  URN =		{urn:nbn:de:0030-drops-253417},
  doi =		{10.4230/LIPIcs.ITCS.2026.54},
  annote =	{Keywords: Sublinear Algorithms, Triangle Counting, Edge Counting, Arboricity}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.116
Decentralized Data Archival: New Definitions and Constructions

Authors: Elaine Shi, Rose Silver, and Changrui Mu

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

Abstract
We initiate the study of a new abstraction called incremental decentralized data archival (iDDA). Specifically, imagine that there is an ever-growing, massive database such as a blockchain, a comprehensive human knowledge base like Wikipedia, or the Internet archive. We want to build a decentralized archival system for such datasets to ensure long-term robustness and sustainability. We identify several important properties that an iDDA scheme should satisfy. First, to promote heterogeneity and decentralization, we want to encourage even weak nodes with limited space (e.g., users' home computers) to contribute. The minimum space requirement to contribute should be approximately independent of the data size. Second, if a collection of nodes together receive rewards commensurate with contributing a total of m blocks of space, then we want the following reassurances: 1) if m is at least the database size, we should be able to reconstruct the entire dataset; and 2) these nodes should actually be committing roughly m space in aggregate - specifically, when m is much larger than the data size, these nodes cannot store only one copy of the database, and be able to impersonate arbitrarily many pseudonyms and get unbounded rewards. We propose new definitions that mathematically formalize the aforementioned requirements of an iDDA scheme. We also devise an efficient construction in the random oracle model which satisfies the desired security requirements. Our scheme incurs only Õ(1) audit cost, as well as Õ(1) update cost for both the publisher and each node, where Õ(⋅) hides polylogarithmic factors. Further, the minimum space provisioning required to contribute is as small as polylogarithmic. Our construction exposes several interesting technical challenges. Specifically, we show that a straightforward application of the standard hierarchical data structure fails, since both our security definition and the underlying cryptographic primitives we employ lack the desired compositional guarantees. We devise novel techniques to overcome these compositional issues, resulting in a construction with provable security while still retaining efficiency. Finally, our new definitions also make a conceptual contribution, and lay the theoretical groundwork for the study of iDDA. We raise several interesting open problems along this direction.
Cite as

Elaine Shi, Rose Silver, and Changrui Mu. Decentralized Data Archival: New Definitions and Constructions. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 116:1-116:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{shi_et_al:LIPIcs.ITCS.2026.116,
  author =	{Shi, Elaine and Silver, Rose and Mu, Changrui},
  title =	{{Decentralized Data Archival: New Definitions and Constructions}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{116:1--116:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.116},
  URN =		{urn:nbn:de:0030-drops-254037},
  doi =		{10.4230/LIPIcs.ITCS.2026.116},
  annote =	{Keywords: Decentralized Data Archival}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2025.36
BlindPerm: Efficient MEV Mitigation with an Encrypted Mempool and Permutation

Authors: Alireza Kavousi, Duc V. Le, Philipp Jovanovic, and George Danezis

Published in: LIPIcs, Volume 361, 29th International Conference on Principles of Distributed Systems (OPODIS 2025)

Abstract
Maximal Extractable Value (MEV) is a crucial challenge in blockchains and cryptocurrencies. A principal countermeasure is using encrypted mempools to hide the transaction payloads until they are committed in a block. However, the existing approaches based on encrypted mempools remain vulnerable to metadata leakage and may not provide sufficient mitigation against block producers due to their sole control in block preparation. In this paper, we propose techniques that utilize randomized permutation on the committed block, offering a multi-layer solution. With a focus on proof-of-stake (PoS) committee-based consensus, we then introduce BlindPerm, a framework that enhances an encrypted mempool with permutation and present various optimizations. Notably, we propose a construction where this enhancement comes at essentially no overhead by piggybacking on the encrypted mempool and without relying on any external entity such as randomness beacon. Further, we illustrate the effectiveness of our solutions by running simulations using historical Ethereum data.
Cite as

