| Title: | Testing whether a subgraph is convex or isometric |
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| Authors: | ID Cabello, Sergio (Author) |
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| Files: |  PDF - Presentation file, download (1,08 MB)
MD5: 5B29D4B9D018CA75239B5A81688741E9
 URL - Source URL, visit https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.12
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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 consider the following two algorithmic problems: given a graph $G$ and a subgraph $H\subseteq G$, decide whether $H$ is an isometric or a geodesically convex subgraph of $G$. It is relatively easy to see that the problems can be solved by computing the distances between all pairs of vertices. We provide a conditional lower bound showing that, for sparse graphs with $n$ vertices and $\Theta(n)$ edges, we cannot expect to solve the problem in $O(n^{2-\varepsilon})$ time for any constant $\varepsilon>0$. We also show that the problem can be solved in subquadratic time for planar graphs and in near-linear time for graphs of bounded treewidth. Finally, we provide a near-linear time algorithm for the setting where $G$ is a plane graph and $H$ is defined by a few cycles in $G$. |
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| Keywords: | convex subgraphs, isometric subgraphs, plane 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. 12:1-12:16 |
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| PID: | 20.500.12556/DiRROS-24738  |
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| UDC: | 004.42:519.17 |
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| DOI: | 10.4230/LIPIcs.WADS.2025.12 |
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| COBISS.SI-ID: | 261640963 |
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| Note: |
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| Publication date in DiRROS: | 16.12.2025 |
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| Views: | 12 |
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| Downloads: | 5 |
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| Metadata: |    |
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