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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 ...##
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On Locality-Sensitive Orderings and Their Applications

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*. ...

##
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Approximating Minimum Manhattan Networks in Higher Dimensions
[article]

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. ...

##
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A Gap-ETH-Tight Approximation Scheme for Euclidean TSP
[article]

2021
*
arXiv
*
pre-print

We determine

arXiv:2011.03778v2
fatcat:kkhvkz6ktrgznf3kw72ecxacgy
*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*. ...##
###
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
*

Thus,

doi:10.1137/1.9781611973105.132
dblp:conf/soda/AbrahamCKS13
fatcat:j4w3743jifa7vg25rzs33krpue
*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. ...##
###
A Gap-ETH-Tight Approximation Scheme for Euclidean TSP

2022
*
2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)
*

We determine

doi:10.1109/focs52979.2021.00043
fatcat:k7swjioourdidkytk5ccbg3rom
*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*. ...##
###
Multistage SFM: A Coarse-to-Fine Approach for 3D Reconstruction
[article]

2016
*
arXiv
*
pre-print

We present a multistage approach

arXiv:1512.06235v3
fatcat:s4ohbzc3h5gnzpy5igyjeh6cnq
*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. ...##
###
Light orthogonal networks with constant geometric dilation

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. ...

##
###
Path-Fault-Tolerant Approximate Shortest-Path Trees
[article]

2015
*
arXiv
*
pre-print

This consists

arXiv:1507.01695v1
fatcat:u754yg7ynrhsjnssk27rl72gee
*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 ...##
###
Approximating the Generalized Minimum Manhattan Network Problem

2017
*
Algorithmica
*

We consider

doi:10.1007/s00453-017-0298-0
fatcat:3xwqsqmlffefhhiwio65em6qce
*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. ...##
###
Approximating the Generalized Minimum Manhattan Network Problem
[chapter]

2013
*
Lecture Notes in Computer Science
*

We consider

doi:10.1007/978-3-642-45030-3_67
fatcat:sbhipgnybnhx3hi2side2n3iii
*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. ...##
###
Near-Shortest Path Routing in Hybrid Communication Networks
[article]

2022
*
arXiv
*
pre-print

A sizable portion

arXiv:2202.08008v1
fatcat:5lnsmu3yzncatmld373hfgymsm
*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. ...##
###
Traveling with a Pez Dispenser (or, Routing Issues in MPLS)

2005
*
SIAM journal on computing (Print)
*

These routing algorithms on general graphs are obtained by finding a tree cover

doi:10.1137/s0097539702409927
fatcat:rp6m5t5tmvczphmkc6ajep2tda
*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. ...##
###
An Integer Linear Programming Model for View Selection on Overlapping Camera Clusters

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. ...

##
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Sublinear Fully Distributed Partition with Applications

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. ...

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