| Naslov: | Connectivity with uncertainty regions given as line segments |
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| Avtorji: | ID Cabello, Sergio (Avtor)
ID Gajser, David (Avtor) |
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| Datoteke: |  RAZ_Cabello_Sergio_2024.pdf (685,93 KB)
MD5: DB4D9F8EFC927B763D18C6AFE0557AC9
 http://dx.doi.org/10.1007/s00453-023-01200-5
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| Jezik: | Angleški jezik |
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| Vrsta gradiva: | Znanstveno delo |
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| Tipologija: | 1.01 - Izvirni znanstveni članek |
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| Organizacija: | FNM - Fakulteta za naravoslovje in matematiko
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| Opis: | For a set $\mathcal{Q}$ of points in the plane and a real number $δ$ ≥ 0, let $\mathbb{G}_δ(\mathcal{Q})$ be the graph defined on $\mathcal{Q}$ by connecting each pair of points at distance at most $δ$. We consider the connectivity of $\mathbb{G}_δ(\mathcal{Q})$ in the best scenario when the location of a few of the points is uncertain, but we know for each uncertain point a line segment that contains it. More precisely, we consider the following optimization problem: given a set $\mathcal{P}$ of $n$ – $k$ points in the plane and a set $\mathcal{S}$ of $k$ line segments in the plane, find the minimum $δ$ ≥ 0 with the property that we can select one point $p_s$ ∈ $s$ for each segment $s$ ∈ $\mathcal{S}$ and the corresponding graph $\mathbb{G}_δ(\mathcal{P} ∪ \{p_s$ | $s ∈ \mathcal{S}\})$ is connected. It is known that the problem is NP-hard. We provide an algorithm to exactly compute an optimal solution in $\mathcal{O}( f (k)n$ ${\rm log}$ $n)$ time, for a computable function $f$ (·). This implies that the problem is FPT when parameterized by $k$. The best previous algorithm uses $\mathcal{O}((k!)^kk^{k+1} · n^{2k})$ time and computes the solution up to fixed precision. |
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| Ključne besede: | computational geometry, uncertainty, geometric optimization, fixed parameter tractability, parametric search |
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| Status publikacije: | Objavljeno |
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| Verzija publikacije: | Objavljena publikacija |
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| Poslano v recenzijo: | 17.03.2023 |
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| Datum sprejetja članka: | 11.12.2023 |
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| Datum objave: | 09.01.2024 |
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| Leto izida: | 2024 |
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| Št. strani: | str. 1512-1544 |
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| Številčenje: | Letn. 6, št. 5 |
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| PID: | 20.500.12556/DKUM-88567  |
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| UDK: | 519.17 |
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| COBISS.SI-ID: | 180364547 |
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| DOI: | 10.1007/s00453-023-01200-5 |
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| ISSN pri članku: | 0178-4617 |
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| Datum objave v DKUM: | 21.10.2025 |
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| Število ogledov: | 112 |
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| Število prenosov: | 6 |
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| Metapodatki: |    |
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| Področja: | Ostalo
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