9 Search Results for "Wesolek, Alexandra"

Document
DOI: 10.4230/LIPIcs.SWAT.2026.9
QPTAS for MWIS and Finding Large Sparse Induced Subgraphs in Graphs with Few Independent Long Holes

Authors: Édouard Bonnet, Jadwiga Czyżewska, Tomáš Masařík, Marcin Pilipczuk, and Paweł Rzążewski

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract
We present a quasipolynomial-time approximation scheme (QPTAS) for the Maximum Independent Set (MWIS) in graphs with a bounded number of pairwise vertex-disjoint and non-adjacent long induced cycles. More formally, for every fixed s and t, we show a QPTAS for MWIS in graphs that exclude sC_t as an induced minor. Combining this with known results, we obtain a QPTAS for the problem of finding a largest induced subgraph of bounded treewidth with given hereditary property definable in Counting Monadic Second Order Logic, in the same classes of graphs. This is a step towards a conjecture of Gartland and Lokshtanov which asserts that for any planar graph H, graphs that exclude H as an induced minor admit a polynomial-time algorithm for the latter problem. This conjecture is notoriously open and even its weaker variants are confirmed only for very restricted graphs H.
Cite as

Édouard Bonnet, Jadwiga Czyżewska, Tomáš Masařík, Marcin Pilipczuk, and Paweł Rzążewski. QPTAS for MWIS and Finding Large Sparse Induced Subgraphs in Graphs with Few Independent Long Holes. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 9:1-9:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bonnet_et_al:LIPIcs.SWAT.2026.9,
  author =	{Bonnet, \'{E}douard and Czy\.{z}ewska, Jadwiga and Masa\v{r}{\'\i}k, Tom\'{a}\v{s} and Pilipczuk, Marcin and Rz\k{a}\.{z}ewski, Pawe{\l}},
  title =	{{QPTAS for MWIS and Finding Large Sparse Induced Subgraphs in Graphs with Few Independent Long Holes}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{9:1--9:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.9},
  URN =		{urn:nbn:de:0030-drops-260454},
  doi =		{10.4230/LIPIcs.SWAT.2026.9},
  annote =	{Keywords: independent set, long holes, QPTAS, induced subgraphs}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.16
Flip Distance of Non-Crossing Spanning Trees: NP-Hardness and Improved Bounds

Authors: Håvard Bakke Bjerkevik, Joseph Dorfer, Linda Kleist, Torsten Ueckerdt, and Birgit Vogtenhuber

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
We consider the problem of reconfiguring non-crossing spanning trees on point sets. For a set P of n points in general position in the plane, the flip graph ℱ(P) has a vertex for each non-crossing spanning tree on P and an edge between any two spanning trees that can be transformed into each other by the exchange of a single edge (coined a flip). This flip graph has been intensively studied, lately with an emphasis on determining its diameter diam(ℱ(P)) for sets P of n points in convex position. For this case, the current best bounds are 14/9⋅n - O(1) ≤ diam(ℱ(P)) < 15/9⋅n - 3, obtained in a recent breakthrough work [Bjerkevik, Kleist, Ueckerdt, and Vogtenhuber; SODA 2025]. The crucial tool for both the upper and lower bound are so-called conflict graphs, which the authors stated might be the key ingredient for determining the diameter (up to lower-order terms). In this paper, we pick up the concept of conflict graphs from the above-mentioned work and show that this tool is even more versatile than previously hoped. As our first main result, we use conflict graphs to show that computing the flip distance between two non-crossing spanning trees is NP-hard, even for point sets in convex position. Interestingly, the result still holds for more constrained flip operations, concretely, compatible flips (where the removed and the added edge do not cross) and rotations (where the removed and the added edge share an endpoint). Additionally, we present new insights on the diameter of the flip graph, by this directly extending the line of research from [BKUV SODA25]. Their lower bound is based on a constant-size pair of trees, one of which is of a type we refer to as stacked. We show that if one of the trees is stacked, then the lower bound is indeed optimal up to a constant term, that is, there exists a flip sequence of length at most 14/9⋅(n-1) to any other tree. Lastly, we improve the lower bound on the diameter of the flip graph ℱ(P) for n points in convex position to 11/7⋅n-o(n).
Cite as

