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Documents authored by Kosinas, Evangelos

Document
DOI: 10.4230/LIPIcs.ESA.2025.36
Efficient Contractions of Dynamic Graphs - With Applications

Authors: Monika Henzinger, Evangelos Kosinas, Robin Münk, and Harald Räcke

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

Abstract
A non-trivial minimum cut (NMC) sparsifier is a multigraph Ĝ that preserves all non-trivial minimum cuts of a given undirected graph G. We introduce a flexible data structure for fully dynamic graphs that can efficiently provide an NMC sparsifier upon request at any point during the sequence of updates. We employ simple dynamic forest data structures to achieve a fast from-scratch construction of the sparsifier at query time. Based on the strength of the adversary and desired type of time bounds, the data structure comes with different guarantees. Specifically, let G be a fully dynamic simple graph with n vertices and minimum degree δ. Then our data structure supports an insertion/deletion of an edge to/from G in n^o(1) worst-case time. Furthermore, upon request, it can return w.h.p. an NMC sparsifier of G that has O(n/δ) vertices and O(n) edges, in Ô(n) time. The probabilistic guarantees hold against an adaptive adversary. Alternatively, the update and query times can be improved to Õ(1) and Õ(n) respectively, if amortized-time guarantees are sufficient, or if the adversary is oblivious. Throughout the paper, we use Õ to hide polylogarithmic factors and Ô to hide subpolynomial (i.e., n^o(1)) factors. We discuss two applications of our new data structure. First, it can be used to efficiently report a cactus representation of all minimum cuts of a fully dynamic simple graph. Building this cactus for the NMC sparsifier instead of the original graph allows for a construction time that is sublinear in the number of edges. Against an adaptive adversary, we can with high probability output the cactus representation in worst-case Ô(n) time. Second, our data structure allows us to efficiently compute the maximal k-edge-connected subgraphs of undirected simple graphs, by repeatedly applying a minimum cut algorithm on the NMC sparsifier. Specifically, we can compute with high probability the maximal k-edge-connected subgraphs of a simple graph with n vertices and m edges in Õ(m+n²/k) time. This improves the best known time bounds for k = Ω(n^{1/8}) and naturally extends to the case of fully dynamic graphs.
Cite as

Monika Henzinger, Evangelos Kosinas, Robin Münk, and Harald Räcke. Efficient Contractions of Dynamic Graphs - With Applications. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 36:1-36:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{henzinger_et_al:LIPIcs.ESA.2025.36,
  author =	{Henzinger, Monika and Kosinas, Evangelos and M\"{u}nk, Robin and R\"{a}cke, Harald},
  title =	{{Efficient Contractions of Dynamic Graphs - With Applications}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{36:1--36:14},
  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.2025.36},
  URN =		{urn:nbn:de:0030-drops-245047},
  doi =		{10.4230/LIPIcs.ESA.2025.36},
  annote =	{Keywords: Graph Algorithms, Cut Sparsifiers, Dynamic Algorithms}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.110
An Optimal 3-Fault-Tolerant Connectivity Oracle

Authors: Evangelos Kosinas

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

Abstract
We present an optimal oracle for answering connectivity queries in undirected graphs in the presence of at most three vertex failures. Specifically, we show that we can process a graph G in O(n+m) time, in order to build a data structure that occupies O(n) space, which can be used in order to answer queries of the form "given a set F of at most three vertices, and two vertices x and y not in F, are x and y connected in G⧵ F?" in constant time, where n and m denote the number of vertices and edges, respectively, of G. The idea is to rely on the DFS-based framework introduced by Kosinas [ESA'23], for handling connectivity queries in the presence of multiple vertex failures. Our technical contribution is to show how to appropriately extend the toolkit of the DFS-based parameters, in order to optimally handle up to three vertex failures. Our approach has the interesting property that it does not rely on a compact representation of vertex cuts, and has the potential to provide optimal solutions for more vertex failures. Furthermore, we show that the DFS-based framework can be easily extended in order to answer vertex-cut queries, and the number of connected components in the presence of multiple vertex failures. In the case of three vertex failures, we can answer such queries in O(log n) time.
Cite as

