7 Search Results for "Chekan, Vera"


Document
Tight Bounds for Connected Odd Cycle Transversal Parameterized by Clique-Width

Authors: Narek Bojikian and Stefan Kratsch

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)


Abstract
Recently, Bojikian and Kratsch [ICALP 2024] presented a novel approach to tackle connectivity problems parameterized by clique-width (cw), based on counting (modulo 2) the number of representations of partial solutions, while allowing for possibly multiple representations to exist for the same partial solution. Using this technique, they got a SETH-tight bound of 𝒪^*(3^{cw}) for the Steiner Tree problem, which was left open by Hegerfeld and Kratsch [ESA 2023]. We use the same technique to solve the Connected Odd Cycle Transversal problem in time 𝒪^*(12^{cw}). Moreover, we prove that our result is tight by providing a SETH-based lower bound excluding algorithms with running time 𝒪^*((12-ε)^{cw}). This answers another question of Hegerfeld and Kratsch [ESA 2023].

Cite as

Narek Bojikian and Stefan Kratsch. Tight Bounds for Connected Odd Cycle Transversal Parameterized by Clique-Width. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 19:1-19:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)


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@InProceedings{bojikian_et_al:LIPIcs.IPEC.2025.19,
  author =	{Bojikian, Narek and Kratsch, Stefan},
  title =	{{Tight Bounds for Connected Odd Cycle Transversal Parameterized by Clique-Width}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{19:1--19:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.19},
  URN =		{urn:nbn:de:0030-drops-251516},
  doi =		{10.4230/LIPIcs.IPEC.2025.19},
  annote =	{Keywords: Parameterized complexity, connected odd cycle transversal, clique-width}
}
Document
Tight Bounds for Some Classical Problems Parameterized by Cutwidth

Authors: Narek Bojikian, Vera Chekan, and Stefan Kratsch

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


Abstract
Cutwidth is a widely studied parameter and it quantifies how well a graph can be decomposed along small edge-cuts. It complements pathwidth, which captures decomposition by small vertex separators, and it is well-known that cutwidth upper-bounds pathwidth. The SETH-tight parameterized complexity of problems on graphs of bounded pathwidth (and treewidth) has been actively studied over the past decade while for cutwidth the complexity of many classical problems remained open. For Hamiltonian Cycle, it is known that a (2+√2)^{pw} n^𝒪(1) algorithm is optimal for pathwidth under SETH [Cygan et al. JACM 2018]. Van Geffen et al. [J. Graph Algorithms Appl. 2020] and Bojikian et al. [STACS 2023] asked which running time is optimal for this problem parameterized by cutwidth. We answer this question with (1+√2)^{ctw} n^𝒪(1) by providing matching upper and lower bounds. Second, as our main technical contribution, we close the gap left by van Heck [2018] for Partition Into Triangles (and Triangle Packing) by improving both upper and lower bound and getting a tight bound of ∛{3}^{ctw} n^𝒪(1), which to our knowledge exhibits the only known tight non-integral basis apart from Hamiltonian Cycle [Cygan et al. JACM 2018] and C₄-Hitting Set [SODA 2025]. We show that the cuts inducing a disjoint union of paths of length three (unions of so-called Z-cuts) lie at the core of the complexity of the problem - usually lower-bound constructions use simpler cuts inducing either a matching or a disjoint union of bicliques. Finally, we determine the optimal running times for Max Cut (2^{ctw} n^𝒪(1)) and Induced Matching (3^{ctw} n^𝒪(1)) by providing matching lower bounds for the existing algorithms - the latter result also answers an open question for treewidth by Chaudhary and Zehavi [WG 2023].

Cite as

Narek Bojikian, Vera Chekan, and Stefan Kratsch. Tight Bounds for Some Classical Problems Parameterized by Cutwidth. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)


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@InProceedings{bojikian_et_al:LIPIcs.ESA.2025.13,
  author =	{Bojikian, Narek and Chekan, Vera and Kratsch, Stefan},
  title =	{{Tight Bounds for Some Classical Problems Parameterized by Cutwidth}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{13:1--13:17},
  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.2025.13},
  URN =		{urn:nbn:de:0030-drops-244815},
  doi =		{10.4230/LIPIcs.ESA.2025.13},
  annote =	{Keywords: Parameterized complexity, cutwidth, Hamiltonian cycle, triangle packing, max cut, induced matching}
}
Document
Track A: Algorithms, Complexity and Games
Towards the Proximity Conjecture on Group-Labeled Matroids