Håvard Bakke Bjerkevik, Joseph Dorfer, Linda Kleist, Torsten Ueckerdt, and Birgit Vogtenhuber. Flip Distance of Non-Crossing Spanning Trees: NP-Hardness and Improved Bounds. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bjerkevik_et_al:LIPIcs.SoCG.2026.16,
  author =	{Bjerkevik, H\r{a}vard Bakke and Dorfer, Joseph and Kleist, Linda and Ueckerdt, Torsten and Vogtenhuber, Birgit},
  title =	{{Flip Distance of Non-Crossing Spanning Trees: NP-Hardness and Improved Bounds}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{16:1--16:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.16},
  URN =		{urn:nbn:de:0030-drops-258225},
  doi =		{10.4230/LIPIcs.SoCG.2026.16},
  annote =	{Keywords: Non-crossing, spanning tree, plane graph, flip graph, reconfiguration, diameter, complexity, NP-hard, edge exchange, compatible flip, rotation, happy edge property}
}
Document
DOI: 10.4230/LIPIcs.GD.2025.5
Constrained Flips in Plane Spanning Trees

Authors: Oswin Aichholzer, Joseph Dorfer, and Birgit Vogtenhuber

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

Abstract
A flip in a plane spanning tree T is the operation of removing one edge from T and adding another edge such that the resulting structure is again a plane spanning tree. For trees on a set of points in convex position we study two classic types of constrained flips: (1) Compatible flips are flips in which the removed and inserted edge do not cross each other. We relevantly improve the previous upper bound of 2n-O(√n) on the diameter of the compatible flip graph to (5n/3)-O(1), by this matching the upper bound for unrestricted flips by Bjerkevik, Kleist, Ueckerdt, and Vogtenhuber [SODA 2025] up to an additive constant of 1. We further show that no shortest compatible flip sequence removes an edge that is already in its target position. Using this so-called happy edge property, we derive a fixed-parameter tractable algorithm to compute the shortest compatible flip sequence between two given trees. (2) Rotations are flips in which the removed and inserted edge share a common vertex. Besides showing that the happy edge property does not hold for rotations, we improve the previous upper bound of 2n-O(1) for the diameter of the rotation graph to (7n/4)-O(1).
Cite as

Oswin Aichholzer, Joseph Dorfer, and Birgit Vogtenhuber. Constrained Flips in Plane Spanning Trees. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 5:1-5:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{aichholzer_et_al:LIPIcs.GD.2025.5,
  author =	{Aichholzer, Oswin and Dorfer, Joseph and Vogtenhuber, Birgit},
  title =	{{Constrained Flips in Plane Spanning Trees}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{5:1--5:18},
  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.2025.5},
  URN =		{urn:nbn:de:0030-drops-249913},
  doi =		{10.4230/LIPIcs.GD.2025.5},
  annote =	{Keywords: Non-crossing spanning trees, Flip Graphs, Diameter, Complexity, Happy edges}
}
Document
Poster Abstract
DOI: 10.4230/LIPIcs.GD.2025.47
Reconfigurations of Plane Caterpillars and Paths (Poster Abstract)

Authors: Todor Antić, Guillermo Gamboa Quintero, and Jelena Glišić

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

Abstract
Let S be a point set in the plane, and let 𝒫(S) and 𝒞(S) be the sets of all plane spanning paths and caterpillars on S. We study reconfiguration operations on 𝒫(S) and 𝒞(S). In particular, we prove that all of the commonly studied reconfigurations on plane spanning trees still yield connected reconfiguration graphs for caterpillars when S is in convex position. If S is in general position, we show that the rotation, compatible flip and flip graphs of 𝒞(S) are connected while the slide graph is sometimes disconnected, but always has a component of size 1/4(3ⁿ-1). We then study sizes of connected components in reconfiguration graphs of plane spanning paths. In this direction, we show that no component of size at most 7 can exist in the flip graph on 𝒫(S).
Cite as

Todor Antić, Guillermo Gamboa Quintero, and Jelena Glišić. Reconfigurations of Plane Caterpillars and Paths (Poster Abstract). In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 47:1-47:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{antic_et_al:LIPIcs.GD.2025.47,
  author =	{Anti\'{c}, Todor and Gamboa Quintero, Guillermo and Gli\v{s}i\'{c}, Jelena},
  title =	{{Reconfigurations of Plane Caterpillars and Paths}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{47:1--47:5},
  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.2025.47},
  URN =		{urn:nbn:de:0030-drops-250337},
  doi =		{10.4230/LIPIcs.GD.2025.47},
  annote =	{Keywords: reconfiguration graph, caterpillar, path, geometric graph}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.16
Isometric-Universal Graphs for Trees

