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Documents authored by de Vos, Tijn

Document
DOI: 10.4230/LIPIcs.DISC.2025.26
Towards Constant Time Multi-Call Rumor Spreading on Small-Set Expanders

Authors: Emilio Cruciani, Sebastian Forster, and Tijn de Vos

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

Abstract
We study a multi-call variant of the classic PUSH&PULL rumor spreading process where nodes can contact k of their neighbors instead of a single one during both PUSH and PULL operations. We show that rumor spreading can be made faster at the cost of an increased amount of communication between the nodes. As a motivating example, consider the process on a complete graph of n nodes: while the standard PUSH&PULL protocol takes Θ(log n) rounds, we prove that our k-PUSH&PULL variant completes in Θ(log_{k} n) rounds, with high probability. We generalize this result in an expansion-sensitive way, as has been done for the classic PUSH&PULL protocol for different notions of expansion, e.g., conductance and vertex expansion. We consider small-set vertex expanders, graphs in which every sufficiently small subset of nodes has a large neighborhood, ensuring strong local connectivity. In particular, when the expansion parameter satisfies ϕ > 1, these graphs have a diameter of o(log n), as opposed to other standard notions of expansion. Since the graph’s diameter is a lower bound on the number of rounds required for rumor spreading, this makes small-set expanders particularly well-suited for fast information dissemination. We prove that k-PUSH&PULL takes O(log_{ϕ} n ⋅ log_{k} n) rounds in these expanders, with high probability. We complement this with a simple lower bound of Ω(log_{ϕ} n+ log_{k} n) rounds.
Cite as

Emilio Cruciani, Sebastian Forster, and Tijn de Vos. Towards Constant Time Multi-Call Rumor Spreading on Small-Set Expanders. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 26:1-26:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cruciani_et_al:LIPIcs.DISC.2025.26,
  author =	{Cruciani, Emilio and Forster, Sebastian and de Vos, Tijn},
  title =	{{Towards Constant Time Multi-Call Rumor Spreading on Small-Set Expanders}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{26:1--26:25},
  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.2025.26},
  URN =		{urn:nbn:de:0030-drops-248434},
  doi =		{10.4230/LIPIcs.DISC.2025.26},
  annote =	{Keywords: small set expansion, vertex expansion, rumor spreading, multi-call rumor spreading, push\&pull protocol}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2025.60
Brief Announcement: Distributed Sparsest Cut via Eigenvalue Estimation

Authors: Yannic Maus and Tijn de Vos

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

Abstract
We give new, improved bounds for approximating the sparsest cut value or in other words the conductance ϕ of a graph in the CONGEST model. As our main result, we present an algorithm running in O(log² n/ϕ) rounds in which every vertex outputs a value ̃ ϕ satisfying ϕ ≤ ̃ ϕ ≤ √{2.01ϕ}. In most regimes, our algorithm improves significantly over the previously fastest algorithm for the problem [Chen, Meierhans, Probst Gutenberg, Saranurak; SODA 25]. Additionally, our result generalizes to k-way conductance. We obtain these results, by approximating the eigenvalues of the normalized Laplacian matrix L: = I-Deg^{-1/2}ADeg^ {-1/2}, where, A is the adjacency matrix and Deg is the diagonal matrix with the weighted degrees on the diagonal. We show our algorithms are near-optimal by proving a lower bound for computing the smallest non-trivial eigenvalue of L, even in the stronger LOCAL model The previous state of the art sparsest cut algorithm is in the technical realm of expander decompositions. Our algorithms, on the other hand, are relatively simple and easy to implement. At the core, they rely on the well-known power method, which comes down to repeatedly multiplying the Laplacian with a vector. This operation can be performed in a single round in the CONGEST model. All our algorithms apply to weighted, undirected graphs. Our lower bounds apply even in unweighted graphs.
Cite as