Alireza Kavousi, Duc V. Le, Philipp Jovanovic, and George Danezis. BlindPerm: Efficient MEV Mitigation with an Encrypted Mempool and Permutation. In 29th International Conference on Principles of Distributed Systems (OPODIS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 361, pp. 36:1-36:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kavousi_et_al:LIPIcs.OPODIS.2025.36,
  author =	{Kavousi, Alireza and Le, Duc V. and Jovanovic, Philipp and Danezis, George},
  title =	{{BlindPerm: Efficient MEV Mitigation with an Encrypted Mempool and Permutation}},
  booktitle =	{29th International Conference on Principles of Distributed Systems (OPODIS 2025)},
  pages =	{36:1--36:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-409-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{361},
  editor =	{Arusoaie, Andrei and Onica, Emanuel and Spear, Michael and Tucci-Piergiovanni, Sara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2025.36},
  URN =		{urn:nbn:de:0030-drops-252091},
  doi =		{10.4230/LIPIcs.OPODIS.2025.36},
  annote =	{Keywords: Encrypted mempool, maximal extractable value, distributed systems}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.16
Designing Compact ILPs via Fast Witness Verification

Authors: Michał Włodarczyk

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

Abstract
The standard formalization of preprocessing in parameterized complexity is given by kernelization. In this work, we depart from this paradigm and study a different type of preprocessing for problems without polynomial kernels, still aiming at producing instances that are easily solvable in practice. Specifically, we ask for which parameterized problems an instance (I,k) can be reduced in polynomial time to an integer linear program (ILP) with poly(k) constraints. We show that this property coincides with the parameterized complexity class WK[1], previously studied in the context of Turing kernelization lower bounds. In turn, the class WK[1] enjoys an elegant characterization in terms of witness verification protocols: a yes-instance should admit a witness of size poly(k) that can be verified in time poly(k). By combining known data structures with new ideas, we design such protocols for several problems, such as r-Way Cut, Vertex Multiway Cut, Steiner Tree, and Minimum Common String Partition, thus showing that they can be modeled by compact ILPs. We also present explicit ILP and MILP formulations for Weighted Vertex Cover on graphs with small (unweighted) vertex cover number. We believe that these results will provide a background for a systematic study of ILP-oriented preprocessing procedures for parameterized problems.
Cite as

Michał Włodarczyk. Designing Compact ILPs via Fast Witness Verification. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{wlodarczyk:LIPIcs.IPEC.2025.16,
  author =	{W{\l}odarczyk, Micha{\l}},
  title =	{{Designing Compact ILPs via Fast Witness Verification}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{16:1--16:18},
  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.2025.16},
  URN =		{urn:nbn:de:0030-drops-251481},
  doi =		{10.4230/LIPIcs.IPEC.2025.16},
  annote =	{Keywords: integer programming, kernelization, nondeterminism, multiway cut}
}
Document
Use Case
DOI: 10.4230/TGDK.3.3.5
LLM-Supported Manufacturing Mapping Generation

Authors: Wilma Johanna Schmidt, Irlan Grangel-González, Adrian Paschke, and Evgeny Kharlamov

Published in: TGDK, Volume 3, Issue 3 (2025). Transactions on Graph Data and Knowledge, Volume 3, Issue 3

Abstract
In large manufacturing companies, such as Bosch, that operate thousands of production lines with each comprising up to dozens of production machines and other equipment, even simple inventory questions such as of location and quantities of a particular equipment type require non-trivial solutions. Addressing these questions requires to integrate multiple heterogeneous data sets which is time consuming and error prone and demands domain as well as knowledge experts. Knowledge graphs (KGs) are practical for consolidating inventory data by bringing it into the same format and linking inventory items. However, the KG creation and maintenance itself pose challenges as mappings are needed to connect data sets and ontologies. In this work, we address these challenges by exploring LLM-supported and context-enhanced generation of both YARRRML and RML mappings. Facing large ontologies in the manufacturing domain and token limitations in LLM prompts, we further evaluate ontology reduction methods in our approach. We evaluate our approach both quantitatively against reference mappings created manually by experts and, for YARRRML, also qualitatively with expert feedback. This work extends the exploration of the challenges with LLM-supported and context-enhanced mapping generation YARRRML [Schmidt et al., 2025] by comprehensive analyses on RML mappings and an ontology reduction evaluation. We further publish the source code of this work. Our work provides a valuable support when creating manufacturing mappings and supports data and schema updates.
Cite as