Authors: Dániel Garamvölgyi, Ryuhei Mizutani, Taihei Oki, Tamás Schwarcz, and Yutaro Yamaguchi

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


Abstract
Consider a matroid M whose ground set is equipped with a labeling to an abelian group. A basis of M is called F-avoiding if the sum of the labels of its elements is not in a forbidden label set F. Hörsch, Imolay, Mizutani, Oki, and Schwarcz (2024) conjectured that if an F-avoiding basis exists, then any basis can be transformed into an F-avoiding basis by exchanging at most |F| elements. This proximity conjecture is known to hold for certain specific groups; in the case where |F| ≤ 2; or when the matroid is subsequence-interchangeably base orderable (SIBO), which is a weakening of the so-called strongly base orderable (SBO) property. In this paper, we settle the proximity conjecture for sparse paving matroids or in the case where |F| ≤ 4. Related to the latter result, we present the first known example of a non-SIBO matroid. We further address the setting of multiple group-label constraints, showing proximity results for the cases of two labelings, SIBO matroids, matroids representable over a fixed, finite field, and sparse paving matroids.

Cite as

Dániel Garamvölgyi, Ryuhei Mizutani, Taihei Oki, Tamás Schwarcz, and Yutaro Yamaguchi. Towards the Proximity Conjecture on Group-Labeled Matroids. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 85:1-85:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)


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@InProceedings{garamvolgyi_et_al:LIPIcs.ICALP.2025.85,
  author =	{Garamv\"{o}lgyi, D\'{a}niel and Mizutani, Ryuhei and Oki, Taihei and Schwarcz, Tam\'{a}s and Yamaguchi, Yutaro},
  title =	{{Towards the Proximity Conjecture on Group-Labeled Matroids}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{85:1--85:17},
  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.2025.85},
  URN =		{urn:nbn:de:0030-drops-234628},
  doi =		{10.4230/LIPIcs.ICALP.2025.85},
  annote =	{Keywords: sparse paving matroid, subsequence-interchangeable base orderability, congruency constraint, multiple labelings}
}
Document
Polychromatic Coloring of Tuples in Hypergraphs

Authors: Ahmad Biniaz, Jean-Lou De Carufel, Anil Maheshwari, Michiel Smid, Shakhar Smorodinsky, and Miloš Stojaković

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


Abstract
A hypergraph H consists of a set V of vertices and a set E of hyperedges that are subsets of V. A t-tuple of H is a subset of t vertices of V. A t-tuple k-coloring of H is a mapping of its t-tuples into k colors. A coloring is called (t,k,f)-polychromatic if each hyperedge of E that has at least f vertices contains tuples of all the k colors. Let f_H(t,k) be the minimum f such that H has a (t,k,f)-polychromatic coloring. For a family of hypergraphs ℋ let f_H(t,k) be the maximum f_H(t,k) over all hypergraphs H in H. Determining f_H(t,k) has been an active research direction in recent years. This is challenging even for t = 1. We present several new results in this direction for t ≥ 2. - Let H be the family of hypergraphs H that is obtained by taking any set P of points in ℝ², setting V: = P and E: = {d ∩ P: d is a disk in ℝ²}. We prove that f_ H(2,k) ≤ 3.7^k, that is, the pairs of points (2-tuples) can be k-colored such that any disk containing at least 3.7^k points has pairs of all colors. We generalize this result to points and balls in higher dimensions. - For the family H of hypergraphs that are defined by grid vertices and axis-parallel rectangles in the plane, we show that f_H(2,k) ≤ √{ck ln k} for some constant c. We then generalize this to higher dimensions, to other shapes, and to tuples of larger size. - For the family H of shrinkable hypergraphs of VC-dimension at most d we prove that f_ H(d+1,k) ≤ c^k for some constant c = c(d). Towards this bound, we obtain a result of independent interest: Every hypergraph with n vertices and with VC-dimension at most d has a (d+1)-tuple T of depth at least n/c, i.e., any hyperedge that contains T also contains n/c other vertices. - For the relationship between t-tuple coloring and vertex coloring in any hypergraph H we establish the inequality 1/e⋅ tk^{1/t} ≤ f_H(t,k) ≤ f_H(1,tk^{1/t}). For the special case of k = 2, referred to as the bichromatic coloring, we prove that t+1 ≤ f_H(t,2) ≤ max{f_H(1,2), t+1}; this improves upon the previous best known upper bound. - We study the relationship between tuple coloring and epsilon nets. In particular we show that if f_H(1,k) = O(k) for a hypergraph H with n vertices, then for any 0 < ε < 1 the t-tuples of H can be partitioned into Ω((εn/t)^t) ε-t-nets. This bound is tight when t is a constant.