Evangelos Kosinas. An Optimal 3-Fault-Tolerant Connectivity Oracle. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 110:1-110:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kosinas:LIPIcs.ICALP.2025.110,
  author =	{Kosinas, Evangelos},
  title =	{{An Optimal 3-Fault-Tolerant Connectivity Oracle}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{110:1--110:20},
  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.2025.110},
  URN =		{urn:nbn:de:0030-drops-234879},
  doi =		{10.4230/LIPIcs.ICALP.2025.110},
  annote =	{Keywords: Graphs, Connectivity, Fault-Tolerant, Oracles}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.72
Connectivity Oracles for Predictable Vertex Failures

Authors: Bingbing Hu, Evangelos Kosinas, and Adam Polak

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
The problem of designing connectivity oracles supporting vertex failures is one of the basic data structures problems for undirected graphs. It is already well understood: previous works [Duan-Pettie STOC'10; Long-Saranurak FOCS'22] achieve query time linear in the number of failed vertices, and it is conditionally optimal as long as we require preprocessing time polynomial in the size of the graph and update time polynomial in the number of failed vertices. We revisit this problem in the paradigm of algorithms with predictions: we ask if the query time can be improved if the set of failed vertices can be predicted beforehand up to a small number of errors. More specifically, we design a data structure that, given a graph G = (V,E) and a set of vertices predicted to fail D̂ ⊆ V of size d = |D̂|, preprocesses it in time Õ(d|E|) and then can receive an update given as the symmetric difference between the predicted and the actual set of failed vertices D̂△D = (D̂ ⧵ D) ∪ (D ⧵ D̂) of size η = |D̂△D|, process it in time Õ(η⁴), and after that answer connectivity queries in G ⧵ D in time O(η). Viewed from another perspective, our data structure provides an improvement over the state of the art for the fully dynamic subgraph connectivity problem in the sensitivity setting [Henzinger-Neumann ESA'16]. We argue that the preprocessing time and query time of our data structure are conditionally optimal under standard fine-grained complexity assumptions.
Cite as

Bingbing Hu, Evangelos Kosinas, and Adam Polak. Connectivity Oracles for Predictable Vertex Failures. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 72:1-72:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hu_et_al:LIPIcs.ESA.2024.72,
  author =	{Hu, Bingbing and Kosinas, Evangelos and Polak, Adam},
  title =	{{Connectivity Oracles for Predictable Vertex Failures}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{72:1--72:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John 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.2024.72},
  URN =		{urn:nbn:de:0030-drops-211437},
  doi =		{10.4230/LIPIcs.ESA.2024.72},
  annote =	{Keywords: Data structures, graph connectivity, algorithms with predictions}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.75
Connectivity Queries Under Vertex Failures: Not Optimal, but Practical

Authors: Evangelos Kosinas

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

Abstract
We revisit once more the problem of designing an oracle for answering connectivity queries in undirected graphs in the presence of vertex failures. Specifically, given an undirected graph G with n vertices and m edges and an integer d_⋆ ≪ n, the goal is to preprocess the graph in order to construct a data structure 𝒟 such that, given a set of vertices F with |F| = d ≤ d_⋆, we can derive an oracle from 𝒟 that can efficiently answer queries of the form "is x connected with y in G⧵F?". Very recently, Long and Saranurak (FOCS 2022) provided a solution to this problem that is almost optimal with respect to the preprocessing time, the space usage, the update time, and the query time. However, their solution is highly complicated, and it seems very difficult to be implemented efficiently. Furthermore, it does not settle the complexity of the problem in the regime where d_⋆ is a constant. Here, we provide a much simpler solution to this problem, that uses only textbook data structures. Our algorithm is deterministic, it has preprocessing time and space complexity O(d_⋆ m log n), update time O(d⁴ log n), and query time O(d). These bounds compare very well with the previous best, especially considering the simplicity of our approach. In fact, if we assume that d_⋆ is a constant (d_⋆ ≥ 4), then our algorithm provides some trade-offs that improve the state of the art in some respects. Finally, the data structure that we provide is flexible with respect to d_⋆: it can be adapted to increases and decreases, in time and space that are almost proportional to the change in d_⋆ and the size of the graph.
Cite as