Wilma Johanna Schmidt, Irlan Grangel-González, Adrian Paschke, and Evgeny Kharlamov. LLM-Supported Manufacturing Mapping Generation. In Transactions on Graph Data and Knowledge (TGDK), Volume 3, Issue 3, pp. 5:1-5:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@Article{schmidt_et_al:TGDK.3.3.5,
  author =	{Schmidt, Wilma Johanna and Grangel-Gonz\'{a}lez, Irlan and Paschke, Adrian and Kharlamov, Evgeny},
  title =	{{LLM-Supported Manufacturing Mapping Generation}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{5:1--5:22},
  ISSN =	{2942-7517},
  year =	{2025},
  volume =	{3},
  number =	{3},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.3.3.5},
  URN =		{urn:nbn:de:0030-drops-252164},
  doi =		{10.4230/TGDK.3.3.5},
  annote =	{Keywords: Mapping Generation, Knowledge Graph Construction, Ontology Reduction, RML, YARRRML, LLM, Manufacturing}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.43
New Approximate Distance Oracles and Their Applications

Authors: Avi Kadria and Liam Roditty

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

Abstract
Let G = (V, E) be an undirected graph with n vertices and m edges, and let μ = m/n. A distance oracle is a data structure designed to answer approximate distance queries, with the goal of achieving low stretch, efficient space usage, and fast query time. While much of the prior work focused on distance oracles with constant query time, this paper presents a comprehensive study of distance oracles with non-constant query time. We explore the tradeoffs between space, stretch, and query time of distance oracles in various regimes. Specifically, we consider both weighted and unweighted graphs in the regimes of stretch < 2 and stretch ≥ 2. In addition, we demonstrate several applications of our new distance oracles to the n-Pairs Shortest Paths (n-PSP) problem and the All Nodes Shortest Cycles (ANSC) problem. Our main contributions are: - Weighted graphs: We present a new three-way trade-off between stretch, space, and query time, offering a natural extension of the classical Thorup–Zwick distance oracle [STOC’01 and JACM’05] to regimes with larger query time. Specifically, for any 0 < r < 1/2 and integer k ≥ 1, we construct a (2k(1 - 2r) - 1)-stretch distance oracle with Õ(m + n^{1 + 1/k}) space and Õ(μ n^r) query time. This construction provides an asymptotic improvement over the classical (2k - 1)-stretch and O(n^{1 + 1/k})-space tradeoff of Thorup and Zwick in sparse graphs, at the cost of increased query time. We also improve upon a result of Dalirrooyfard et al. [FOCS’22], who presented a (2k - 2)-stretch distance oracle with O(m + n^{1 + 1/k}) space and O(μ n^{1/k}) query time. In our oracle we reduce the stretch from (2k - 2) to (2k - 5) while preserving the same space and query time. - Unweighted graphs: We present a (2k - 5, 4 + 2_{odd})-approximation distance oracle with O(n^{1 + 1/k}) space and O(n^{1/k}) query time. This improves upon a (2k - 2, 2_{odd})-approximation distance oracle of Dalirrooyfard et al. [FOCS’22] while maintaining the same space and query time. We also present a distance oracle that given u,v ∈ V returns an estimate d̂(u,v) ≤ d(u,v) + 2⌈ d(u,v) / 3 ⌉ + 2, using O(n^{4/3 + 2ε}) space and O(n^{1 - 3ε}) query time. To the best of our knowledge, this is the first distance oracle that simultaneously achieves a multiplicative stretch < 2, and a space complexity O(n^{1.5 - α}), for some α > 0. - Applications for n-PSP and ANSC: We present an Õ(m^{1 - 1/(k+1)} n)-time algorithm for the n-PSP problem, that for every input pair ⟨s_i,t_i⟩, where i ∈ [n], returns an estimate d̂(s_i, t_i) such that d̂(s_i,t_i) ≤ d(s_i,t_i) + 2⌈d(s_i,t_i)/2k⌉. By allowing a small additive error, this result circumvents the conditional running time lower bound of Ω(m^{2 - 2/(k+1)} ⋅ n^{1/(k+1) - o(1)}), established by Dalirrooyfard et al. [FOCS’22] for achieving (1 + 1/k)-stretch. Additionally, we present an Õ(mn^{1 - 1/k})-time algorithm for the ANSC problem that computes, for every u ∈ V, an estimate ĉ_u such that ĉ_u ≤ SC(u) + 2⌈SC(u)/2(k - 1)⌉, where SC(u) denotes the length of the shortest cycle containing u. This improves upon the Õ(m^{2 - 2/k}n^{1/k})-time algorithm of Dalirrooyfard et al. [FOCS'22], while achieving the same approximation guarantee. We obtain our results by developing several new techniques, among them are the borderline vertices technique and the middle vertex technique, which may be of independent interest.
Cite as

