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A Parallel Approximation Algorithm for Minimum Weight Triangulation [chapter]

Joachim Gudmundsson, Christos Levcopoulos
1998 Lecture Notes in Computer Science  
longer that 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.  ... 
doi:10.1007/978-3-540-49382-2_21 fatcat:4zvguo74tfd7xcaw42huc4udza

Tight lower bounds for minimum weight triangulation heuristics

Christos Levcopoulos, Drago Krznaric
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.  ... 
doi:10.1016/0020-0190(95)00200-6 fatcat:xv3tpujtszbnzoqo3rbebgzfqy

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

Jan Remy, Angelika Steger
2009 Journal of the ACM  
Very recently 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.  ... 
doi:10.1145/1516512.1516517 fatcat:vejnzpezubbjfhlpzdihesqhfe

A quasi-polynomial time approximation scheme for minimum weight triangulation

Jan Remy, Angelika Steger
2006 Proceedings of the thirty-eighth annual ACM symposium on Theory of computing - STOC '06  
Very recently 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.  ... 
doi:10.1145/1132516.1132563 dblp:conf/stoc/RemyS06 fatcat:plv5w56jhjbgvfzwfchjm7j2zq

A distributed triangulation algorithm for wireless sensor networks on 2D and 3D surface

Hongyu Zhou, Hongyi Wu, Su Xia, Miao Jin, Ning Ding
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.  ... 
doi:10.1109/infcom.2011.5934879 dblp:conf/infocom/ZhouWXJD11 fatcat:7lrh6uedpjfh5pi5mmksnq2qma

A new asymmetric inclusion region for minimum weight triangulation

Shiyan Hu
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.  ... 
doi:10.1007/s10898-009-9409-z fatcat:ea2in3ygabd2dirdpqqzjryn2e

Minimum-weight triangulation is NP-hard

Wolfgang Mulzer, Günter Rote
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.  ... 
doi:10.1145/1346330.1346336 fatcat:dfonpqgdc5eyzieyp6rm2dysp4

Minimum weight triangulation is NP-hard

Unknown
2006 Proceedings of the twenty-second annual symposium on Computational geometry - SCG '06  
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.  ...  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.  ... 
doi:10.1145/1137856.1137859 dblp:conf/compgeom/MulzerR06 fatcat:znouhrmdunh5na5lx3wsnanutu

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

José Correa, Guillermo Durán, Luerbio Faria, Miguel Pizaña, Gelasio Salazar
2016 Discrete Applied Mathematics  
Dourado, Lucia Penso, and Dieter Rautenbach, shows that it is NP-hard to minimize losses in burning trees in a 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.  ... 
doi:10.1016/j.dam.2016.05.007 fatcat:tbv2l3vfjnhenltu7ipqrn23hu

Efficient Multi-View Reconstruction of Large-Scale Scenes using Interest Points, Delaunay Triangulation and Graph Cuts

Patrick Labatut, Jean-Philippe Pons, Renaud Keriven
2007 2007 IEEE 11th International Conference on Computer Vision  
Then it builds an adaptive tetrahedral decomposition of space by computing 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.  ... 
doi:10.1109/iccv.2007.4408892 dblp:conf/iccv/LabatutPK07 fatcat:kbcqvm724jc6xaxoompcykaaha

A Grid-Based Approximation Algorithm for the Minimum Weight Triangulation Problem [article]

Sharath Raghvendra, Mariëtte C. Wessels
2017 arXiv   pre-print
consisting of level < i edges of some 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.  ... 
arXiv:1706.03263v1 fatcat:vojsv3v6bbci7dnacmezkdw2nm

A Grid-Based Approximation Algorithm for the Minimum Weight Triangulation Problem [chapter]

Sharath Raghvendra, Mariëtte C. Wessels
2018 Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms  
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 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.  ... 
doi:10.1137/1.9781611975031.7 dblp:conf/soda/RaghvendraW18 fatcat:j6ol4ghsezdexcgfjarqdyike4
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