12 Search Results for "Boldi, Paolo"

Document
DOI: 10.4230/LIPIcs.ITCS.2026.36
Beyond 2-Edge-Connectivity: Algorithms and Impossibility for Content-Oblivious Leader Election

Authors: Yi-Jun Chang, Lyuting Chen, and Haoran Zhou

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

Abstract
The content-oblivious model, introduced by Censor-Hillel, Cohen, Gelles, and Sela (PODC 2022; Distributed Computing 2023), captures an extremely weak form of communication where nodes can only send asynchronous, content-less pulses. They showed that in 2-edge-connected networks, any distributed algorithm can be simulated in the content-oblivious model, provided that a unique leader is designated a priori. Subsequent works of Frei, Gelles, Ghazy, and Nolin (DISC 2024) and Chalopin et al. (DISC 2025) developed content-oblivious leader election algorithms, first for unoriented rings and then for general 2-edge-connected graphs. These results establish that all graph problems are solvable in content-oblivious, 2-edge-connected networks. Much less is known about networks that are not 2-edge-connected. Censor-Hillel, Cohen, Gelles, and Sela showed that no non-constant function f(x,y) can be computed correctly by two parties using content-oblivious communication over a single edge, where one party holds x and the other holds y. This seemingly ruled out many natural graph problems on non-2-edge-connected graphs. In this work, we show that, with the knowledge of network topology G, leader election is possible in a wide range of graphs. Our main contributions are as follows: Impossibility: Graphs symmetric about an edge admit no randomized terminating leader election algorithm, even when nodes have unique identifiers and full knowledge of G. Leader election algorithms: Trees that are not symmetric about any edge admit a quiescently terminating leader election algorithm with topology knowledge, even in anonymous networks, using O(n²) messages, where n is the number of nodes. Moreover, even-diameter trees admit a terminating leader election given only the knowledge of the network diameter D = 2r, with message complexity O(nr). Necessity of topology knowledge: In the family of graphs 𝒢 = {P₃, P₅}, both the 3-path P₃ and the 5-path P₅ admit a quiescently terminating leader election if nodes know the topology exactly. However, if nodes only know that the underlying topology belongs to 𝒢, then terminating leader election is impossible.
Cite as

Yi-Jun Chang, Lyuting Chen, and Haoran Zhou. Beyond 2-Edge-Connectivity: Algorithms and Impossibility for Content-Oblivious Leader Election. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 36:1-36:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chang_et_al:LIPIcs.ITCS.2026.36,
  author =	{Chang, Yi-Jun and Chen, Lyuting and Zhou, Haoran},
  title =	{{Beyond 2-Edge-Connectivity: Algorithms and Impossibility for Content-Oblivious Leader Election}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{36:1--36:23},
  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.2026.36},
  URN =		{urn:nbn:de:0030-drops-253239},
  doi =		{10.4230/LIPIcs.ITCS.2026.36},
  annote =	{Keywords: Asynchronous model, fault tolerance, quiescent termination}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.4
How Pinball Wizards Simulate a Turing Machine

Authors: Rosemary U. Adejoh, Andreas Jakoby, Sneha Mohanty, and Christian Schindelhauer

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

Abstract
We introduce and investigate the computational complexity of a novel physical problem known as the Pinball Wizard problem. It involves an idealized pinball moving through a maze composed of one-way gates (outswing doors), plane walls, parabolic walls, moving plane walls, and bumpers that cause acceleration or deceleration. Given the initial position and velocity of the pinball, the task is to decide whether it will hit a specified target point. By simulating a two-stack pushdown automaton, we show that the problem is Turing-complete - even in two-dimensional space. In our construction, each step of the automaton corresponds to a constant number of reflections. Thus, deciding the Pinball Wizard problem is at least as hard as the Halting problem. Furthermore, our construction allows bumpers to be replaced with moving walls. In this case, even a ball moving at constant speed - a so-called ray particle - can be used, demonstrating that the Ray Particle Tracing problem is also Turing-complete.
Cite as

Rosemary U. Adejoh, Andreas Jakoby, Sneha Mohanty, and Christian Schindelhauer. How Pinball Wizards Simulate a Turing Machine. 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. 4:1-4:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{adejoh_et_al:LIPIcs.FSTTCS.2025.4,
  author =	{Adejoh, Rosemary U. and Jakoby, Andreas and Mohanty, Sneha and Schindelhauer, Christian},
  title =	{{How Pinball Wizards Simulate a Turing Machine}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{4:1--4:18},
  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.2025.4},
  URN =		{urn:nbn:de:0030-drops-250832},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.4},
  annote =	{Keywords: Pinball Wizard problem, Halting problem, Turing-complete}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.22
The Complexity Landscape of Dynamic Distributed Subgraph Finding