Avi Kadria and Liam Roditty. New Approximate Distance Oracles and Their Applications. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 43:1-43:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kadria_et_al:LIPIcs.ISAAC.2025.43,
  author =	{Kadria, Avi and Roditty, Liam},
  title =	{{New Approximate Distance Oracles and Their Applications}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{43:1--43:17},
  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.2025.43},
  URN =		{urn:nbn:de:0030-drops-249514},
  doi =		{10.4230/LIPIcs.ISAAC.2025.43},
  annote =	{Keywords: Distance oracles, Fine-grained algorithms, Graph algorithms, Data structures}
}
Document
DOI: 10.4230/LIPIcs.GD.2025.17
Visualizing Treewidth

Authors: Alvin Chiu, Thomas Depian, David Eppstein, Michael T. Goodrich, and Martin Nöllenburg

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

Abstract
A witness drawing of a graph is a visualization that clearly shows a given property of a graph. We study and implement various drawing paradigms for witness drawings to clearly show that graphs have bounded pathwidth or treewidth. Our approach draws the tree decomposition or path decomposition as a tree of bags, with induced subgraphs shown in each bag, and with "tracks" for each graph vertex connecting its copies in multiple bags. Within bags, we optimize the vertex layout to avoid crossings of edges and tracks. We implement a visualization prototype for crossing minimization using dynamic programming for graphs of small width and heuristic approaches for graphs of larger width. We introduce a taxonomy of drawing styles, which render the subgraph for each bag as an arc diagram with one or two pages or as a circular layout with straight-line edges, and we render tracks either with straight lines or with orbital-radial paths.
Cite as

Alvin Chiu, Thomas Depian, David Eppstein, Michael T. Goodrich, and Martin Nöllenburg. Visualizing Treewidth. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 17:1-17:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chiu_et_al:LIPIcs.GD.2025.17,
  author =	{Chiu, Alvin and Depian, Thomas and Eppstein, David and Goodrich, Michael T. and N\"{o}llenburg, Martin},
  title =	{{Visualizing Treewidth}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{17:1--17:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.17},
  URN =		{urn:nbn:de:0030-drops-250034},
  doi =		{10.4230/LIPIcs.GD.2025.17},
  annote =	{Keywords: Graph drawing, witness drawings, pathwidth, treewidth}
}
Document
DOI: 10.4230/LIPIcs.GD.2025.14
OOPS: Optimized One-Planarity Solver via SAT

