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A Fast and Simple Algorithm for Computing Approximate Euclidean Minimum Spanning Trees
2015
Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms
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the true minimum spanning tree. ...
The Euclidean minimum spanning tree (EMST) is a fundamental and widely studied structure. ...
For example, it is well known that the exact EMST is the minimum bottleneck spanning tree, meaning that it minimizes the maximum edge length. ...
doi:10.1137/1.9781611974331.ch85
dblp:conf/soda/AryaM16
fatcat:gmesap77ube7rgq23mr5mwz3ke
Reactive Proximity Data Structures for Graphs
[article]
2020
arXiv
pre-print
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Definition 3 (Reactive bichromatic closest-pair data structure). ...
In another paper [41] , we use this data structure as part of an algorithm for Steiner TSP in road networks. ...
arXiv:1803.04555v2
fatcat:nlw3k663eve7bb656xkp2x2whm
When crossings count --- approximating the minimum spanning tree
2000
Proceedings of the sixteenth annual symposium on Computational geometry - SCG '00
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We present an (1+ε)-approximation algorithm for computing the minimum-spanning tree of points in a planar arrangement of lines, where the metric is the number of crossings between the spanning tree and ...
It is easy to verify that if we have triangle inequality then the Steiner tree weight is at least half the weight of the MST. ...
Lemma 2.6 ([Aga91]) There exists a Steiner tree M of P , so that W opt (P, L) = O(n √ n), and this is tight in the worst case (even for the case the arcs are lines). ...
doi:10.1145/336154.336197
dblp:conf/compgeom/Har-PeledI00
fatcat:nepv767f7vdt7ob2vzghnteblq
When Crossings Count - Approximating the Minimum Spanning Tree
[article]
2003
arXiv
pre-print
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the spanning tree and the lines. ...
In the first part of the paper, we present an (1+\mu)-approximation algorithm to the minimum-spanning tree of points in a planar arrangement of lines, where the metric is the number of crossings between ...
It is easy to verify that if we have triangle inequality then the Steiner tree weight is at least half the weight of the MST. ...
arXiv:cs/0303001v1
fatcat:zddqulqhungndhiiixcr57xjhq
Red-Blue-Partitioned MST, TSP, and Matching
[article]
2018
arXiv
pre-print
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: min-sum, min-max, and bottleneck. ...
Three structures have been investigated by ArkinBCCJKMM17---spanning trees, traveling salesperson tours, and perfect matchings---and the three objectives to optimize for when computing such pairs of structures ...
First consider a set of 2n points V = V L ∪ V R in a metric space, arranged in the form of two full binary trees T L , T R (with root points L , R , respectively, and each with λ leaf points and n = 2λ ...
arXiv:1807.08065v2
fatcat:joq4sccibnhuhc6ihc6q75liue
Euclidean TSP, Motorcycle Graphs, and Other New Applications of Nearest-Neighbor Chains
[article]
2019
arXiv
pre-print
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We apply it to a diverse class of geometric problems: we construct the greedy multi-fragment tour for Euclidean TSP in O(nlog n) time in any fixed dimension and for Steiner TSP in planar graphs in O(n√ ...
Algorithm 4 shows the full pseudo code. Algorithm 4 Nearest-neighbor-chain algorithm for motorcycle graphs. ...
It is a tree-like structure similar to the medial axis of a polygon, but which consists of straight segments only. ...
arXiv:1902.06875v3
fatcat:irn2mhfvr5futge4dtzraidesi
Disk Intersection Graphs: Models, Data Structures, and Algorithms
[article]
2016
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This list includes computing the chromatic number, a maximum independent set, a maximum connected dominating set, finding hamiltonian cycles and paths, and finding steiner trees. ...
We show how to maintain a maximal bichromatic matching M between R and B with respect to D(R ∪ B). ...
doi:10.17169/refubium-8433
fatcat:fkeiflaucrbgzptx7sryysj4ua
Abstract
1991
Bulletin of the Psychonomic Society
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STEINER, University of Basel (read by Gerhard F. ...
A fmal test evaluated her ability to generalize conceptual use of fractions with liquids (juice presented in glasses), including 1-3 full glasses, or glasses that were 'h or 1,4 full. ...
doi:10.3758/bf03333973
fatcat:rgrc3vz6gbfcfhw5srwul35jr4