| Title: | Algorithms for distance problems in continuous graphs |
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| Authors: | ID Cabello, Sergio (Author)
ID Garijo, Delia (Author)
ID Kalb, Antonia (Author)
ID Klute, Fabian (Author)
ID Parada, Irene (Author)
ID Silveira, Rodrigo I. (Author) |
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| Files: |  PDF - Presentation file, download (946,64 KB)
MD5: 1579CD8B964FC7804ED311E0CB11A34C
 URL - Source URL, visit https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.13
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| Language: | English |
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| Typology: | 1.08 - Published Scientific Conference Contribution |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | We study the problem of computing the diameter and the mean distance of a continuous graph, i.e., a connected graph where all points along the edges, instead of only the vertices, must be taken into account. It is known that for continuous graphs with $m$ edges these values can be computed in roughly $O(m^2)$ time. In this paper, we use geometric techniques to obtain subquadratic time algorithms to compute the diameter and the mean distance of a continuous graph for two well-established classes of sparse graphs. We show that the diameter and the mean distance of a continuous graph of treewidth at most $k$ can be computed in $O(n \log^{O(k)} n)$ time, where $n$ is the number of vertices in the graph. We also show that computing the diameter and mean distance of a continuous planar graph with $n$ vertices and $F$ faces takes $O(n F \log n)$ time. |
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| Keywords: | diameter, mean distance, continuous graphs, treewidth, planar graphs |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Year of publishing: | 2025 |
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| Number of pages: | Str. 13:1-13:16 |
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| PID: | 20.500.12556/DiRROS-24740  |
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| UDC: | 004.42:519.17 |
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| DOI: | 10.4230/LIPIcs.WADS.2025.13 |
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| COBISS.SI-ID: | 261662723 |
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| Publication date in DiRROS: | 16.12.2025 |
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| Views: | 7 |
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| Downloads: | 6 |
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| Metadata: |    |
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