Authors: Sergey Pupyrev

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

Abstract
We present OOPS (Optimized One-Planarity Solver), a practical heuristic for recognizing 1-planar graphs and several important subclasses. A graph is 1-planar if it can be drawn in the plane such that each edge is crossed at most once - a natural generalization of planar graphs that has received increasing attention in graph drawing and beyond-planar graph theory. Although testing planarity can be done in linear time, recognizing 1-planar graphs is NP-complete, making effective practical algorithms especially valuable. The core idea of our approach is to reduce the recognition of 1-planarity to a propositional satisfiability (SAT) instance, enabling the use of modern SAT solvers to efficiently explore the search space. Despite the inherent complexity of the problem, our method is substantially faster in practice than naïve or brute-force algorithms. In addition to demonstrating the empirical performance of our solver on synthetic and real-world instances, we show how OOPS can be used as a discovery tool in theoretical graph theory. Specifically, we employ OOPS to investigate two research problems concerning 1-planarity of specific graph families. Our implementation of the algorithm is publicly available to support further exploration in the field.
Cite as

Sergey Pupyrev. OOPS: Optimized One-Planarity Solver via SAT. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 14:1-14:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{pupyrev:LIPIcs.GD.2025.14,
  author =	{Pupyrev, Sergey},
  title =	{{OOPS: Optimized One-Planarity Solver via SAT}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{14:1--14:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.14},
  URN =		{urn:nbn:de:0030-drops-250004},
  doi =		{10.4230/LIPIcs.GD.2025.14},
  annote =	{Keywords: beyond planarity, 1-planar graph, SAT, book embeddings, upward 1-planarity}
}
Document
DOI: 10.4230/LIPIcs.GD.2025.4
Heuristics for Exact 1-Planarity Testing

Authors: Simon D. Fink, Miriam Münch, Matthias Pfretzschner, and Ignaz Rutter

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

Abstract
Since many real-world graphs are nonplanar, the study of graphs that allow few crossings per edge has been an active subfield of graph theory in recent years. One of the most natural generalizations of planar graphs are the so-called 1-planar graphs that admit a drawing with at most one crossing per edge. Unfortunately, testing whether a graph is 1-planar is known to be NP-complete even for very restricted graph classes. On the positive side, Binucci, Didimo and Montecchiani [Binucci et al., 2023] presented the first practical algorithm for testing 1-planarity based on an easy-to-implement backtracking strategy. We build on this idea and systematically explore the design choices of such algorithms and propose several new ingredients, such as different branching strategies and multiple filter criteria that allow us to reject certain branches in the search tree early on. We conduct an extensive experimental evaluation that evaluates the efficiency and effectiveness of these ingredients. Given a time limit of three hours per instance, our best configuration is able to solve more than 95% of the non-planar instances from the well-known North and Rome graphs with up to 50 vertices. Notably, the median running time for solved instances is well below 4 seconds.
Cite as

Simon D. Fink, Miriam Münch, Matthias Pfretzschner, and Ignaz Rutter. Heuristics for Exact 1-Planarity Testing. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 4:1-4:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fink_et_al:LIPIcs.GD.2025.4,
  author =	{Fink, Simon D. and M\"{u}nch, Miriam and Pfretzschner, Matthias and Rutter, Ignaz},
  title =	{{Heuristics for Exact 1-Planarity Testing}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{4:1--4:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.4},
  URN =		{urn:nbn:de:0030-drops-249909},
  doi =		{10.4230/LIPIcs.GD.2025.4},
  annote =	{Keywords: 1-Planarity, Experiments, Backtracking}
}
Document
DOI: 10.4230/LIPIcs.GD.2025.30
Universal Quality Metrics for Graph Drawings: Which Graphs Excite Us Most?