Evangelos Kosinas. Connectivity Queries Under Vertex Failures: Not Optimal, but Practical. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 75:1-75:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{kosinas:LIPIcs.ESA.2023.75,
  author =	{Kosinas, Evangelos},
  title =	{{Connectivity Queries Under Vertex Failures: Not Optimal, but Practical}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{75:1--75:13},
  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.2023.75},
  URN =		{urn:nbn:de:0030-drops-187289},
  doi =		{10.4230/LIPIcs.ESA.2023.75},
  annote =	{Keywords: Graphs, Connectivity, Fault-Tolerant, Oracles}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.60
Computing the 4-Edge-Connected Components of a Graph: An Experimental Study

Authors: Loukas Georgiadis, Giuseppe F. Italiano, and Evangelos Kosinas

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Abstract
The notions of edge-cuts and k-edge-connected components are fundamental in graph theory with numerous practical applications. Very recently, the first linear-time algorithms for computing all the 3-edge cuts and the 4-edge-connected components of a graph have been introduced. In this paper we present carefully engineered implementations of these algorithms and evaluate their efficiency in practice, by performing a thorough empirical study using both real-world graphs taken from a variety of application areas, as well as artificial graphs. To the best of our knowledge, this is the first experimental study for these problems, which highlights the merits and weaknesses of each technique. Furthermore, we present an improved algorithm for computing the 4-edge-connected components of an undirected graph in linear time. The new algorithm uses only elementary data structures, and is implementable in the pointer machine model of computation.
Cite as

Loukas Georgiadis, Giuseppe F. Italiano, and Evangelos Kosinas. Computing the 4-Edge-Connected Components of a Graph: An Experimental Study. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 60:1-60:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{georgiadis_et_al:LIPIcs.ESA.2022.60,
  author =	{Georgiadis, Loukas and Italiano, Giuseppe F. and Kosinas, Evangelos},
  title =	{{Computing the 4-Edge-Connected Components of a Graph: An Experimental Study}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{60:1--60:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva 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.2022.60},
  URN =		{urn:nbn:de:0030-drops-169988},
  doi =		{10.4230/LIPIcs.ESA.2022.60},
  annote =	{Keywords: Connectivity Cuts, Edge Connectivity, Graph Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ESA.2021.47
Computing the 4-Edge-Connected Components of a Graph in Linear Time

Authors: Loukas Georgiadis, Giuseppe F. Italiano, and Evangelos Kosinas

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
We present the first linear-time algorithm that computes the 4-edge-connected components of an undirected graph. Hence, we also obtain the first linear-time algorithm for testing 4-edge connectivity. Our results are based on a linear-time algorithm that computes the 3-edge cuts of a 3-edge-connected graph G, and a linear-time procedure that, given the collection of all 3-edge cuts, partitions the vertices of G into the 4-edge-connected components.
Cite as

Loukas Georgiadis, Giuseppe F. Italiano, and Evangelos Kosinas. Computing the 4-Edge-Connected Components of a Graph in Linear Time. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 47:1-47:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{georgiadis_et_al:LIPIcs.ESA.2021.47,
  author =	{Georgiadis, Loukas and Italiano, Giuseppe F. and Kosinas, Evangelos},
  title =	{{Computing the 4-Edge-Connected Components of a Graph in Linear Time}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{47:1--47:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus 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.2021.47},
  URN =		{urn:nbn:de:0030-drops-146286},
  doi =		{10.4230/LIPIcs.ESA.2021.47},
  annote =	{Keywords: Cuts, Edge Connectivity, Graph Algorithms}
}
Document
DOI: 10.4230/LIPIcs.SEA.2021.20
Computing Vertex-Edge Cut-Pairs and 2-Edge Cuts in Practice

Authors: Loukas Georgiadis, Konstantinos Giannis, Giuseppe F. Italiano, and Evangelos Kosinas

Published in: LIPIcs, Volume 190, 19th International Symposium on Experimental Algorithms (SEA 2021)