Authors: Edgar Baucher, François Dross, and Cyril Gavoille

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

Abstract
We consider the problem of finding the smallest graph that contains two input trees each with at most n vertices preserving their distances. In other words, we look for an isometric-universal graph with the minimum number of vertices for two given trees. We prove that this problem can be solved in time O(n^{5/2}log{n}). We extend this result to forests instead of trees, and propose an algorithm with running time O(n^{7/2}log{n}). As a key ingredient, we show that a smallest isometric-universal graph of two trees essentially is a tree. Furthermore, we prove that these results cannot be extended. Firstly, we show that deciding whether there exists an isometric-universal graph with t vertices for three forests is NP-complete. Secondly, we show that any smallest isometric-universal graph cannot be a tree for some families of three trees. This latter result has implications for greedy strategies solving the smallest isometric-universal graph problem.
Cite as

Edgar Baucher, François Dross, and Cyril Gavoille. Isometric-Universal Graphs for Trees. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 16:1-16:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{baucher_et_al:LIPIcs.MFCS.2025.16,
  author =	{Baucher, Edgar and Dross, Fran\c{c}ois and Gavoille, Cyril},
  title =	{{Isometric-Universal Graphs for Trees}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{16:1--16:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.16},
  URN =		{urn:nbn:de:0030-drops-241237},
  doi =		{10.4230/LIPIcs.MFCS.2025.16},
  annote =	{Keywords: tree, forest, isometric subgraph, universal graph, distance-preserving}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.8
Rapid Mixing of the Flip Chain over Non-Crossing Spanning Trees

Authors: Konrad Anand, Weiming Feng, Graham Freifeld, Heng Guo, Mark Jerrum, and Jiaheng Wang

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
We show that the flip chain for non-crossing spanning trees of n+1 points in convex position mixes in time O(n⁸log n). We use connections between Fuss-Catalan structures to construct a comparison argument with a chain similar to Wilson’s lattice path chain (Wilson 2004).
Cite as

Konrad Anand, Weiming Feng, Graham Freifeld, Heng Guo, Mark Jerrum, and Jiaheng Wang. Rapid Mixing of the Flip Chain over Non-Crossing Spanning Trees. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{anand_et_al:LIPIcs.SoCG.2025.8,
  author =	{Anand, Konrad and Feng, Weiming and Freifeld, Graham and Guo, Heng and Jerrum, Mark and Wang, Jiaheng},
  title =	{{Rapid Mixing of the Flip Chain over Non-Crossing Spanning Trees}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{8:1--8:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.8},
  URN =		{urn:nbn:de:0030-drops-231607},
  doi =		{10.4230/LIPIcs.SoCG.2025.8},
  annote =	{Keywords: non-crossing spanning trees, Markov chain, mixing time}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2024.22
Reconfiguration of Plane Trees in Convex Geometric Graphs

Authors: Nicolas Bousquet, Lucas de Meyer, Théo Pierron, and Alexandra Wesolek

Published in: LIPIcs, Volume 293, 40th International Symposium on Computational Geometry (SoCG 2024)

Abstract
A non-crossing spanning tree of a set of points in the plane is a spanning tree whose edges pairwise do not cross. Avis and Fukuda in 1996 proved that there always exists a flip sequence of length at most 2n-4 between any pair of non-crossing spanning trees (where n denotes the number of points). Hernando et al. proved that the length of a minimal flip sequence can be of length at least (3/2) n. Two recent results of Aichholzer et al. and Bousquet et al. improved the Avis and Fukuda upper bound by proving that there always exists a flip sequence of length respectively at most 2n-log n and 2n-√n when the points are in convex position. We pursue the investigation of the convex case by improving the upper bound by a linear factor for the first time in 30 years. We prove that there always exists a flip sequence between any pair of non-crossing spanning trees T₁,T₂ of length at most c n where c ≈ 1.95. Our result is actually stronger since we prove that, for any two trees T₁,T₂, there exists a flip sequence from T₁ to T₂ of length at most c |T₁ ⧵ T₂|. We also improve the best lower bound in terms of the symmetric difference by proving that there exists a pair of trees T₁,T₂ such that a minimal flip sequence has length (5/3) |T₁ ⧵ T₂|, improving the lower bound of Hernando et al. by considering the symmetric difference instead of the number of vertices. We generalize this lower bound construction to non-crossing flips (where we close the gap between upper and lower bounds) and rotations.
Cite as

Nicolas Bousquet, Lucas de Meyer, Théo Pierron, and Alexandra Wesolek. Reconfiguration of Plane Trees in Convex Geometric Graphs. In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 22:1-22:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bousquet_et_al:LIPIcs.SoCG.2024.22,
  author =	{Bousquet, Nicolas and de Meyer, Lucas and Pierron, Th\'{e}o and Wesolek, Alexandra},
  title =	{{Reconfiguration of Plane Trees in Convex Geometric Graphs}},
  booktitle =	{40th International Symposium on Computational Geometry (SoCG 2024)},
  pages =	{22:1--22:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-316-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{293},
  editor =	{Mulzer, Wolfgang and Phillips, Jeff M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2024.22},
  URN =		{urn:nbn:de:0030-drops-199673},
  doi =		{10.4230/LIPIcs.SoCG.2024.22},
  annote =	{Keywords: Reconfiguration, Non-crossing trees, flip distance}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.23
Maximum Independent Set When Excluding an Induced Minor: K₁ + tK₂ and tC₃ ⊎ C₄