Authors: Yi-Jun Chang, Lyuting Chen, Yanyu Chen, Gopinath Mishra, and Mingyang Yang

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

Abstract
Bonne and Censor-Hillel (ICALP 2019) initiated the study of distributed subgraph finding in dynamic networks of limited bandwidth. For the case where the target subgraph is a clique, they determined the tight bandwidth complexity bounds in nearly all settings. However, several open questions remain, and very little is known about finding subgraphs beyond cliques. In this work, we consider these questions and explore subgraphs beyond cliques in the deterministic setting. For finding cliques, we establish an Ω(log log n) bandwidth lower bound for one-round membership-detection under edge insertions only and an Ω(log log log n) bandwidth lower bound for one-round detection under both edge insertions and node insertions. Moreover, we demonstrate new algorithms to show that our lower bounds are tight in bounded-degree networks when the target subgraph is a triangle. Prior to our work, no lower bounds were known for these problems. For finding subgraphs beyond cliques, we present a complete characterization of the bandwidth complexity of the membership-listing problem for every target subgraph, every number of rounds, and every type of topological change: node insertions, node deletions, edge insertions, and edge deletions. We also show partial characterizations for one-round membership-detection and listing.
Cite as

Yi-Jun Chang, Lyuting Chen, Yanyu Chen, Gopinath Mishra, and Mingyang Yang. The Complexity Landscape of Dynamic Distributed Subgraph Finding. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 22:1-22:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chang_et_al:LIPIcs.DISC.2025.22,
  author =	{Chang, Yi-Jun and Chen, Lyuting and Chen, Yanyu and Mishra, Gopinath and Yang, Mingyang},
  title =	{{The Complexity Landscape of Dynamic Distributed Subgraph Finding}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{22:1--22:20},
  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.2025.22},
  URN =		{urn:nbn:de:0030-drops-248399},
  doi =		{10.4230/LIPIcs.DISC.2025.22},
  annote =	{Keywords: Distributed algorithms, dynamic algorithms, subgraph finding}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.9
MorphisHash: Improving Space Efficiency of ShockHash for Minimal Perfect Hashing

Authors: Stefan Hermann

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

Abstract
A minimal perfect hash function (MPHF) maps a set of n keys to unique positions {1, …, n}. Representing an MPHF requires at least log₂(e)≈ 1.443 bits per key. ShockHash is a technique to construct an MPHF and requires just slightly more space. It gives each key two random candidate positions. If each key can be mapped to one of its two candidate positions such that there is exactly one key mapped to each position, then an MPHF is found. If not, ShockHash repeats the process with a new set of random candidate positions. ShockHash has to store how many repetitions were required and for each key to which of the two candidate positions it is mapped. However, when a given set of candidate positions can be used as MPHF then there is not only one but multiple ways of mapping the keys to one of their candidate positions such that the mapping results in an MPHF. This redundancy makes up for the majority of the remaining space overhead in ShockHash. In this paper, we present MorphisHash which almost completely eliminates this redundancy. Our theoretical result is that MorphisHash saves Θ(ln(n)) bits in expectation compared to ShockHash. This corresponds to a factor of 20 less space overhead in practice. Just like ShockHash, MorphisHash can be used as a building block within RecSplit to obtain MorphisHash-RS. When compared for same space consumption, MorphisHash-RS can be constructed up to 21 times faster than ShockHash-RS. The technique to accomplish this might be of a more general interest to compress data structures.
Cite as

Stefan Hermann. MorphisHash: Improving Space Efficiency of ShockHash for Minimal Perfect Hashing. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 9:1-9:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hermann:LIPIcs.ESA.2025.9,
  author =	{Hermann, Stefan},
  title =	{{MorphisHash: Improving Space Efficiency of ShockHash for Minimal Perfect Hashing}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{9:1--9:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.9},
  URN =		{urn:nbn:de:0030-drops-244779},
  doi =		{10.4230/LIPIcs.ESA.2025.9},
  annote =	{Keywords: compressed data structure, perfect hashing, random graph, pseudoforest, component}
}
Document
DOI: 10.4230/LIPIcs.SEA.2025.11
CluStRE: Streaming Graph Clustering with Multi-Stage Refinement

