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Page 4223 of Mathematical Reviews Vol. , Issue 99f
[page]
1999
Mathematical Reviews
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99f:68159 68R10
Krumme, David W. (1-TUFT-EEC; Medford, MA
An optimal disjoint pair of additive spanners for the 3D grid. ...
This paper exhibits a pair of (x + 4)-spanners for the infinite three-dimensional grid, and shows that 4 is the least integer K for which there exists an edge-disjoint pair of delay-K spanners.”
99f:68160 ...
On Locality-Sensitive Orderings and Their Applications
2018
Innovations in Theoretical Computer Science
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The same approach works for quadtrees -one can shift the quadtree constructed for a point set several times such that for any pair of points in the quadtree, there will be a shift where the two points ...
One can order the points of P according to this traversal, resulting in an ordering ≺ of the underlying set [0, 1) 2 . ...
In addition, the successor and predecessor (of the same color) need to recompute their pairs. ...
doi:10.4230/lipics.itcs.2019.21
dblp:conf/innovations/ChanHJ19
fatcat:hjjfo76x25hrlewclaavnsgr5m
Approximating Minimum Manhattan Networks in Higher Dimensions
[article]
2012
arXiv
pre-print
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For 3D, we also give a 4(k-1)-approximation algorithm for the case that the terminals are contained in the union of k > 2 parallel planes. ...
The problem is NP-hard in 2D and there is no PTAS for 3D (unless P= NP). Approximation algorithms are known for 2D, but not for 3D. ...
This work was started at the 2009 Bertinoro Workshop on Graph Drawing. We thank the organizers Beppe Liotta and Walter Didimo for creating an inspiring atmosphere. ...
arXiv:1107.0901v2
fatcat:64b4lnvq65gvrbcw2ienjb5riu
A Gap-ETH-Tight Approximation Scheme for Euclidean TSP
[article]
2021
arXiv
pre-print
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We determine the optimal dependence on ε in the running time of an algorithm that computes a (1+ε)-approximate tour, under a plausible assumption. ...
We revisit the classic task of finding the shortest tour of n points in d-dimensional Euclidean space, for any fixed constant d ≥ 2. ...
Bodlaender for his double counting argument in Lemma 6.13, Artur Czumaj for sharing the full version of [17] with us, and Hung Le for answering multiple questions regarding spanners. ...
arXiv:2011.03778v2
fatcat:kkhvkz6ktrgznf3kw72ecxacgy
Low-distortion Inference of Latent Similarities from a Multiplex Social Network
[chapter]
2013
Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms
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Thus, an observed social network provides a noisy signal about the latent underlying "social space:" the way in which individuals are similar or dissimilar. ...
The observed social network is the unlabeled union of these graphs, i.e., the presence or absence of edges can be observed, but not their origins. ...
Acknowledgments We would like to thank Christian Borgs, Jennifer Chayes, Moises Goldszmidt, Bobby Kleinberg, Jon Kleinberg, Peter Monge, Satish Rao and Ken Wilbur for useful discussions and pointers. ...
doi:10.1137/1.9781611973105.132
dblp:conf/soda/AbrahamCKS13
fatcat:j4w3743jifa7vg25rzs33krpue
A Gap-ETH-Tight Approximation Scheme for Euclidean TSP
2022
2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)
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We determine the optimal dependence on ε in the running time of an algorithm that computes a (1 + ε)-approximate tour, under a plausible assumption. ...
We revisit the classic task of finding the shortest tour of n points in d-dimensional Euclidean space, for any fixed constant d 2. ...
Bodlaender for his double counting argument in Lemma 5.13 and Hung Le for answering multiple questions regarding spanners. ...
doi:10.1109/focs52979.2021.00043
fatcat:k7swjioourdidkytk5ccbg3rom
Multistage SFM: A Coarse-to-Fine Approach for 3D Reconstruction
[article]
2016
arXiv
pre-print
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We present a multistage approach for SFM reconstruction of a single component that breaks the sequential nature of the incremental SFM methods. ...
Several methods have been proposed for large-scale 3D reconstruction from large, unorganized image collections. ...
We would also like to thank the authors of Bhowmick et al. (2014) for sharing the curated image set of Hampi Vitthala Temple. ...
arXiv:1512.06235v3
fatcat:s4ohbzc3h5gnzpy5igyjeh6cnq
Light orthogonal networks with constant geometric dilation
2009
Journal of Discrete Algorithms
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An orthogonal spanner network for a given set of n points in the plane is a plane straight line graph with axis-aligned edges that connects all input points. ...
We show that for any set of n points in the plane, there is an orthogonal spanner network that (i) is short having a total edge length at most a constant times the length of a Euclidean minimum spanning ...
