7 Search Results for "Christiansen, Aleksander B. G."

Document
DOI: 10.4230/LIPIcs.DISC.2025.12
Distributed Computation with Local Advice

Authors: Alkida Balliu, Sebastian Brandt, Fabian Kuhn, Krzysztof Nowicki, Dennis Olivetti, Eva Rotenberg, and Jukka Suomela

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

Abstract
Algorithms with advice have received ample attention in the distributed and online settings, and they have recently proven useful also in dynamic settings. In this work we study local computation with advice: the goal is to solve a graph problem Π with a distributed algorithm in T(Δ) communication rounds, for some function T that only depends on the maximum degree Δ of the graph, and the key question is how many bits of advice per node are needed. Some of our results regard Locally Checkable Labeling problems (LCLs), which is an important family of problems that includes various coloring and orientation problems on finite-degree graphs. These are constraint-satisfaction graph problems that can be defined with a finite set of valid input/output-labeled neighborhoods. Our main results are: 1) Any locally checkable labeling problem can be solved with only 1 bit of advice per node in graphs with sub-exponential growth (the number of nodes within radius r is sub-exponential in r; for example, grids are such graphs). Moreover, we can make the set of nodes that carry advice bits arbitrarily sparse. As a corollary, any locally checkable labeling problem admits a locally checkable proof with 1 bit per node in graphs with sub-exponential growth. 2) The assumption of sub-exponential growth is complemented by a conditional lower bound: assuming the Exponential-Time Hypothesis, there are locally checkable labeling problems that cannot be solved in general with any constant number of bits per node. 3) In any graph we can find an almost-balanced orientation (indegrees and outdegrees differ by at most one) with 1 bit of advice per node, and again we can make the advice arbitrarily sparse. As a corollary, we can also compress an arbitrary subset of edges so that a node of degree d stores only d/2 + 2 bits, and we can decompress it locally, in T(Δ) rounds. 4) In any graph of maximum degree Δ, we can find a Δ-coloring (if it exists) with 1 bit of advice per node, and again, we can make the advice arbitrarily sparse. 5) In any 3-colorable graph, we can find a 3-coloring with 1 bit of advice per node. As a corollary, in bounded-degree graphs there is a locally checkable proof that certifies 3-colorability with 1 bit of advice per node, while prior work shows that this is not possible with a proof labeling scheme (PLS), which is a more restricted setting where the verifier can only see up to distance 1. Our work shows that for many problems the key threshold is not whether we can achieve 1 bit of advice per node, but whether we can make the advice arbitrarily sparse. To formalize this idea, we develop a general framework of composable schemas that enables us to build algorithms for local computation with advice in a modular fashion: once we have (1) a schema for solving Π₁ and (2) a schema for solving Π₂ assuming an oracle for Π₁, we can also compose them and obtain (3) a schema that solves Π₂ without the oracle. It turns out that many natural problems admit composable schemas, all of them can be solved with only 1 bit of advice, and we can make the advice arbitrarily sparse.
Cite as

Alkida Balliu, Sebastian Brandt, Fabian Kuhn, Krzysztof Nowicki, Dennis Olivetti, Eva Rotenberg, and Jukka Suomela. Distributed Computation with Local Advice. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 12:1-12:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{balliu_et_al:LIPIcs.DISC.2025.12,
  author =	{Balliu, Alkida and Brandt, Sebastian and Kuhn, Fabian and Nowicki, Krzysztof and Olivetti, Dennis and Rotenberg, Eva and Suomela, Jukka},
  title =	{{Distributed Computation with Local Advice}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{12:1--12:19},
  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.2025.12},
  URN =		{urn:nbn:de:0030-drops-248295},
  doi =		{10.4230/LIPIcs.DISC.2025.12},
  annote =	{Keywords: Distributed graph algorithms, LOCAL model, computation with advice, locally checkable labeling problems, proof labeling schemes, locally checkable proofs, graph coloring, exponential-time hypothesis}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.48
Improved Streaming Edge Coloring