Authors: Adil Chhabra, Shai Dorian Peretz, and Christian Schulz

Published in: LIPIcs, Volume 338, 23rd International Symposium on Experimental Algorithms (SEA 2025)

Abstract
We present CluStRE, a novel streaming graph clustering algorithm that balances computational efficiency with high-quality clustering using multi-stage refinement. Unlike traditional in-memory clustering approaches, CluStRE processes graphs in a streaming setting, significantly reducing memory overhead while leveraging re-streaming and evolutionary heuristics to improve solution quality. Our method dynamically constructs a quotient graph, enabling modularity-based optimization while efficiently handling large-scale graphs. We introduce multiple configurations of CluStRE to provide trade-offs between speed, memory consumption, and clustering quality. Experimental evaluations demonstrate that CluStRE improves solution quality by 89.8%, operates 2.6× faster, and uses less than two-thirds of the memory required by the state-of-the-art streaming clustering algorithm on average. Moreover, our strongest mode enhances solution quality by up to 150% on average. With this, CluStRE achieves comparable solution quality to in-memory algorithms, i.e. over 96% of the quality of clustering approaches, including Louvain, effectively bridging the gap between streaming and traditional clustering methods.
Cite as

Adil Chhabra, Shai Dorian Peretz, and Christian Schulz. CluStRE: Streaming Graph Clustering with Multi-Stage Refinement. In 23rd International Symposium on Experimental Algorithms (SEA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 338, pp. 11:1-11:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chhabra_et_al:LIPIcs.SEA.2025.11,
  author =	{Chhabra, Adil and Dorian Peretz, Shai and Schulz, Christian},
  title =	{{CluStRE: Streaming Graph Clustering with Multi-Stage Refinement}},
  booktitle =	{23rd International Symposium on Experimental Algorithms (SEA 2025)},
  pages =	{11:1--11:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-375-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{338},
  editor =	{Mutzel, Petra 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.SEA.2025.11},
  URN =		{urn:nbn:de:0030-drops-232493},
  doi =		{10.4230/LIPIcs.SEA.2025.11},
  annote =	{Keywords: graph clustering, community, streaming, online, memetic, evolutionary}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.114
Optimal Static Fully Indexable Dictionaries

Authors: Jingxun Liang and Renfei Zhou

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

Abstract
Fully indexable dictionaries (FID) store sets of integer keys while supporting rank/select queries. They serve as basic building blocks in many succinct data structures. Despite the great importance of FIDs, no known FID is succinct with efficient query time when the universe size U is a large polynomial in the number of keys n, which is the conventional parameter regime for dictionary problems. In this paper, we design an FID that uses log binom(U,n) + n/((log U/t)^{Ω(t)}) bits of space, and answers rank/select queries in O(t + log log n) time in the worst case, for any parameter 1 ≤ t ≤ log n / log log n, provided U = n^{1 + Θ(1)}. This time-space trade-off matches known lower bounds for FIDs [Pǎtraşcu and Thorup, 2006; Pǎtraşcu and Viola, 2010; Viola, 2023] when t ≤ log^{0.99} n. Our techniques also lead to efficient succinct data structures for the fundamental problem of maintaining n integers each of 𝓁 = Θ(log n) bits and supporting partial-sum queries, with a trade-off between O(t) query time and n𝓁 + n / (log n / t)^{Ω(t)} bits of space. Prior to this work, no known data structure for the partial-sum problem achieves constant query time with n 𝓁 + o(n) bits of space usage.
Cite as

Jingxun Liang and Renfei Zhou. Optimal Static Fully Indexable Dictionaries. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 114:1-114:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{liang_et_al:LIPIcs.ICALP.2025.114,
  author =	{Liang, Jingxun and Zhou, Renfei},
  title =	{{Optimal Static Fully Indexable Dictionaries}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{114:1--114:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.114},
  URN =		{urn:nbn:de:0030-drops-234918},
  doi =		{10.4230/LIPIcs.ICALP.2025.114},
  annote =	{Keywords: data structures, dictionaries, space efficiency}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.32
A Faster Algorithm for Constrained Correlation Clustering