Authors: Gavin J. Mooney, Tim Hegemann, Alexander Wolff, Michael Wybrow, and Helen C. Purchase

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

Abstract
Graphs are drawn for various purposes, and drawings are meant to display various features of a graph (such as planarity, Hamiltonicity). Still, there is a long history in measuring the quality of a graph drawing. Most of the metrics that have been implemented and used in large studies assume that graphs are drawn straight-line. Most of the studies use randomly generated graphs or one of very few existing benchmark sets that consist of graphs with a specific technical background (e.g., telecommunication networks). In this paper, we extend ten commonly used metrics to node-link diagrams where edges can be curves or polygonal chains. We implement these measures and use them to evaluate a new collection of graph drawings that we have extracted from 27 proceedings of the Graph Drawing conference using an automated pipeline. We compare the "metrics landscape" of our new benchmark set, the GD-collection-v1, which seems to mostly contain manually drawn graphs, to the metric landscape of a benchmark set with randomly generated graphs and computer-generated straight-line drawings that has been used in a recent study [Mooney et al.; PacificVis 2024]. Comparing the GD-collection-v1 with the Mooney at al. dataset reveals a distinct metrics landscape: GD drawings come from much smaller graphs (median vertex number 11 vs. 48) and therefore attain higher medians on most readability metrics. For example, Neighbourhood Preservation (0.5 vs. 0.239) is markedly higher in the GD-collection-v1. We also find that a large proportion of extracted drawings contain curved and/or polygonal edges (57%), motivating the extended metric definitions.
Cite as

Gavin J. Mooney, Tim Hegemann, Alexander Wolff, Michael Wybrow, and Helen C. Purchase. Universal Quality Metrics for Graph Drawings: Which Graphs Excite Us Most?. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 30:1-30:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mooney_et_al:LIPIcs.GD.2025.30,
  author =	{Mooney, Gavin J. and Hegemann, Tim and Wolff, Alexander and Wybrow, Michael and Purchase, Helen C.},
  title =	{{Universal Quality Metrics for Graph Drawings: Which Graphs Excite Us Most?}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{30:1--30:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.30},
  URN =		{urn:nbn:de:0030-drops-250162},
  doi =		{10.4230/LIPIcs.GD.2025.30},
  annote =	{Keywords: Graph drawing metrics, metric landscape, straight-line drawings, polyline drawings, curved drawings, automated extraction of graph drawings}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.38
Compact Routing Schemes in Undirected and Directed Graphs

Authors: Avi Kadria and Liam Roditty

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
In this paper, we study the problem of compact routing schemes in weighted undirected and directed graphs. For weighted undirected graphs, more than a decade ago, Chechik [PODC'13] presented a ≈ 3.68k-stretch compact routing scheme that uses Õ(n^{1/k}log{D}) local storage, where D is the normalized diameter, for every k > 1. We present a ≈ 2.64k-stretch compact routing scheme that uses Õ(n^{1/k}) local storage on average in each vertex. This is the first compact routing scheme that uses total local storage of Õ(n^{1+1/k}) while achieving a c ⋅ k stretch, for a constant c < 3. In real-world network protocols, messages are usually transmitted as part of a communication session between two parties. Therefore, more than two decades ago, Thorup and Zwick [SPAA'01] considered compact routing schemes that establish a communication session using a handshake. In their handshake-based compact routing scheme, the handshake is routed along a (4k-5)-stretch path, and the rest of the communication session is routed along an optimal (2k-1)-stretch path. It is straightforward to improve the (4k-5)-stretch of the handshake to ≈ 3.68k-stretch using the compact routing scheme of Chechik [PODC'13]. We improve the handshake stretch to the optimal (2k-1), by borrowing the concept of roundtrip routing from directed graphs to undirected graphs. For weighted directed graphs, more than two decades ago, Roditty, Thorup, and Zwick [SODA'02 and TALG'08] presented a (4k+ε)-stretch compact roundtrip routing scheme that uses Õ(n^{1/k}) local storage for every k ≥ 3. For k = 3, this gives a (12+ε)-roundtrip stretch using Õ(n^{1/3}) local storage. We improve the stretch by developing a 7-roundtrip stretch routing scheme with Õ(n^{1/3}) local storage. In addition, we consider graphs with bounded hop diameter and present an optimal (2k-1)-roundtrip stretch routing scheme that uses Õ(D_{HOP}⋅ n^{1/k}), where D_{HOP} is the hop diameter of the graph.
Cite as