Authors: Shiri Chechik, Hongyi Chen, and Tianyi Zhang

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

Abstract
Given a graph, an edge coloring assigns colors to edges so that no pairs of adjacent edges share the same color. We are interested in edge coloring algorithms under the W-streaming model. In this model, the algorithm does not have enough memory to hold the entire graph, so the edges of the input graph are read from a data stream one by one in an unknown order, and the algorithm needs to print a valid edge coloring in an output stream. The performance of the algorithm is measured by the amount of space and the number of different colors it uses. This streaming edge coloring problem has been studied by several works in recent years. When the input graph contains n vertices and has maximum vertex degree Δ, it is known that in the W-streaming model, an O(Δ²)-edge coloring can be computed deterministically with Õ(n) space [Ansari, Saneian, and Zarrabi-Zadeh, 2022], or an O(Δ^{1.5})-edge coloring can be computed by a Õ(n)-space randomized algorithm [Behnezhad, Saneian, 2024] [Chechik, Mukhtar, Zhang, 2024]. In this paper, we achieve polynomial improvement over previous results. Specifically, we show how to improve the number of colors to Õ(Δ^{4/3+ε}) using space Õ(n) deterministically, for any constant ε > 0. This is the first deterministic result that bypasses the quadratic bound on the number of colors while using near-linear space.
Cite as

Shiri Chechik, Hongyi Chen, and Tianyi Zhang. Improved Streaming Edge Coloring. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 48:1-48:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chechik_et_al:LIPIcs.ICALP.2025.48,
  author =	{Chechik, Shiri and Chen, Hongyi and Zhang, Tianyi},
  title =	{{Improved Streaming Edge Coloring}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{48:1--48:18},
  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.2025.48},
  URN =		{urn:nbn:de:0030-drops-234257},
  doi =		{10.4230/LIPIcs.ICALP.2025.48},
  annote =	{Keywords: edge coloring, streaming}
}
Document
DOI: 10.4230/LIPIcs.SAND.2025.4
On b-Matching and Fully-Dynamic Maximum k-Edge Coloring

Authors: Antoine El-Hayek, Kathrin Hanauer, and Monika Henzinger

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

Abstract
Given a graph G that undergoes a sequence of edge insertions and deletions, we study the Maximum k-Edge Coloring problem (MkEC): Having access to k different colors, color as many edges of G as possible such that no two adjacent edges share the same color. While this problem is different from simply maintaining a b-matching with b = k, the two problems are related. However, maximum b-matching can be solved efficiently in the static setting, whereas MkEC is NP-hard and even APX-hard for k ≥ 2. We present new results on both problems: For b-matching, we show a new integrality gap result and we adapt Wajc’s matching sparsification scheme [David Wajc, 2020] for the case where b is a constant. Using these as basis, we give three new algorithms for the dynamic MkEC problem: Our MatchO algorithm builds on the dynamic (2+ε)-approximation algorithm of Bhattacharya, Gupta, and Mohan [Sayan Bhattacharya et al., 2017] for b-matching and achieves a (2+ε)(k+1)/k-approximation in O(poly(log n, ε^-1)) update time against an oblivious adversary. Our MatchA algorithm builds on the dynamic (7+ε)-approximation algorithm by Bhattacharya, Henzinger, and Italiano [Sayan Bhattacharya et al., 2015] for fractional b-matching and achieves a (7+ε)(3k+3)/(3k-1)-approximation in O(poly(log n, ε^-1)) update time against an adaptive adversary. Moreover, our reductions use the dynamic b-matching algorithm as a black box, so any future improvement in the approximation ratio for dynamic b-matching will automatically translate into a better approximation ratio for our algorithms. Finally, we present a greedy algorithm with O(Δ+k) update time, which guarantees a 2.16 approximation factor.
Cite as

Antoine El-Hayek, Kathrin Hanauer, and Monika Henzinger. On b-Matching and Fully-Dynamic Maximum k-Edge Coloring. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 4:1-4:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{elhayek_et_al:LIPIcs.SAND.2025.4,
  author =	{El-Hayek, Antoine and Hanauer, Kathrin and Henzinger, Monika},
  title =	{{On b-Matching and Fully-Dynamic Maximum k-Edge Coloring}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{4:1--4:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-368-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{330},
  editor =	{Meeks, Kitty and Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.4},
  URN =		{urn:nbn:de:0030-drops-230571},
  doi =		{10.4230/LIPIcs.SAND.2025.4},
  annote =	{Keywords: dynamic algorithm, graph algorithm, matching, b-matching, edge coloring}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.7
Faster Edge Coloring by Partition Sieving