Authors: Nick Fischer, Evangelos Kipouridis, Jonas Klausen, and Mikkel Thorup

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
In the Correlation Clustering problem we are given n nodes, and a preference for each pair of nodes indicating whether we prefer the two endpoints to be in the same cluster or not. The output is a clustering inducing the minimum number of violated preferences. In certain cases, however, the preference between some pairs may be too important to be violated. The constrained version of this problem specifies pairs of nodes that must be in the same cluster as well as pairs that must not be in the same cluster (hard constraints). The output clustering has to satisfy all hard constraints while minimizing the number of violated preferences. Constrained Correlation Clustering is APX-Hard and has been approximated within a factor 3 by van Zuylen et al. [SODA '07]. Their algorithm is based on rounding an LP with Θ(n³) constraints, resulting in an Ω(n^{3ω}) running time. In this work, using a more combinatorial approach, we show how to approximate this problem significantly faster at the cost of a slightly weaker approximation factor. In particular, our algorithm runs in Õ(n³) time (notice that the input size is Θ(n²)) and approximates Constrained Correlation Clustering within a factor 16. To achieve our result we need properties guaranteed by a particular influential algorithm for (unconstrained) Correlation Clustering, the CC-PIVOT algorithm. This algorithm chooses a pivot node u, creates a cluster containing u and all its preferred nodes, and recursively solves the rest of the problem. It is known that selecting pivots at random gives a 3-approximation. As a byproduct of our work, we provide a derandomization of the CC-PIVOT algorithm that still achieves the 3-approximation; furthermore, we show that there exist instances where no ordering of the pivots can give a (3-ε)-approximation, for any constant ε. Finally, we introduce a node-weighted version of Correlation Clustering, which can be approximated within factor 3 using our insights on Constrained Correlation Clustering. As the general weighted version of Correlation Clustering would require a major breakthrough to approximate within a factor o(log n), Node-Weighted Correlation Clustering may be a practical alternative.
Cite as

Nick Fischer, Evangelos Kipouridis, Jonas Klausen, and Mikkel Thorup. A Faster Algorithm for Constrained Correlation Clustering. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 32:1-32:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fischer_et_al:LIPIcs.STACS.2025.32,
  author =	{Fischer, Nick and Kipouridis, Evangelos and Klausen, Jonas and Thorup, Mikkel},
  title =	{{A Faster Algorithm for Constrained Correlation Clustering}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{32:1--32:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine 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.2025.32},
  URN =		{urn:nbn:de:0030-drops-228585},
  doi =		{10.4230/LIPIcs.STACS.2025.32},
  annote =	{Keywords: Clustering, Constrained Correlation Clustering, Approximation}
}
Document
DOI: 10.4230/LIPIcs.SEA.2024.2
Engineering Zuffix Arrays

Authors: Paolo Boldi, Stefano Marchini, and Sebastiano Vigna

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract
Searching patterns in long strings is a classical algorithmic problem with countless practical applications. Suffix trees and suffix arrays (and their variants) are a long-established solution that yields linear-time search (in the size of the pattern). In [Paolo Boldi and Sebastiano Vigna, 2018] it is shown that a z-map gadget can be attached to (enhanced) suffix arrays to improve their theoretical query time, obtaining a data structure called zuffix array. The main contribution of this paper is to show that a carefully engineered implementation of the z-map gadget does provide significant speedups with respect to enhanced suffix arrays on real-world datasets, albeit doubling the required space. In particular, for large alphabets we observe a sevenfold improvement in query time with respect to enhanced suffix arrays; even in the worst case (small alphabets), the query time is almost halved. Thus, zuffix arrays provide a very interesting new point in the space-time tradeoff spectrum.
Cite as

Paolo Boldi, Stefano Marchini, and Sebastiano Vigna. Engineering Zuffix Arrays. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 2:1-2:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{boldi_et_al:LIPIcs.SEA.2024.2,
  author =	{Boldi, Paolo and Marchini, Stefano and Vigna, Sebastiano},
  title =	{{Engineering Zuffix Arrays}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{2:1--2:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.2},
  URN =		{urn:nbn:de:0030-drops-203677},
  doi =		{10.4230/LIPIcs.SEA.2024.2},
  annote =	{Keywords: Suffix trees, suffix arrays, z-fast tries}
}
Document
Survey
DOI: 10.4230/TGDK.1.1.12
Structural Summarization of Semantic Graphs Using Quotients

