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A Parallel Approximation Algorithm for Minimum Weight Triangulation
[chapter]

1998
*
Lecture Notes in Computer Science
*

longer that

doi:10.1007/978-3-540-49382-2_21
fatcat:4zvguo74tfd7xcaw42huc4udza
*the**minimum**weight**triangulation*. ... This is done by developing a relaxed version of*the**quasi*-*greedy**triangulation*algorithm. ... A*minimum**weight**triangulation*of S or MWT(S) is a*triangulation*of S such that |T | is minimized. ...##
###
Tight lower bounds for minimum weight triangulation heuristics

1996
*
Information Processing Letters
*

*The*

*minimum*spanning tree heuristic is obtained by optimally

*triangulating*a subgraph of

*the*Delaunay

*triangulation*, whereas

*the*

*greedy*spanning tree heuristic is obtained by optimally

*triangulating*a ... subgraph of

*the*

*greedy*

*triangulation*. ... Up to date,

*the*only known polynomial time heuristic for

*the*

*minimum*

*weight*

*triangulation*which achieves a constant-factor

*approximation*ratio is

*the*so-called

*quasi*-

*greedy*

*triangulation*[ 71. ...

##
###
Page 1281 of Mathematical Reviews Vol. , Issue 2001B
[page]

2001
*
Mathematical Reviews
*

algorithm for

*minimum**weight**triangulation*. ...*The*analysis shows that*the*relaxed version still outputs a*triangulation*which is within a constant factor longer than*the**minimum**weight**triangulation*. ...##
###
Page 7570 of Mathematical Reviews Vol. , Issue 96m
[page]

1996
*
Mathematical Reviews
*

Rade Zivaljevié (Belgrade)
96m:52019 52B55 68U05 Levcopoulos, Christos (S-LUND-C; Lund); Krznaric, Drago (S-LUND-C; Lund)

*Quasi*-*greedy**triangulations**approximating**the**minimum**weight**triangulation*. ... This, together with*the*previously known lower bound, settles*the*ques- tion of*the*worst-case*approximation*ratio between*the**greedy*and*the**minimum**weight**triangulation*. ...##
###
A quasi-polynomial time approximation scheme for minimum weight triangulation

2009
*
Journal of the ACM
*

Very recently

doi:10.1145/1516512.1516517
fatcat:vejnzpezubbjfhlpzdihesqhfe
*the*problem was shown to be N P-hard by Mulzer and Rote. In this paper, we present a*quasi*-polynomial time*approximation*scheme for*Minimum**Weight**Triangulation*. ...*The**Minimum**Weight**Triangulation*problem is to find a*triangulation*T * of*minimum*length for a given set of points P in*the*Euclidean plane. ... CONCLUDING REMARKS In this paper we introduced a*quasi*-polynomial time*approximation*scheme for*Minimum**Weight**Triangulation*. ...##
###
A quasi-polynomial time approximation scheme for minimum weight triangulation

2006
*
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing - STOC '06
*

Very recently

doi:10.1145/1132516.1132563
dblp:conf/stoc/RemyS06
fatcat:plv5w56jhjbgvfzwfchjm7j2zq
*the*problem was shown to be N P-hard by Mulzer and Rote. In this paper, we present a*quasi*-polynomial time*approximation*scheme for*Minimum**Weight**Triangulation*. ...*The**Minimum**Weight**Triangulation*problem is to find a*triangulation*T * of*minimum*length for a given set of points P in*the*Euclidean plane. ... CONCLUDING REMARKS In this paper we introduced a*quasi*-polynomial time*approximation*scheme for*Minimum**Weight**Triangulation*. ...##
###
A distributed triangulation algorithm for wireless sensor networks on 2D and 3D surface

2011
*
2011 Proceedings IEEE INFOCOM
*

*Triangulation*serves as

*the*basis for many geometrybased algorithms in wireless sensor networks. ... In this paper we propose a distributed algorithm that produces a

*triangulation*for an arbitrary sensor network, with no constraints on communication model or granularity of

*the*

*triangulation*. ...

*Triangulation*under

*Quasi*-UDG (α = 0.4). (h)

*Triangulation*under

*Quasi*-UDG (α = 0.6). (i)

*Triangulation*under Log-normal. (j)

*Triangulation*with k = 1. (k)

*Triangulation*with k = 2. ...

##
###
A new asymmetric inclusion region for minimum weight triangulation

2009
*
Journal of Global Optimization
*

*The*

*minimum*

*weight*

*triangulation*, or MWT in short, is defined as a

*triangulation*of P with

*the*

*minimum*

*weight*. ... intersected segmented between

*the*complete graph and

*the*

*greedy*

*triangulation*of

*the*point set. ... We show that

*the*one-sided circle-disconnected ( √ 2β)skeleton is a subgraph of a

*minimum*

*weight*

*triangulation*. ...

