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pro vyhledávání: '"Unit Disk Graphs"'
Autor:
An, Shinwoo, Cho, Kyungjin, Jang, Leo, Jung, Byeonghyeon, Lee, Yudam, Oh, Eunjin, Shin, Donghun, Shin, Hyeonjun, Song, Chanho
In this paper, we study fundamental parameterized problems such as $k$-Path/Cycle, Vertex Cover, Triangle Hitting Set, Feedback Vertex Set, and Cycle Packing for dynamic unit disk graphs. Given a vertex set $V$ changing dynamically under vertex inser
Externí odkaz:
http://arxiv.org/abs/2409.13403
We introduce a new balanced separator theorem for unit-disk graphs involving two shortest paths combined with the 1-hop neighbours of those paths and two other vertices. This answers an open problem of Yan, Xiang and Dragan [CGTA '12] and improves th
Externí odkaz:
http://arxiv.org/abs/2407.15980
Autor:
Brewer, Bruce W., Wang, Haitao
Let $V$ be a set of $n$ points in the plane. The unit-disk graph $G = (V, E)$ has vertex set $V$ and an edge $e_{uv} \in E$ between vertices $u, v \in V$ if the Euclidean distance between $u$ and $v$ is at most 1. The weight of each edge $e_{uv}$ is
Externí odkaz:
http://arxiv.org/abs/2407.03176
Autor:
Rout, Sasmita, Das, Gautam Kumar
Let $G=(V, E)$ be a simple undirected graph with no isolated vertex. A set $D_t\subseteq V$ is a total dominating set of $G$ if $(i)$ $D_t$ is a dominating set, and $(ii)$ the set $D_t$ induces a subgraph with no isolated vertex. The total dominating
Externí odkaz:
http://arxiv.org/abs/2404.03511
Publikováno v:
Phys. Rev. A 110, 022442 (2024)
Recent progress in quantum computing and quantum simulation of many-body systems with arrays of neutral atoms using Rydberg excitation has provided unforeseen opportunities towards computational advantage in solving various optimization problems. The
Externí odkaz:
http://arxiv.org/abs/2405.09803
We study the classic \textsc{(Uncapacitated) Facility Location} problem on Unit Disk Graphs (UDGs). For a given point set $P$ in the plane, the unit disk graph UDG(P) on $P$ has vertex set $P$ and an edge between two distinct points $p, q \in P$ if a
Externí odkaz:
http://arxiv.org/abs/2405.08931
Finding the diameter of a graph in general cannot be done in truly subquadratic assuming the Strong Exponential Time Hypothesis (SETH), even when the underlying graph is unweighted and sparse. When restricting to concrete classes of graphs and assumi
Externí odkaz:
http://arxiv.org/abs/2401.12881
Autor:
An, Shinwoo, Oh, Eunjin
In this paper, we consider the Cycle Packing problem on unit disk graphs defined as follows. Given a unit disk graph G with n vertices and an integer k, the goal is to find a set of $k$ vertex-disjoint cycles of G if it exists. Our algorithm runs in
Externí odkaz:
http://arxiv.org/abs/2403.11426
Akademický článek
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Autor:
Nederlof, Jesper, Szilágyi, Krisztina
In this paper we investigate the parameterized complexity of the task of counting and detecting occurrences of small patterns in unit disk graphs: Given an $n$-vertex unit disk graph $G$ with an embedding of ply $p$ (that is, the graph is represented
Externí odkaz:
http://arxiv.org/abs/2312.06377