Authors: Ansgar Scherp, David Richerby, Till Blume, Michael Cochez, and Jannik Rau

Published in: TGDK, Volume 1, Issue 1 (2023): Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge, Volume 1, Issue 1

Abstract
Graph summarization is the process of computing a compact version of an input graph while preserving chosen features of its structure. We consider semantic graphs where the features include edge labels and label sets associated with a vertex. Graph summaries are typically much smaller than the original graph. Applications that depend on the preserved features can perform their tasks on the summary, but much faster or with less memory overhead, while producing the same outcome as if they were applied on the original graph. In this survey, we focus on structural summaries based on quotients that organize vertices in equivalence classes of shared features. Structural summaries are particularly popular for semantic graphs and have the advantage of defining a precise graph-based output. We consider approaches and algorithms for both static and temporal graphs. A common example of quotient-based structural summaries is bisimulation, and we discuss this in detail. While there exist other surveys on graph summarization, to the best of our knowledge, we are the first to bring in a focused discussion on quotients, bisimulation, and their relation. Furthermore, structural summarization naturally connects well with formal logic due to the discrete structures considered. We complete the survey with a brief description of approaches beyond structural summaries.
Cite as

Ansgar Scherp, David Richerby, Till Blume, Michael Cochez, and Jannik Rau. Structural Summarization of Semantic Graphs Using Quotients. In Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge (TGDK), Volume 1, Issue 1, pp. 12:1-12:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{scherp_et_al:TGDK.1.1.12,
  author =	{Scherp, Ansgar and Richerby, David and Blume, Till and Cochez, Michael and Rau, Jannik},
  title =	{{Structural Summarization of Semantic Graphs Using Quotients}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{12:1--12:25},
  ISSN =	{2942-7517},
  year =	{2023},
  volume =	{1},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.1.1.12},
  URN =		{urn:nbn:de:0030-drops-194862},
  doi =		{10.4230/TGDK.1.1.12},
  annote =	{Keywords: graph summarization, quotients, stratified bisimulation}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2022.28
Self-Stabilizing Clock Synchronization in Dynamic Networks

Authors: Bernadette Charron-Bost and Louis Penet de Monterno

Published in: LIPIcs, Volume 253, 26th International Conference on Principles of Distributed Systems (OPODIS 2022)

Abstract
We consider the fundamental problem of periodic clock synchronization in a synchronous multi-agent system. Each agent holds a clock with an arbitrary initial value, and clocks must eventually be congruent, modulo some positive integer P. Previous algorithms worked in static networks with drastic connectivity properties and assumed that global informations are available at each node. In this paper, we propose a finite-state algorithm for time-varying topologies that does not require any global knowledge on the network. The only assumption is the existence of some integer D such that any two nodes can communicate in each sequence of D consecutive rounds, which extends the notion of strong connectivity in static network to dynamic communication patterns. The smallest such D is called the dynamic diameter of the network. If an upper bound on the diameter is provided, then our algorithm achieves synchronization within 3D rounds, whatever the value of the upper bound. Otherwise, using an adaptive mechanism, synchronization is achieved with little performance overhead. Our algorithm is parameterized by a function g, which can be tuned to favor either time or space complexity. Then, we explore a further relaxation of the connectivity requirement: our algorithm still works if there exists a positive integer R such that the network is rooted over each sequence of R consecutive rounds, and if eventually the set of roots is stable. In particular, it works in any rooted static network.
Cite as

Bernadette Charron-Bost and Louis Penet de Monterno. Self-Stabilizing Clock Synchronization in Dynamic Networks. In 26th International Conference on Principles of Distributed Systems (OPODIS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 253, pp. 28:1-28:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{charronbost_et_al:LIPIcs.OPODIS.2022.28,
  author =	{Charron-Bost, Bernadette and Penet de Monterno, Louis},
  title =	{{Self-Stabilizing Clock Synchronization in Dynamic Networks}},
  booktitle =	{26th International Conference on Principles of Distributed Systems (OPODIS 2022)},
  pages =	{28:1--28:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-265-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{253},
  editor =	{Hillel, Eshcar and Palmieri, Roberto and Rivi\`{e}re, Etienne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2022.28},
  URN =		{urn:nbn:de:0030-drops-176480},
  doi =		{10.4230/LIPIcs.OPODIS.2022.28},
  annote =	{Keywords: Self-stabilization, Clock synchronization, Dynamic networks}
}
Document
DOI: 10.4230/LIPIcs.FUN.2018.10
Kings, Name Days, Lazy Servants and Magic