##
###
Minimum-weight triangulation is NP-hard

2008
*
Journal of the ACM
*

*the*

*minimum*-

*weight*

*triangulation*. ... In

*the*

*minimum*-

*weight*

*triangulation*(MWT) problem, we are looking for a

*triangulation*of a given point set that minimizes

*the*sum of

*the*edge lengths. ... Levcopoulos and Krznaric [26] introduce

*quasi*-

*greedy*

*triangulations*, which

*approximate*

*the*MWT within a constant factor. ...

##
###
Minimum weight triangulation is NP-hard

2006
*
Proceedings of the twenty-second annual symposium on Computational geometry - SCG '06
*

In

doi:10.1145/1137856.1137859
dblp:conf/compgeom/MulzerR06
fatcat:znouhrmdunh5na5lx3wsnanutu
*the**minimum**weight**triangulation*(MWT) problem, we are looking for a*triangulation*of a given point set that minimizes*the*sum of*the*edge lengths. ... A*triangulation*of a planar point set S is a maximal plane straight-line graph with vertex set S. ... Levcopoulos and Krznaric [26] introduce*quasi*-*greedy**triangulations*, which*approximate**the*MWT within a constant factor. ...##
###
Page 2783 of Mathematical Reviews Vol. , Issue 99d
[page]

1991
*
Mathematical Reviews
*

Lund);
Krznaric, Drago (S-LUND-C; Lund)

*Quasi*-*greedy**triangulations**approximating**the**minimum**weight**triangulation*. ...*The*edge-flipping distance between two*triangulations*of*the*same set of points is*the**minimum*number of edge-flipping operations needed to convert one into*the*other. ...##
###
Preface: LAGOS'13: Seventh Latin-American Algorithms, Graphs, and Optimization Symposium, Playa del Carmen, México — 2013

2016
*
Discrete Applied Mathematics
*

Dourado, Lucia Penso, and Dieter Rautenbach, shows that it is NP-hard to minimize losses in burning trees in a

doi:10.1016/j.dam.2016.05.007
fatcat:tbv2l3vfjnhenltu7ipqrn23hu
*weighted*version of Hartnell's firefighter game (1995), but also provides two*approximation*... Slash and burn on graphs -Firefighting with general*weights*, by Vitor Costa, Simone Dantas, Mitre C. ... and*the*Sociedad Matemática Mexicana for their financial support, which made*the*organization of this event possible. ...##
###
Efficient Multi-View Reconstruction of Large-Scale Scenes using Interest Points, Delaunay Triangulation and Graph Cuts

2007
*
2007 IEEE 11th International Conference on Computer Vision
*

Then it builds an adaptive tetrahedral decomposition of space by computing

doi:10.1109/iccv.2007.4408892
dblp:conf/iccv/LabatutPK07
fatcat:kbcqvm724jc6xaxoompcykaaha
*the*3D Delaunay*triangulation*of*the*3D point set. ... A globally optimal label assignment, as regards photo-consistency of*the*output mesh and compatibility with*the*visibility of keypoints in input images, is efficiently found as a*minimum*cut solution in ... This ranges from a tight bounding box to a closer*approximation*by*the*visual hull. ...##
###
A Grid-Based Approximation Algorithm for the Minimum Weight Triangulation Problem
[article]

2017
*
arXiv
*
pre-print

consisting of level < i edges of some

arXiv:1706.03263v1
fatcat:vojsv3v6bbci7dnacmezkdw2nm
*minimum**weight**triangulation*. ... Given a set of n points on a plane, in*the**Minimum**Weight**Triangulation*problem, we wish to find a*triangulation*that minimizes*the*sum of Euclidean length of its edges. ... In*the*following section, we present our algorithm to compute an*approximate**Minimum**Weight**triangulation*. ...##
###
A Grid-Based Approximation Algorithm for the Minimum Weight Triangulation Problem
[chapter]

2018
*
Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms
*

Given a set of n points on a plane, in

doi:10.1137/1.9781611975031.7
dblp:conf/soda/RaghvendraW18
fatcat:j6ol4ghsezdexcgfjarqdyike4
*the**Minimum**Weight**Triangulation*problem, we wish to find a*triangulation*that minimizes*the*sum of Euclidean length of its edges. ... In this paper we present a novel polynomial-time algorithm that computes a 14-*approximation*of*the**minimum**weight**triangulation*-a constant that is significantly smaller than what has been previously known ... In*the*following section, we present our algorithm to compute an*approximate**Minimum**Weight**triangulation*. ...
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