Yannic Maus and Tijn de Vos. Brief Announcement: Distributed Sparsest Cut via Eigenvalue Estimation. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 60:1-60:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{maus_et_al:LIPIcs.DISC.2025.60,
  author =	{Maus, Yannic and de Vos, Tijn},
  title =	{{Brief Announcement: Distributed Sparsest Cut via Eigenvalue Estimation}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{60:1--60:7},
  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.2025.60},
  URN =		{urn:nbn:de:0030-drops-248763},
  doi =		{10.4230/LIPIcs.DISC.2025.60},
  annote =	{Keywords: CONGEST, Sparsest Cut, Laplacian, Eigenvalues, Spectral Graph Theory}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.58
New Tradeoffs for Decremental Approximate All-Pairs Shortest Paths

Authors: Michal Dory, Sebastian Forster, Yasamin Nazari, and Tijn de Vos

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We provide new tradeoffs between approximation and running time for the decremental all-pairs shortest paths (APSP) problem. For undirected graphs with m edges and n nodes undergoing edge deletions, we provide four new approximate decremental APSP algorithms, two for weighted and two for unweighted graphs. Our first result is (2+ε)-APSP with total update time Õ(m^{1/2}n^{3/2}) (when m = n^{1+c} for any constant 0 < c < 1). Prior to our work the fastest algorithm for weighted graphs with approximation at most 3 had total Õ(mn) update time for (1+ε)-APSP [Bernstein, SICOMP 2016]. Our second result is (2+ε, W_{u,v})-APSP with total update time Õ(nm^{3/4}), where the second term is an additive stretch with respect to W_{u,v}, the maximum weight on the shortest path from u to v. Our third result is (2+ε)-APSP for unweighted graphs in Õ(m^{7/4}) update time, which for sparse graphs (m = o(n^{8/7})) is the first subquadratic (2+ε)-approximation. Our last result for unweighted graphs is (1+ε, 2(k-1))-APSP, for k ≥ 2, with Õ(n^{2-1/k}m^{1/k}) total update time (when m = n^{1+c} for any constant c > 0). For comparison, in the special case of (1+ε, 2)-approximation, this improves over the state-of-the-art algorithm by [Henzinger, Krinninger, Nanongkai, SICOMP 2016] with total update time of Õ(n^{2.5}). All of our results are randomized, work against an oblivious adversary, and have constant query time.
Cite as

Michal Dory, Sebastian Forster, Yasamin Nazari, and Tijn de Vos. New Tradeoffs for Decremental Approximate All-Pairs Shortest Paths. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 58:1-58:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dory_et_al:LIPIcs.ICALP.2024.58,
  author =	{Dory, Michal and Forster, Sebastian and Nazari, Yasamin and de Vos, Tijn},
  title =	{{New Tradeoffs for Decremental Approximate All-Pairs Shortest Paths}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{58:1--58:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.58},
  URN =		{urn:nbn:de:0030-drops-202012},
  doi =		{10.4230/LIPIcs.ICALP.2024.58},
  annote =	{Keywords: Decremental Shortest Path, All-Pairs Shortest Paths}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.61
Faster Cut Sparsification of Weighted Graphs

Authors: Sebastian Forster and Tijn de Vos

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
A cut sparsifier is a reweighted subgraph that maintains the weights of the cuts of the original graph up to a multiplicative factor of (1±ε). This paper considers computing cut sparsifiers of weighted graphs of size O(nlog (n)/ε²). Our algorithm computes such a sparsifier in time O(m⋅min(α(n)log(m/n),log (n))), both for graphs with polynomially bounded and unbounded integer weights, where α(⋅) is the functional inverse of Ackermann’s function. This improves upon the state of the art by Benczúr and Karger (SICOMP 2015), which takes O(mlog² (n)) time. For unbounded weights, this directly gives the best known result for cut sparsification. Together with preprocessing by an algorithm of Fung et al. (SICOMP 2019), this also gives the best known result for polynomially-weighted graphs. Consequently, this implies the fastest approximate min-cut algorithm, both for graphs with polynomial and unbounded weights. In particular, we show that it is possible to adapt the state of the art algorithm of Fung et al. for unweighted graphs to weighted graphs, by letting the partial maximum spanning forest (MSF) packing take the place of the Nagamochi-Ibaraki (NI) forest packing. MSF packings have previously been used by Abraham at al. (FOCS 2016) in the dynamic setting, and are defined as follows: an M-partial MSF packing of G is a set ℱ = {F₁, … , F_M}, where F_i is a maximum spanning forest in G⧵ ⋃_{j = 1}^{i-1}F_j. Our method for computing (a sufficient estimation of) the MSF packing is the bottleneck in the running time of our sparsification algorithm.
Cite as