Acknowledgements We thank Ansgar Grüne and Minghui Jiang for interesting discussions on the topic. We are also grateful to the anonymous referees for many useful comments and suggestions. ...
doi:10.1016/j.jda.2008.07.007
fatcat:72swxfhbgzdxnkmqzvre5h34dy
Path-Fault-Tolerant Approximate Shortest-Path Trees
[article]
2015
arXiv
pre-print
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This consists of a simultaneous fault of a set F of at most f adjacent edges along a shortest path emanating from the source, and it is recognized as one of the most frequent disruption in an SPT. ...
Moreover, we show that our construction can be further refined to get a stretch factor of 3 and a size of O(n n) for the special case f=2, and that it can be converted into a very efficient approximate-distance ...
There exists an O(n) time algorithm to compute an ancestorleaf path Q in T G (r) whose removal splits T G (r) into a set of disjoint subtrees T G (r, r 1 ), . . . , T G (r, r j ) such that, for each i ...
arXiv:1507.01695v1
fatcat:u754yg7ynrhsjnssk27rl72gee
Approximating the Generalized Minimum Manhattan Network Problem
2017
Algorithmica
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We consider the generalized minimum Manhattan network problem (GMMN). The input to this problem is a set R of n pairs of terminals, which are points in R 2 . ...
As a corollary, we obtain an exponential improvement upon the previously best O(n ε )-ratio for MMN in d dimensions [ESA'11]. ...
We thank Andreas Spillner for pointing us to the application of Manhattan networks in phylogenetics. ...
doi:10.1007/s00453-017-0298-0
fatcat:3xwqsqmlffefhhiwio65em6qce
Approximating the Generalized Minimum Manhattan Network Problem
[chapter]
2013
Lecture Notes in Computer Science
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We consider the generalized minimum Manhattan network problem (GMMN). The input to this problem is a set R of n pairs of terminals, which are points in R 2 . ...
As a corollary, we obtain an exponential improvement upon the previously best O(n ε )-ratio for MMN in d dimensions [ESA'11]. ...
We thank Andreas Spillner for pointing us to the application of Manhattan networks in phylogenetics. ...
doi:10.1007/978-3-642-45030-3_67
fatcat:sbhipgnybnhx3hi2side2n3iii
Near-Shortest Path Routing in Hybrid Communication Networks
[article]
2022
arXiv
pre-print
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A sizable portion of the previous research for the 𝖧𝖸𝖡𝖱𝖨𝖣 model revolves around basic communication primitives and computing distances or shortest paths in networks. ...
In this paper, we extend this study to a related fundamental problem of computing compact routing schemes for near-shortest paths in the local communication graph. ...
By definition, a pair of points in an UDG is connected with an edge if the distance between them is small enough. The same is true for a pair of edges in a UDG. ...
arXiv:2202.08008v1
fatcat:5lnsmu3yzncatmld373hfgymsm
Traveling with a Pez Dispenser (or, Routing Issues in MPLS)
2005
SIAM journal on computing (Print)
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These routing algorithms on general graphs are obtained by finding a tree cover of a graph, i.e., a small family of subtrees of the graph such that, for each pair of vertices, one of the trees in the family ...
(See the papers [4] and [2] for two other conventional routing schemes which are name-independent.) Spanners. ...
We would like to thank Jon Kleinberg, Bruce Shepherd, Eva Tardos, Peter Winkler, and Francis Zane for discussions and helpful comments. ...
doi:10.1137/s0097539702409927
fatcat:rp6m5t5tmvczphmkc6ajep2tda
An Integer Linear Programming Model for View Selection on Overlapping Camera Clusters
2014
2014 2nd International Conference on 3D Vision
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The solution of the ILP leads to an optimal subset of selected cameras. ...
We express the problem with an Integer Linear Programming (ILP) model, where cameras are modeled with binary variables, while the linear constraints enforce the completeness of the 3D reconstruction. ...
They first estimate reconstruction accuracy between pairs of overlapping images, from which they form a graph and find the skeletal by means of a maximum-leaf t-spanner algorithm. Li et al. ...
doi:10.1109/3dv.2014.25
dblp:conf/3dim/MauroRSLG14
fatcat:img6z3y2gzbgrcqmlw3eoph7vy
Sublinear Fully Distributed Partition with Applications
2009
Theory of Computing Systems
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For these two bounds, we prove that there exist some graphs for which the expected number of rounds is either O(ln(n)) or (n 2 ). For specific topologies, additional bounds are given. ...
We apply our algorithms for constructing low stretch graph spanners and network synchronizers in sublinear deterministic time in the CON GEST model. ...
The spanner is obtained by considering the set of edges spanning each cluster and by selecting an inter-cluster edge for each pair of two neighboring clusters. ...
doi:10.1007/s00224-009-9190-x
fatcat:2rw7jclsezci7nhhifv4nwo27m
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