Avi Kadria and Liam Roditty. Compact Routing Schemes in Undirected and Directed Graphs. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 38:1-38:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kadria_et_al:LIPIcs.DISC.2025.38,
  author =	{Kadria, Avi and Roditty, Liam},
  title =	{{Compact Routing Schemes in Undirected and Directed Graphs}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{38:1--38:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.38},
  URN =		{urn:nbn:de:0030-drops-248555},
  doi =		{10.4230/LIPIcs.DISC.2025.38},
  annote =	{Keywords: Routing schemes, Compact routing schemes, Distance oracles, Computer networks, Graph algorithms}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.14
Energy-Efficient Maximal Independent Sets in Radio Networks

Authors: Dominick Banasik, Varsha Dani, Fabien Dufoulon, Aayush Gupta, Thomas P. Hayes, and Gopal Pandurangan

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
The maximal independent set (MIS) is one of the most fundamental problems in distributed computing, and it has been studied intensively for over four decades. This paper focuses on the MIS problem in the radio network model, a standard model widely used to model wireless networks, particularly ad hoc wireless and sensor networks. Energy is a premium resource in these networks, which are typically battery-powered. Hence, designing distributed algorithms that use as little energy as possible is crucial. We use the well-established energy model where a node can be sleeping or awake in a round, and only the awake rounds (when it can send or listen) determine the energy complexity of the algorithm, which we want to minimize. We present new, more energy-efficient MIS algorithms in radio networks with arbitrary and unknown graph topology. We present algorithms for two popular variants of the radio model - with collision detection (CD) and without collision detection (no-CD). Specifically, we obtain the following results: 1) CD model: We present a randomized distributed MIS algorithm with energy complexity O(log n), round complexity O(log² n), and failure probability 1 / poly(n), where n is the network size. We show that our energy complexity is optimal by showing a matching Ω(log n) lower bound. 2) no-CD model: In the more challenging no-CD model, we present a randomized distributed MIS algorithm with energy complexity O(log²n log log n), round complexity O(log³ n log Δ), and failure probability 1 / poly(n). The energy complexity of our algorithm is significantly lower than the round (and energy) complexity of O(log³ n) of the best known distributed MIS algorithm of Davies [PODC 2023] for arbitrary graph topology.
Cite as

Dominick Banasik, Varsha Dani, Fabien Dufoulon, Aayush Gupta, Thomas P. Hayes, and Gopal Pandurangan. Energy-Efficient Maximal Independent Sets in Radio Networks. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 14:1-14:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{banasik_et_al:LIPIcs.DISC.2025.14,
  author =	{Banasik, Dominick and Dani, Varsha and Dufoulon, Fabien and Gupta, Aayush and Hayes, Thomas P. and Pandurangan, Gopal},
  title =	{{Energy-Efficient Maximal Independent Sets in Radio Networks}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{14:1--14:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.14},
  URN =		{urn:nbn:de:0030-drops-248311},
  doi =		{10.4230/LIPIcs.DISC.2025.14},
  annote =	{Keywords: Distributed Computing, Energy Complexity, Sleeping Model, Radio Networks, Maximal Independent Set}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2025.15
Exact and Heuristic Dynamic Taxi Sharing with Transfers Using Shortest-Path Speedup Techniques

Authors: Johannes Breitling and Moritz Laupichler

Published in: OASIcs, Volume 137, 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025)