Authors: Shyan Akmal and Tomohiro Koana

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

Abstract
In the Edge Coloring problem, we are given an undirected graph G with n vertices and m edges, and are tasked with finding the smallest positive integer k so that the edges of G can be assigned k colors in such a way that no two edges incident to the same vertex are assigned the same color. Edge Coloring is a classic NP-hard problem, and so significant research has gone into designing fast exponential-time algorithms for solving Edge Coloring and its variants exactly. Prior work showed that Edge Coloring can be solved in 2^mpoly(n) time and polynomial space, and in graphs with average degree d in 2^{(1-ε_d)m}⋅poly(n) time and exponential space, where ε_d = (1/d)^Θ(d³). We present an algorithm that solves Edge Coloring in 2^{m-3n/5}⋅poly(n) time and polynomial space. Our result is the first algorithm for this problem which simultaneously runs in faster than 2^m⋅poly(m) time and uses only polynomial space. In graphs of average degree d, our algorithm runs in 2^{(1-6/(5d))m}⋅poly(n) time, which has far better dependence in d than previous results. We also consider a generalization of Edge Coloring called List Edge Coloring, where each edge e in the input graph comes with a list L_e ⊆ {1, …, k} of colors, and we must determine whether we can assign each edge a color from its list so that no two edges incident to the same vertex receive the same color. We show that this problem can be solved in 2^{(1-6/(5k))m}⋅poly(n) time and polynomial space. The previous best algorithm for List Edge Coloring took 2^m⋅poly(n) time and space. Our algorithms are algebraic, and work by constructing a special polynomial P based off the input graph that contains a multilinear monomial (i.e., a monomial where every variable has degree at most one) if and only if the answer to the List Edge Coloring problem on the input graph is YES. We then solve the problem by detecting multilinear monomials in P. Previous work also employed such monomial detection techniques to solve Edge Coloring. We obtain faster algorithms both by carefully constructing our polynomial P, and by improving the runtimes for certain structured monomial detection problems using a technique we call partition sieving.
Cite as

Shyan Akmal and Tomohiro Koana. Faster Edge Coloring by Partition Sieving. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{akmal_et_al:LIPIcs.STACS.2025.7,
  author =	{Akmal, Shyan and Koana, Tomohiro},
  title =	{{Faster Edge Coloring by Partition Sieving}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{7:1--7:18},
  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.2025.7},
  URN =		{urn:nbn:de:0030-drops-228328},
  doi =		{10.4230/LIPIcs.STACS.2025.7},
  annote =	{Keywords: Coloring, Edge coloring, Chromatic index, Matroid, Pfaffian, Algebraic algorithm}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2024.20
Sparsity-Parameterised Dynamic Edge Colouring

Authors: Aleksander B. G. Christiansen, Eva Rotenberg, and Juliette Vlieghe

Published in: LIPIcs, Volume 294, 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024)

Abstract
We study the edge-colouring problem, and give efficient algorithms where the number of colours is parameterised by the graph’s arboricity, α. In a dynamic graph, subject to insertions and deletions, we give a deterministic algorithm that updates a proper Δ + O(α) edge colouring in poly(log n) amortized time. Our algorithm is fully adaptive to the current value of the maximum degree and arboricity. In this fully-dynamic setting, the state-of-the-art edge-colouring algorithms are either a randomised algorithm using (1 + ε)Δ colours in poly(log n, ε^{-1}) time per update, or the naive greedy algorithm which is a deterministic 2Δ -1 edge colouring with log(Δ) update time. Compared to the (1+ε)Δ algorithm, our algorithm is deterministic and asymptotically faster, and when α is sufficiently small compared to Δ, it even uses fewer colours. In particular, ours is the first Δ+O(1) edge-colouring algorithm for dynamic forests, and dynamic planar graphs, with polylogarithmic update time. Additionally, in the static setting, we show that we can find a proper edge colouring with Δ + 2α colours in O(mlog n) time. Moreover, the colouring returned by our algorithm has the following local property: every edge uv is coloured with a colour in {1, max{deg(u), deg(v)} + 2α}. The time bound matches that of the greedy algorithm that computes a 2Δ-1 colouring of the graph’s edges, and improves the number of colours when α is sufficiently small compared to Δ.
Cite as