Authors: Paolo Boldi and Sebastiano Vigna

Published in: LIPIcs, Volume 100, 9th International Conference on Fun with Algorithms (FUN 2018)

Abstract
Once upon a time, a king had a very, very long list of names of his subjects. The king was also a bit obsessed with name days: every day he would ask his servants to look the list for all persons having their name day. Reading every day the whole list was taking an enormous amount of time to the king's servants. One day, the chancellor had a magnificent idea: he wrote a book with instructions. The number of pages in the book was equal to the number of names, but following the instructions one could find all people having their name day by looking at only a few pages - in fact, as many pages as the length of the name - and just glimpsing at the list. Everybody was happy, but in time the king's servants got lazy: when the name was very long they would find excuses to avoid looking at so many pages, and some name days were skipped. Desperate, the king made a call through its reign, and a fat sorceress answered. There was a way to look at much, much fewer pages using an additional magic book. But sometimes, very rarely, it would not work (magic does not always work). The king accepted the offer, and name days parties restarted. Only, once every a few thousand years, the magic book fails, and the assistants have to go by the chancellor book. So the parties start a bit later. But they start anyway.
Cite as

Paolo Boldi and Sebastiano Vigna. Kings, Name Days, Lazy Servants and Magic. In 9th International Conference on Fun with Algorithms (FUN 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 100, pp. 10:1-10:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{boldi_et_al:LIPIcs.FUN.2018.10,
  author =	{Boldi, Paolo and Vigna, Sebastiano},
  title =	{{Kings, Name Days, Lazy Servants and Magic}},
  booktitle =	{9th International Conference on Fun with Algorithms (FUN 2018)},
  pages =	{10:1--10:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-067-5},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{100},
  editor =	{Ito, Hiro and Leonardi, Stefano and Pagli, Linda and Prencipe, Giuseppe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2018.10},
  URN =		{urn:nbn:de:0030-drops-88017},
  doi =		{10.4230/LIPIcs.FUN.2018.10},
  annote =	{Keywords: Suffix trees, suffix arrays, z-fast tries, prefix search}
}
Document
DOI: 10.4230/DagSemProc.07071.3
A Deeper Investigation of PageRank as a Function of the Damping Factor

Authors: Paolo Boldi, Massimo Santini, and Sebastiano Vigna

Published in: Dagstuhl Seminar Proceedings, Volume 7071, Web Information Retrieval and Linear Algebra Algorithms (2007)

Abstract
PageRank is defined as the stationary state of a Markov chain. The chain is obtained by perturbing the transition matrix induced by a web graph with a damping factor $alpha$ that spreads uniformly part of the rank. The choice of $alpha$ is eminently empirical, and in most cases the original suggestion $alpha=0.85$ by Brin and Page is still used. In this paper, we give a mathematical analysis of PageRank when $alpha$ changes. In particular, we show that, contrarily to popular belief, for real-world graphs values of $alpha$ close to $1$ do not give a more meaningful ranking. Then, we give closed-form formulae for PageRank derivatives of any order, and by proving that the $k$-th iteration of the Power Method gives exactly the PageRank value obtained using a Maclaurin polynomial of degree $k$, we show how to obtain an approximation of the derivatives. Finally, we view PageRank as a linear operator acting on the preference vector and show a tight connection between iterated computation and derivation.
Cite as

Paolo Boldi, Massimo Santini, and Sebastiano Vigna. A Deeper Investigation of PageRank as a Function of the Damping Factor. In Web Information Retrieval and Linear Algebra Algorithms. Dagstuhl Seminar Proceedings, Volume 7071, pp. 1-19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{boldi_et_al:DagSemProc.07071.3,
  author =	{Boldi, Paolo and Santini, Massimo and Vigna, Sebastiano},
  title =	{{A Deeper Investigation of PageRank as a Function of the Damping Factor}},
  booktitle =	{Web Information Retrieval and Linear Algebra Algorithms},
  pages =	{1--19},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7071},
  editor =	{Andreas Frommer and Michael W. Mahoney and Daniel B. Szyld},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07071.3},
  URN =		{urn:nbn:de:0030-drops-10722},
  doi =		{10.4230/DagSemProc.07071.3},
  annote =	{Keywords: PageRank, damping factor, Markov chains}
}
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