Abstract
We introduce a first-of-its-kind efficient, exact algorithm for the dynamic taxi-sharing problem with single-transfer journeys, i.e., a dispatcher that assigns traveler requests to a fleet of shared taxi-like vehicles allowing transfers between vehicles. We extend an existing no-transfer solution by collecting all viable pickup and dropoff vehicles for a request and computing the optimal transfer point for every pair of vehicles. We analyze underlying shortest-path problems and employ state-of-the-art routing algorithms to compute distances on-the-fly, which serves as the basis of dispatching requests with exact and up-to-date travel time information. We utilize constraints on existing routes, pruning techniques for transfer points, and both instruction- and thread-level parallelism to speed up the computation of the best assignment for every traveler. In addition to the exact variant, we propose a tunable heuristic approach that sacrifices solution quality in favor of improved running time. We evaluate our algorithm on a large road network with realistic input sets (up to 150000 requests). We demonstrate the effectiveness of our speedup techniques and the heuristic. We show first results on the benefits of transfers for taxi sharing on dense request sets, proving that our algorithm is well suited for the analysis of taxi sharing with transfers on large input instances.
Cite as

Johannes Breitling and Moritz Laupichler. Exact and Heuristic Dynamic Taxi Sharing with Transfers Using Shortest-Path Speedup Techniques. In 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025). Open Access Series in Informatics (OASIcs), Volume 137, pp. 15:1-15:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{breitling_et_al:OASIcs.ATMOS.2025.15,
  author =	{Breitling, Johannes and Laupichler, Moritz},
  title =	{{Exact and Heuristic Dynamic Taxi Sharing with Transfers Using Shortest-Path Speedup Techniques}},
  booktitle =	{25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025)},
  pages =	{15:1--15:22},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-404-8},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{137},
  editor =	{Sauer, Jonas and Schmidt, Marie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2025.15},
  URN =		{urn:nbn:de:0030-drops-247718},
  doi =		{10.4230/OASIcs.ATMOS.2025.15},
  annote =	{Keywords: Dynamic taxi sharing, ride pooling, dial-a-ride problem, transfers, route planning}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2025.12
Separator-Based Alternative Paths in Customizable Contraction Hierarchies

Authors: Scott Bacherle, Thomas Bläsius, and Michael Zündorf

Published in: OASIcs, Volume 137, 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025)

Abstract
We propose an algorithm for computing alternatives to the shortest path in a road network, based on the speed-up technique CCH (customizable contraction hierarchy). Computing alternative paths is a well-studied problem, motivated by the fact that route-planning applications benefit from presenting different high-quality options the user can choose from. Another crucial feature of modern routing applications is the inclusion of live traffic, which requires speed-up techniques that allow efficient metric updates. Besides CCH, the other speed-up technique supporting metric updates is CRP (customizable route planning). Of the two, CCH is the more modern solution with the advantages of providing faster queries and being substantially simpler to implement efficiently. However, so far, CCH has been lacking a way of computing alternative paths. While for CRP, the commonly used plateau method for computing alternatives can be applied, this is not so straightforward for CCH. With this paper, we make CCH a viable option for alternative paths, by proposing a new separator-based approach to computing alternative paths that works hand-in-hand with the CCH data structure. With our experiments, we demonstrate that CCH can indeed be used to compute alternative paths efficiently. With this, we provide an alternative to CRP that is simpler and has lower query times.
Cite as

Scott Bacherle, Thomas Bläsius, and Michael Zündorf. Separator-Based Alternative Paths in Customizable Contraction Hierarchies. In 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025). Open Access Series in Informatics (OASIcs), Volume 137, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bacherle_et_al:OASIcs.ATMOS.2025.12,
  author =	{Bacherle, Scott and Bl\"{a}sius, Thomas and Z\"{u}ndorf, Michael},
  title =	{{Separator-Based Alternative Paths in Customizable Contraction Hierarchies}},
  booktitle =	{25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025)},
  pages =	{12:1--12:16},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-404-8},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{137},
  editor =	{Sauer, Jonas and Schmidt, Marie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2025.12},
  URN =		{urn:nbn:de:0030-drops-247685},
  doi =		{10.4230/OASIcs.ATMOS.2025.12},
  annote =	{Keywords: Alternative routes, realistic road networks, customizable contraction hierarchies, route planning, shortest paths}
}
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