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Page 4223 of Mathematical Reviews Vol. , Issue 99f [page]

1999 Mathematical Reviews  
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

Timothy M. Chan, Sariel Har-Peled, Mitchell Jones, Michael Wagner
2018 Innovations in Theoretical Computer Science  
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]

Aparna Das, Emden R. Gansner, Michael Kaufmann, Stephen Kobourov, Joachim Spoerhase, Alexander Wolff
2012 arXiv   pre-print
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]

Sándor Kisfaludi-Bak, Jesper Nederlof, Karol Węgrzycki
2021 arXiv   pre-print
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]

Ittai Abraham, Shiri Chechik, David Kempe, Aleksandrs Slivkins
2013 Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms  
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

Sandor Kisfaludi-Bak, Jesper Nederlof, Karol Wegrzycki
2022 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)  
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]

Rajvi Shah and Aditya Deshpande and P J Narayanan
2016 arXiv   pre-print
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

Adrian Dumitrescu, Csaba D. Tóth
2009 Journal of Discrete Algorithms  
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]

Annalisa D'Andrea, Mattia D'Emidio, Daniele Frigioni, Stefano Leucci, Guido Proietti
2015 arXiv   pre-print
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

Aparna Das, Krzysztof Fleszar, Stephen Kobourov, Joachim Spoerhase, Sankar Veeramoni, Alexander Wolff
2017 Algorithmica  
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]

Aparna Das, Krzysztof Fleszar, Stephen Kobourov, Joachim Spoerhase, Sankar Veeramoni, Alexander Wolff
2013 Lecture Notes in Computer Science  
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]

Sam Coy, Artur Czumaj, Michael Feldmann, Kristian Hinnenthal, Fabian Kuhn, Christian Scheideler, Philipp Schneider, Martijn Struijs
2022 arXiv   pre-print
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)

Anupam Gupta, Amit Kumar, Rajeev Rastogi
2005 SIAM journal on computing (Print)  
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

Massimo Mauro, Hayko Riemenschneider, Alberto Signoroni, Riccardo Leonardi, Luc Van Gool
2014 2014 2nd International Conference on 3D Vision  
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

Bilel Derbel, Mohamed Mosbah, Akka Zemmari
2009 Theory of Computing Systems  
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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