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Documents authored by Orponen, Pekka

Document
DOI: 10.4230/LIPIcs.MFCS.2026.7
A Congestion Parameter for Depth-First Graph Traversals

Authors: Codaline Bourotte, Gwendal Ducloz, Pekka Orponen, and Shinnosuke Seki

Published in: LIPIcs, Volume 386, 51st International Symposium on Mathematical Foundations of Computer Science (MFCS 2026)

Abstract
We explore a new graph parameter, KLX number, which quantifies the minimum edge congestion of depth-first search (DFS) traversals of a given graph. Originally motivated by a problem in RNA nanostructure design, this parameter is also of independent theoretical interest. Informally, the KLX number of a graph is defined as the minimum, over all its DFS traversals, of the maximum number of back edges that are simultaneously open during the traversal. We provide full characterisations and linear-time recognition algorithms for graphs with KLX numbers 0, 1 and 2. We also relate KLX to tree-width, proving that any graph satisfies TW ≤ KLX+1. Furthermore, we show that the property KLX ≤ k is MSO₂-expressible for every fixed k. Combined with the tree-width bound, this result implies that determining whether a graph has KLX number at most k can be achieved in linear time for any constant k.
Cite as

Codaline Bourotte, Gwendal Ducloz, Pekka Orponen, and Shinnosuke Seki. A Congestion Parameter for Depth-First Graph Traversals. In 51st International Symposium on Mathematical Foundations of Computer Science (MFCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 386, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bourotte_et_al:LIPIcs.MFCS.2026.7,
  author =	{Bourotte, Codaline and Ducloz, Gwendal and Orponen, Pekka and Seki, Shinnosuke},
  title =	{{A Congestion Parameter for Depth-First Graph Traversals}},
  booktitle =	{51st International Symposium on Mathematical Foundations of Computer Science (MFCS 2026)},
  pages =	{7:1--7:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-442-0},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{386},
  editor =	{Kouck\'{y}, Michal and Petrișan, Daniela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2026.7},
  URN =		{urn:nbn:de:0030-drops-273889},
  doi =		{10.4230/LIPIcs.MFCS.2026.7},
  annote =	{Keywords: KLX, depth-first search, DFS trees, k-connectedness, tree-width, parameterised complexity, monadic second-order logic, Courcelle’s theorem, RNA nanotechnology}
}
Document
DOI: 10.4230/LIPIcs.DNA.31.6
Secondary Structure Design for Cotranscriptional 3D RNA Origami Wireframes

Authors: Pekka Orponen, Shinnosuke Seki, and Antti Elonen

Published in: LIPIcs, Volume 347, 31st International Conference on DNA Computing and Molecular Programming (DNA 31) (2025)

Abstract
We address the task of secondary structure design for de novo 3D RNA origami wireframe structures in a way that takes into account the specifics of a cotranscriptional folding setting. We consider two issues: firstly, avoiding the topological obstacle of "polymerase trapping", where some helical domain cannot be hybridised due to a closed kissing-loop pair blocking the winding of the strand relative to the polymerase-DNA-template complex; and secondly, minimising the number of distinct kissing-loop designs needed, by reusing KL pairs that have already been hybridised in the folding process. For the first task, we present an efficient strand-routing method that guarantees the absence of polymerase traps for any 3D wireframe model, and for the second task, we provide a graph-theoretic formulation of the minimisation problem, show that it is NP-complete in the general case, and outline a branch-and-bound type enumerative approach to solving it. Key concepts in both cases are depth-first search in graphs and the ensuing DFS spanning trees. Both algorithms have been implemented in the DNAforge design tool (https://dnaforge.org) and we present some examples of the results.
Cite as

Pekka Orponen, Shinnosuke Seki, and Antti Elonen. Secondary Structure Design for Cotranscriptional 3D RNA Origami Wireframes. In 31st International Conference on DNA Computing and Molecular Programming (DNA 31). Leibniz International Proceedings in Informatics (LIPIcs), Volume 347, pp. 6:1-6:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{orponen_et_al:LIPIcs.DNA.31.6,
  author =	{Orponen, Pekka and Seki, Shinnosuke and Elonen, Antti},
  title =	{{Secondary Structure Design for Cotranscriptional 3D RNA Origami Wireframes}},
  booktitle =	{31st International Conference on DNA Computing and Molecular Programming (DNA 31)},
  pages =	{6:1--6:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-399-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{347},
  editor =	{Schaeffer, Josie and Zhang, Fei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.31.6},
  URN =		{urn:nbn:de:0030-drops-238558},
  doi =		{10.4230/LIPIcs.DNA.31.6},
  annote =	{Keywords: RNA origami, wireframe nanostructures, cotranscriptional folding, secondary structure, kissing loops, algorithms, self-assembly}
}
Document
DOI: 10.4230/LIPIcs.DNA.30.4
Designing 3D RNA Origami Nanostructures with a Minimum Number of Kissing Loops

Authors: Antti Elonen and Pekka Orponen

Published in: LIPIcs, Volume 314, 30th International Conference on DNA Computing and Molecular Programming (DNA 30) (2024)

Abstract
We present a general design technique for rendering any 3D wireframe model, that is any connected graph linearly embedded in 3D space, as an RNA origami nanostructure with a minimum number of kissing loops. The design algorithm, which applies some ideas and methods from topological graph theory, produces renderings that contain at most one kissing-loop pair for many interesting model families, including for instance all fully triangulated wireframes and the wireframes of all Platonic solids. The design method is already implemented and available for use in the design tool DNAforge (https://dnaforge.org).
Cite as

Antti Elonen and Pekka Orponen. Designing 3D RNA Origami Nanostructures with a Minimum Number of Kissing Loops. In 30th International Conference on DNA Computing and Molecular Programming (DNA 30). Leibniz International Proceedings in Informatics (LIPIcs), Volume 314, pp. 4:1-4:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{elonen_et_al:LIPIcs.DNA.30.4,
  author =	{Elonen, Antti and Orponen, Pekka},
  title =	{{Designing 3D RNA Origami Nanostructures with a Minimum Number of Kissing Loops}},
  booktitle =	{30th International Conference on DNA Computing and Molecular Programming (DNA 30)},
  pages =	{4:1--4:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-344-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{314},
  editor =	{Seki, Shinnosuke and Stewart, Jaimie Marie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.30.4},
  URN =		{urn:nbn:de:0030-drops-209325},
  doi =		{10.4230/LIPIcs.DNA.30.4},
  annote =	{Keywords: RNA origami, wireframe nanostructures, polyhedra, kissing loops, topological graph embeddings, self-assembly}
}
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