Zobrazeno 1 - 10
of 344
pro vyhledávání: '"Toth, P D"'
We present algorithms for the online minimum hitting set problem: Given a set $P$ of $n$ points in the plane and a sequence of geometric objects that arrive one-by-one, we need to maintain a hitting set at all times. For disks of radii in the interva
Externí odkaz:
http://arxiv.org/abs/2412.04646
Autor:
Aloupis, Greg, Biniaz, Ahmad, Bose, Prosenjit, De Carufel, Jean-Lou, Eppstein, David, Maheshwari, Anil, Odak, Saeed, Smid, Michiel, Tóth, Csaba D., Valtr, Pavel
Edge crossings in geometric graphs are sometimes undesirable as they could lead to unwanted situations such as collisions in motion planning and inconsistency in VLSI layout. Short geometric structures such as shortest perfect matchings, shortest spa
Externí odkaz:
http://arxiv.org/abs/2410.05580
Autor:
Akitaya, Hugo A., Biniaz, Ahmad, Demaine, Erik D., Kleist, Linda, Stock, Frederick, Tóth, Csaba D.
For a set of red and blue points in the plane, a minimum bichromatic spanning tree (MinBST) is a shortest spanning tree of the points such that every edge has a red and a blue endpoint. A MinBST can be computed in $O(n\log n)$ time where $n$ is the n
Externí odkaz:
http://arxiv.org/abs/2409.11614
Euclidean spanners are important geometric objects that have been extensively studied since the 1980s. The two most basic "compactness'' measures of a Euclidean spanner $E$ are the size (number of edges) $|E|$ and the weight (sum of edge weights) $\|
Externí odkaz:
http://arxiv.org/abs/2409.08227
Autor:
Bhore, Sujoy, Keszegh, Balázs, Kupavskii, Andrey, Le, Hung, Louvet, Alexandre, Pálvölgyi, Dömötör, Tóth, Csaba D.
We study spanners in planar domains, including polygonal domains, polyhedral terrain, and planar metrics. Previous work showed that for any constant $\epsilon\in (0,1)$, one could construct a $(2+\epsilon)$-spanner with $O(n\log(n))$ edges (SICOMP 20
Externí odkaz:
http://arxiv.org/abs/2404.05045
Low-distortional metric embeddings are a crucial component in the modern algorithmic toolkit. In an online metric embedding, points arrive sequentially and the goal is to embed them into a simple space irrevocably, while minimizing the distortion. Ou
Externí odkaz:
http://arxiv.org/abs/2310.14078
Autor:
Tóth, Csaba D.
Publikováno v:
Journal of Graph Algorithms and Applications, 28(2):37-45, 2024
It is shown that every $n$-vertex graph that admits a 2-bend RAC drawing in the plane, where the edges are polylines with two bends per edge and any pair of edges can only cross at a right angle, has at most $20n-24$ edges for $n\geq 3$. This improve
Externí odkaz:
http://arxiv.org/abs/2308.02663
A fundamental question is whether one can maintain a maximum independent set in polylogarithmic update time for a dynamic collection of geometric objects in Euclidean space. Already, for a set of intervals, it is known that no dynamic algorithm can m
Externí odkaz:
http://arxiv.org/abs/2308.00979
Motivated by the problem of redistricting, we study area-preserving reconfigurations of connected subdivisions of a simple polygon. A connected subdivision of a polygon $\mathcal{R}$, called a district map, is a set of interior disjoint connected pol
Externí odkaz:
http://arxiv.org/abs/2307.00704
Autor:
Dumitrescu, Adrian, Tóth, Csaba D.
Publikováno v:
Theor. Comput. Sci. 1019: 114818 (2024)
We introduce the Observation Route Problem ($\textsf{ORP}$) defined as follows: Given a set of $n$ pairwise disjoint compact regions in the plane, find a shortest tour (route) such that an observer walking along this tour can see (observe) some point
Externí odkaz:
http://arxiv.org/abs/2306.11522