Aleksander B. G. Christiansen, Eva Rotenberg, and Juliette Vlieghe. Sparsity-Parameterised Dynamic Edge Colouring. In 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 294, pp. 20:1-20:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{christiansen_et_al:LIPIcs.SWAT.2024.20,
  author =	{Christiansen, Aleksander B. G. and Rotenberg, Eva and Vlieghe, Juliette},
  title =	{{Sparsity-Parameterised Dynamic Edge Colouring}},
  booktitle =	{19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024)},
  pages =	{20:1--20:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-318-8},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{294},
  editor =	{Bodlaender, Hans L.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2024.20},
  URN =		{urn:nbn:de:0030-drops-200608},
  doi =		{10.4230/LIPIcs.SWAT.2024.20},
  annote =	{Keywords: edge colouring, arboricity, hierarchical partition, dynamic algorithms, amortized analysis}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2022.34
On Dynamic α + 1 Arboricity Decomposition and Out-Orientation

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

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

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

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

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@InProceedings{christiansen_et_al:LIPIcs.MFCS.2022.34,
  author =	{Christiansen, Aleksander B. G. and Holm, Jacob and Rotenberg, Eva and Thomassen, Carsten},
  title =	{{On Dynamic \alpha + 1 Arboricity Decomposition and Out-Orientation}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{34:1--34:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.34},
  URN =		{urn:nbn:de:0030-drops-168320},
  doi =		{10.4230/LIPIcs.MFCS.2022.34},
  annote =	{Keywords: Dynamic graphs, bounded arboricity, data structures}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.42
Fully-Dynamic α + 2 Arboricity Decompositions and Implicit Colouring

Authors: Aleksander B. G. Christiansen and Eva Rotenberg

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

Abstract
The arboricity α of a graph is the smallest number of forests necessary to cover its edges, and an arboricity decomposition of a graph is a decomposition of its edges into forests. The best near-linear time algorithm for arboricity decomposition guarantees at most α +2 forests if the graph has arboricity α (Blumenstock and Fischer [Markus Blumenstock and Frank Fischer, 2020]). In this paper, we study arboricity decomposition for dynamic graphs, that is, graphs that are subject to insertions and deletions of edges. We give an algorithm that, provided the arboricity of the dynamic graph never exceeds α, maintains an α+2 arboricity decomposition of the graph in poly(log n,α) update time, thus matching the number of forests currently obtainable in near-linear time for static (non-changing) graphs. Our construction goes via dynamic bounded out-degree orientations, and we present a fully-dynamic algorithm that explicitly orients the edges of the dynamic graph, such that no vertex has an out-degree exceeding ⌊ (1+ε)α ⌋ + 2. Our algorithm is deterministic and has a worst-case update time of O(ε^{-6}α² log³ n). The state-of-the-art explicit, deterministic, worst-case algorithm for bounded out-degree orientations maintains a β⋅ α + log_β n out-orientation in O(β²α²+βαlog_β n) time [Tsvi Kopelowitz et al., 2014]. As a consequence, we get an algorithm that maintains an implicit vertex colouring with 4⋅ 2^α colours, in amortised poly-log n update time, and with O(α log n) worst-case query time. Thus, at the expense of log n-factors in the update time, we improve on the number of colours from 2^O(α) to O(2^α) compared to the state-of-the-art for implicit dynamic colouring [Monika Henzinger et al., 2020].
Cite as

Aleksander B. G. Christiansen and Eva Rotenberg. Fully-Dynamic α + 2 Arboricity Decompositions and Implicit Colouring. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 42:1-42:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{christiansen_et_al:LIPIcs.ICALP.2022.42,
  author =	{Christiansen, Aleksander B. G. and Rotenberg, Eva},
  title =	{{Fully-Dynamic \alpha + 2 Arboricity Decompositions and Implicit Colouring}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{42:1--42:20},
  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.2022.42},
  URN =		{urn:nbn:de:0030-drops-163835},
  doi =		{10.4230/LIPIcs.ICALP.2022.42},
  annote =	{Keywords: Dynamic graphs, bounded arboricity, graph colouring, data structures}
}
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