Authors: Édouard Bonnet, Julien Duron, Colin Geniet, Stéphan Thomassé, and Alexandra Wesolek

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
Dallard, Milanič, and Štorgel [arXiv '22] ask if, for every class excluding a fixed planar graph H as an induced minor, Maximum Independent Set can be solved in polynomial time, and show that this is indeed the case when H is any planar complete bipartite graph, or the 5-vertex clique minus one edge, or minus two disjoint edges. A positive answer would constitute a far-reaching generalization of the state-of-the-art, when we currently do not know if a polynomial-time algorithm exists when H is the 7-vertex path. Relaxing tractability to the existence of a quasipolynomial-time algorithm, we know substantially more. Indeed, quasipolynomial-time algorithms were recently obtained for the t-vertex cycle, C_t [Gartland et al., STOC '21], and the disjoint union of t triangles, tC₃ [Bonamy et al., SODA '23]. We give, for every integer t, a polynomial-time algorithm running in n^O(t⁵) when H is the friendship graph K₁ + tK₂ (t disjoint edges plus a vertex fully adjacent to them), and a quasipolynomial-time algorithm running in n^{O(t² log n) + f(t)}, with f a single-exponential function, when H is tC₃ ⊎ C₄ (the disjoint union of t triangles and a 4-vertex cycle). The former generalizes the algorithm readily obtained from Alekseev’s structural result on graphs excluding tK₂ as an induced subgraph [Alekseev, DAM '07], while the latter extends Bonamy et al.’s result.
Cite as

Édouard Bonnet, Julien Duron, Colin Geniet, Stéphan Thomassé, and Alexandra Wesolek. Maximum Independent Set When Excluding an Induced Minor: K₁ + tK₂ and tC₃ ⊎ C₄. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 23:1-23:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bonnet_et_al:LIPIcs.ESA.2023.23,
  author =	{Bonnet, \'{E}douard and Duron, Julien and Geniet, Colin and Thomass\'{e}, St\'{e}phan and Wesolek, Alexandra},
  title =	{{Maximum Independent Set When Excluding an Induced Minor: K₁ + tK₂ and tC₃ ⊎ C₄}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{23:1--23:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. 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.2023.23},
  URN =		{urn:nbn:de:0030-drops-186769},
  doi =		{10.4230/LIPIcs.ESA.2023.23},
  annote =	{Keywords: Maximum Independent Set, forbidden induced minors, quasipolynomial-time algorithms}
}
Document
DOI: 10.4230/LIPIcs.DISC.2021.13
A Tight Local Algorithm for the Minimum Dominating Set Problem in Outerplanar Graphs

Authors: Marthe Bonamy, Linda Cook, Carla Groenland, and Alexandra Wesolek

Published in: LIPIcs, Volume 209, 35th International Symposium on Distributed Computing (DISC 2021)

Abstract
We show that there is a deterministic local algorithm (constant-time distributed graph algorithm) that finds a 5-approximation of a minimum dominating set on outerplanar graphs. We show there is no such algorithm that finds a (5-ε)-approximation, for any ε > 0. Our algorithm only requires knowledge of the degree of a vertex and of its neighbors, so that large messages and unique identifiers are not needed.
Cite as

Marthe Bonamy, Linda Cook, Carla Groenland, and Alexandra Wesolek. A Tight Local Algorithm for the Minimum Dominating Set Problem in Outerplanar Graphs. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 13:1-13:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bonamy_et_al:LIPIcs.DISC.2021.13,
  author =	{Bonamy, Marthe and Cook, Linda and Groenland, Carla and Wesolek, Alexandra},
  title =	{{A Tight Local Algorithm for the Minimum Dominating Set Problem in Outerplanar Graphs}},
  booktitle =	{35th International Symposium on Distributed Computing (DISC 2021)},
  pages =	{13:1--13:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-210-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{209},
  editor =	{Gilbert, Seth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2021.13},
  URN =		{urn:nbn:de:0030-drops-148159},
  doi =		{10.4230/LIPIcs.DISC.2021.13},
  annote =	{Keywords: Outerplanar graphs, dominating set, LOCAL model, constant-factor approximation algorithm}
}
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