Cite as

Ahmad Biniaz, Jean-Lou De Carufel, Anil Maheshwari, Michiel Smid, Shakhar Smorodinsky, and Miloš Stojaković. Polychromatic Coloring of Tuples in Hypergraphs. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 19:1-19:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)


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@InProceedings{biniaz_et_al:LIPIcs.SoCG.2025.19,
  author =	{Biniaz, Ahmad and De Carufel, Jean-Lou and Maheshwari, Anil and Smid, Michiel and Smorodinsky, Shakhar and Stojakovi\'{c}, Milo\v{s}},
  title =	{{Polychromatic Coloring of Tuples in Hypergraphs}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{19:1--19:17},
  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.2025.19},
  URN =		{urn:nbn:de:0030-drops-231718},
  doi =		{10.4230/LIPIcs.SoCG.2025.19},
  annote =	{Keywords: Hypergraph Coloring, Polychromatic Coloring, Geometric Hypergraphs, Cover Decomposable Hypergraphs, Epsilon Nets}
}
Document
Space-Efficient Parameterized Algorithms on Graphs of Low Shrubdepth

Authors: Benjamin Bergougnoux, Vera Chekan, Robert Ganian, Mamadou Moustapha Kanté, Matthias Mnich, Sang-il Oum, Michał Pilipczuk, and Erik Jan van Leeuwen

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


Abstract
Dynamic programming on various graph decompositions is one of the most fundamental techniques used in parameterized complexity. Unfortunately, even if we consider concepts as simple as path or tree decompositions, such dynamic programming uses space that is exponential in the decomposition’s width, and there are good reasons to believe that this is necessary. However, it has been shown that in graphs of low treedepth it is possible to design algorithms which achieve polynomial space complexity without requiring worse time complexity than their counterparts working on tree decompositions of bounded width. Here, treedepth is a graph parameter that, intuitively speaking, takes into account both the depth and the width of a tree decomposition of the graph, rather than the width alone. Motivated by the above, we consider graphs that admit clique expressions with bounded depth and label count, or equivalently, graphs of low shrubdepth. Here, shrubdepth is a bounded-depth analogue of cliquewidth, in the same way as treedepth is a bounded-depth analogue of treewidth. We show that also in this setting, bounding the depth of the decomposition is a deciding factor for improving the space complexity. More precisely, we prove that on n-vertex graphs equipped with a tree-model (a decomposition notion underlying shrubdepth) of depth d and using k labels, - Independent Set can be solved in time 2^𝒪(dk) ⋅ n^𝒪(1) using 𝒪(dk²log n) space; - Max Cut can be solved in time n^𝒪(dk) using 𝒪(dk log n) space; and - Dominating Set can be solved in time 2^𝒪(dk) ⋅ n^𝒪(1) using n^𝒪(1) space via a randomized algorithm. We also establish a lower bound, conditional on a certain assumption about the complexity of Longest Common Subsequence, which shows that at least in the case of Independent Set the exponent of the parametric factor in the time complexity has to grow with d if one wishes to keep the space complexity polynomial.