Sebastian Forster and Tijn de Vos. Faster Cut Sparsification of Weighted Graphs. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 61:1-61:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{forster_et_al:LIPIcs.ICALP.2022.61,
  author =	{Forster, Sebastian and de Vos, Tijn},
  title =	{{Faster Cut Sparsification of Weighted Graphs}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{61:1--61:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.61},
  URN =		{urn:nbn:de:0030-drops-164029},
  doi =		{10.4230/LIPIcs.ICALP.2022.61},
  annote =	{Keywords: Cut Sparsification, Graph Algorithms}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2021.16
An Improved Random Shift Algorithm for Spanners and Low Diameter Decompositions

Authors: Sebastian Forster, Martin Grösbacher, and Tijn de Vos

Published in: LIPIcs, Volume 217, 25th International Conference on Principles of Distributed Systems (OPODIS 2021)

Abstract
Spanners have been shown to be a powerful tool in graph algorithms. Many spanner constructions use a certain type of clustering at their core, where each cluster has small diameter and there are relatively few spanner edges between clusters. In this paper, we provide a clustering algorithm that, given k ≥ 2, can be used to compute a spanner of stretch 2k-1 and expected size O(n^{1+1/k}) in k rounds in the CONGEST model. This improves upon the state of the art (by Elkin, and Neiman [TALG'19]) by making the bounds on both running time and stretch independent of the random choices of the algorithm, whereas they only hold with high probability in previous results. Spanners are used in certain synchronizers, thus our improvement directly carries over to such synchronizers. Furthermore, for keeping the total number of inter-cluster edges small in low diameter decompositions, our clustering algorithm provides the following guarantees. Given β ∈ (0,1], we compute a low diameter decomposition with diameter bound O((log n)/β) such that each edge e ∈ E is an inter-cluster edge with probability at most β⋅ w(e) in O((log n)/β) rounds in the CONGEST model. Again, this improves upon the state of the art (by Miller, Peng, and Xu [SPAA'13]) by making the bounds on both running time and diameter independent of the random choices of the algorithm, whereas they only hold with high probability in previous results.
Cite as

Sebastian Forster, Martin Grösbacher, and Tijn de Vos. An Improved Random Shift Algorithm for Spanners and Low Diameter Decompositions. In 25th International Conference on Principles of Distributed Systems (OPODIS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 217, pp. 16:1-16:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{forster_et_al:LIPIcs.OPODIS.2021.16,
  author =	{Forster, Sebastian and Gr\"{o}sbacher, Martin and de Vos, Tijn},
  title =	{{An Improved Random Shift Algorithm for Spanners and Low Diameter Decompositions}},
  booktitle =	{25th International Conference on Principles of Distributed Systems (OPODIS 2021)},
  pages =	{16:1--16:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-219-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{217},
  editor =	{Bramas, Quentin and Gramoli, Vincent and Milani, Alessia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2021.16},
  URN =		{urn:nbn:de:0030-drops-157914},
  doi =		{10.4230/LIPIcs.OPODIS.2021.16},
  annote =	{Keywords: Spanner, low diameter decomposition, synchronizer, distributed graph algorithms}
}
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