Abstract
We consider two problems regarding the computation of connectivity cuts in undirected graphs, namely identifying vertex-edge cut-pairs and identifying 2-edge cuts, and present an experimental study of efficient algorithms for their computation. In the first problem, we are given a biconnected graph G and our goal is to find all vertices v such that G⧵v is not 2-edge-connected, while in the second problem, we are given a 2-edge-connected graph G and our goal is to find all edges e such that G⧵e is not 2-edge-connected. These problems are motivated by the notion of twinless strong connectivity in directed graphs but are also of independent interest. Moreover, the computation of 2-edge cuts is a main step in algorithms that compute the 3-edge-connected components of a graph. In this paper, we present streamlined versions of two recent linear-time algorithms of Georgiadis and Kosinas that compute all vertex-edge cut-pairs and all 2-edge cuts, respectively. We compare the empirical performance of our vertex-edge cut-pairs algorithm with an alternative linear-time method that exploits the structure of the triconnected components of G. Also, we compare the empirical performance of our 2-edge cuts algorithm with the algorithm of Tsin, which was reported to be the fastest one among the previously existing for this problem. To that end, we conduct a thorough experimental study to highlight the merits and weaknesses of each technique.
Cite as

Loukas Georgiadis, Konstantinos Giannis, Giuseppe F. Italiano, and Evangelos Kosinas. Computing Vertex-Edge Cut-Pairs and 2-Edge Cuts in Practice. In 19th International Symposium on Experimental Algorithms (SEA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 190, pp. 20:1-20:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{georgiadis_et_al:LIPIcs.SEA.2021.20,
  author =	{Georgiadis, Loukas and Giannis, Konstantinos and Italiano, Giuseppe F. and Kosinas, Evangelos},
  title =	{{Computing Vertex-Edge Cut-Pairs and 2-Edge Cuts in Practice}},
  booktitle =	{19th International Symposium on Experimental Algorithms (SEA 2021)},
  pages =	{20:1--20:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-185-6},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{190},
  editor =	{Coudert, David and Natale, Emanuele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2021.20},
  URN =		{urn:nbn:de:0030-drops-137920},
  doi =		{10.4230/LIPIcs.SEA.2021.20},
  annote =	{Keywords: 2-Connectivity, Graph Algorithms, Split Components}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2020.38
Linear-Time Algorithms for Computing Twinless Strong Articulation Points and Related Problems

Authors: Loukas Georgiadis and Evangelos Kosinas

Published in: LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020)

Abstract
A directed graph G = (V,E) is twinless strongly connected if it contains a strongly connected spanning subgraph without any pair of antiparallel (or twin) edges. The twinless strongly connected components (TSCCs) of a directed graph G are its maximal twinless strongly connected subgraphs. These concepts have several diverse applications, such as the design of telecommunication networks and the structural stability of buildings. A vertex v ∈ V is a twinless strong articulation point of G, if the deletion of v increases the number of TSCCs of G. Here, we present the first linear-time algorithm that finds all the twinless strong articulation points of a directed graph. We show that the computation of twinless strong articulation points reduces to the following problem in undirected graphs, which may be of independent interest: Given a 2-vertex-connected undirected graph H, find all vertices v for which there exists an edge e such that H⧵{v,e} is not connected. We develop a linear-time algorithm that not only finds all such vertices v, but also computes the number of edges e such that H⧵{v,e} is not connected. This also implies that for each twinless strong articulation point v which is not a strong articulation point in a strongly connected digraph G, we can compute the number of TSCCs in G⧵v.
Cite as

Loukas Georgiadis and Evangelos Kosinas. Linear-Time Algorithms for Computing Twinless Strong Articulation Points and Related Problems. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 38:1-38:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{georgiadis_et_al:LIPIcs.ISAAC.2020.38,
  author =	{Georgiadis, Loukas and Kosinas, Evangelos},
  title =	{{Linear-Time Algorithms for Computing Twinless Strong Articulation Points and Related Problems}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{38:1--38:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Cao, Yixin and Cheng, Siu-Wing and Li, Minming},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.38},
  URN =		{urn:nbn:de:0030-drops-133820},
  doi =		{10.4230/LIPIcs.ISAAC.2020.38},
  annote =	{Keywords: 2-connectivity, cut pairs, strongly connected components}
}
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