Cite as

Benjamin Bergougnoux, Vera Chekan, Robert Ganian, Mamadou Moustapha Kanté, Matthias Mnich, Sang-il Oum, Michał Pilipczuk, and Erik Jan van Leeuwen. Space-Efficient Parameterized Algorithms on Graphs of Low Shrubdepth. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 18:1-18:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{bergougnoux_et_al:LIPIcs.ESA.2023.18,
  author =	{Bergougnoux, Benjamin and Chekan, Vera and Ganian, Robert and Kant\'{e}, Mamadou Moustapha and Mnich, Matthias and Oum, Sang-il and Pilipczuk, Micha{\l} and van Leeuwen, Erik Jan},
  title =	{{Space-Efficient Parameterized Algorithms on Graphs of Low Shrubdepth}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{18:1--18:18},
  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.2023.18},
  URN =		{urn:nbn:de:0030-drops-186710},
  doi =		{10.4230/LIPIcs.ESA.2023.18},
  annote =	{Keywords: Parameterized complexity, shrubdepth, space complexity, algebraic methods}
}
Document
Tight Algorithmic Applications of Clique-Width Generalizations

Authors: Vera Chekan and Stefan Kratsch

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)


Abstract
In this work, we study two natural generalizations of clique-width introduced by Martin Fürer. Multi-clique-width (mcw) allows every vertex to hold multiple labels [ITCS 2017], while for fusion-width (fw) we have a possibility to merge all vertices of a certain label [LATIN 2014]. Fürer has shown that both parameters are upper-bounded by treewidth thus making them more appealing from an algorithmic perspective than clique-width and asked for applications of these parameters for problem solving. First, we determine the relation between these two parameters by showing that mcw ≤ fw + 1. Then we show that when parameterized by multi-clique-width, many problems (e.g., Connected Dominating Set) admit algorithms with the same running time as for clique-width despite the exponential gap between these two parameters. For some problems (e.g., Hamiltonian Cycle) we show an analogous result for fusion-width: For this we present an alternative view on fusion-width by introducing so-called glue-expressions which might be interesting on their own. All algorithms obtained in this work are tight up to (Strong) Exponential Time Hypothesis.

Cite as

Vera Chekan and Stefan Kratsch. Tight Algorithmic Applications of Clique-Width Generalizations. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 35:1-35:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{chekan_et_al:LIPIcs.MFCS.2023.35,
  author =	{Chekan, Vera and Kratsch, Stefan},
  title =	{{Tight Algorithmic Applications of Clique-Width Generalizations}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{35:1--35:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.35},
  URN =		{urn:nbn:de:0030-drops-185699},
  doi =		{10.4230/LIPIcs.MFCS.2023.35},
  annote =	{Keywords: Parameterized complexity, connectivity problems, clique-width}
}
Document
Tight Bounds for Connectivity Problems Parameterized by Cutwidth

Authors: Narek Bojikian, Vera Chekan, Falko Hegerfeld, and Stefan Kratsch

Published in: LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)


Abstract
In this work we start the investigation of tight complexity bounds for connectivity problems parameterized by cutwidth assuming the Strong Exponential-Time Hypothesis (SETH). Van Geffen et al. [Bas A. M. van Geffen et al., 2020] posed this question for Odd Cycle Transversal and Feedback Vertex Set. We answer it for these two and four further problems, namely Connected Vertex Cover, Connected Dominating Set, Steiner Tree, and Connected Odd Cycle Transversal. For the latter two problems it sufficed to prove lower bounds that match the running time inherited from parameterization by treewidth; for the others we provide faster algorithms than relative to treewidth and prove matching lower bounds. For upper bounds we first extend the idea of Groenland et al. [Carla Groenland et al., 2022] to solve what we call coloring-like problems. Such problems are defined by a symmetric matrix M over 𝔽₂ indexed by a set of colors. The goal is to count the number (modulo some prime p) of colorings of a graph such that M has a 1-entry if indexed by the colors of the end-points of any edge. We show that this problem can be solved faster if M has small rank over 𝔽_p. We apply this result to get our upper bounds for CVC and CDS. The upper bounds for OCT and FVS use a subdivision trick to get below the bounds that matrix rank would yield.

Cite as

Narek Bojikian, Vera Chekan, Falko Hegerfeld, and Stefan Kratsch. Tight Bounds for Connectivity Problems Parameterized by Cutwidth. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 14:1-14:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{bojikian_et_al:LIPIcs.STACS.2023.14,
  author =	{Bojikian, Narek and Chekan, Vera and Hegerfeld, Falko and Kratsch, Stefan},
  title =	{{Tight Bounds for Connectivity Problems Parameterized by Cutwidth}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{14:1--14:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.14},
  URN =		{urn:nbn:de:0030-drops-176667},
  doi =		{10.4230/LIPIcs.STACS.2023.14},
  annote =	{Keywords: Parameterized complexity, connectivity problems, cutwidth}
}
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