Corpus ID: 235727247

Online Euclidean Spanners

@article{Bhore2021OnlineES,
  title={Online Euclidean Spanners},
  author={Sujoy Kumar Bhore and Csaba D. T'oth},
  journal={ArXiv},
  year={2021},
  volume={abs/2107.00684}
}
In this paper, we study the online Euclidean spanners problem for points in R. Given a set S of n points in R, a t-spanner on S is a subgraph of the underlying complete graph G = (S, ( S 2 ) ), that preserves the pairwise Euclidean distances between points in S to within a factor of t, that is the stretch factor. Suppose we are given a sequence of n points (s1, s2, . . . , sn) in R, where point si is presented in step i for i = 1, . . . , n. The objective of an online algorithm is to maintain a… Expand

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References

SHOWING 1-10 OF 55 REFERENCES
Fully Dynamic Geometric Spanners
TLDR
This paper presents the first fully dynamic algorithm for maintaining a spanner whose update time depends solely on the number of points in S and shows how to maintain a (1+ε)-spanner with O(n/εd) edges, where points can be inserted to S in an amortized update time of O(log n) and deleted from S in a amortization time of $\tilde{O}(n^{1/3})$. Expand
Randomized and deterministic algorithms for geometric spanners of small diameter
  • S. Arya, D. Mount, M. Smid
  • Mathematics, Computer Science
  • Proceedings 35th Annual Symposium on Foundations of Computer Science
  • 1994
TLDR
Randomized and deterministic algorithms are given for constructing t-spanners consisting of O(n) edges and having O(log n) diameter and it is shown how to maintain the randomized t-spanner under random insertions and deletions. Expand
Deformable spanners and applications
TLDR
The deformable spanner succinctly encodes all proximity information in a deforming point cloud, giving us efficient kinetic algorithms for problems such as the closest pair, the near neighbors of all points, approximate nearest neighbor search, well-separated pair decomposition, and approximate k-centers. Expand
Minimum weight Euclidean t-spanner is NP-hard
TLDR
It is shown that the problem of deciding whether there exists an Euclidean t-spanner, for a given set of points in the plane, of weight at most w is NP-hard for every real constant t>1, both whether planarity of the t- spanner is required or not. Expand
Geometric spanners with applications in wireless networks
TLDR
It is proved that all SparsY-graphs are weak c-spanners for a constant c and hence they allow us to approximate energy-optimal wireless networks by a constant factor. Expand
Fast Greedy Algorithms for Constructing Sparse Geometric Spanners
TLDR
The first O(nlog n)-time algorithm to compute a geometric t-spanner on V, a connected graph G = (V,E) with edge weights equal to the Euclidean distances between the endpoints, and its degree is bounded by a constant. Expand
Efficient construction of a bounded-degree spanner with low weight
TLDR
An efficient implementation of a greedy algorithm is given that constructs at-spanner having bounded degree such that the total length of all its edges is bounded byO (logn) times the length of a minimum spanning tree forS. Expand
There are Planar Graphs Almost as Good as the Complete Graph
  • P. Chew
  • Computer Science, Mathematics
  • J. Comput. Syst. Sci.
  • 1989
TLDR
It is shown that there is a planar graph G on S with the property that for any points A and B of S there exists an A-to-B path along edges of the graph with path length equal to the straight-line distance between A and A. Expand
On-line generalized Steiner problem
TLDR
A simple randomized algorithm based on on- line generalized Steiner algorithms whose competitive ratio is within a constant factor of the best competitive algorithm for the on-line GSP is provided. Expand
A new way to weigh Malnourished Euclidean graphs
In this paper, we show that any Euclidean graph over a set V of n points in k-dimensional space that satisfies either the leapfrog property or the isolation property has small weight, i.e., hasExpand
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