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A new subgraph of minimum weight triangulations
[chapter]
1996
Lecture Notes in Computer Science
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In this paper, two sufficient conditions for identifying a subgraph of minimum weight triangulation of a planar point set are presented. ...
An O(n 3 ) time algorithm for finding this subgraph from a set of n points is presented. ...
A minimum weight triangulation, denoted by MWT, of S is defined as for all possible T (S), ω(MWT(S)) = min{ω(T (S))}. Garey and Johnson's book (1979) . ...
doi:10.1007/bfb0009503
fatcat:lm77bhrqmnhdzipzshw73pnsny
On Computing New Classes of Optimal Triangulations with Angular Constraints
[chapter]
1999
Lecture Notes in Computer Science
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Manabu Sugai and Professor Kokichi Sugihara and Professor Masao Iri [16] for sharing us their programs for the implementation of our algorithms. ...
The Subgraph of the Minimum Weight Triangulation with Angular Constraints In this section we present the algorithm for computing the subgraph of the minimum weight triangulation with angular constraints ...
In Problem (1) we proposed somewhat more general criteria of the minimum weight triangulation and in Problem (2) a new criterion which is dierent from the minmax angle criterion. ...
doi:10.1007/3-540-68535-9_5
fatcat:644eaoivozftna737eircs2wnq
Computing a subgraph of the minimum weight triangulation
1994
Computational geometry
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Given a set S of n points in the plane, it is shown that the &-skeleton of S is a subgraph of the minimum weight triangulation of S. ...
The $-skeleton of S is the /3-skeleton of S for fi = J5. ...
the Gabriel graph are not the desired subgraphs of the minimum weight triangulation. ...
doi:10.1016/0925-7721(94)90014-0
fatcat:atp3kb4k3vdxhnz47dwblk7c2u
LMT-skeleton heuristics for several new classes of optimal triangulations☆☆This research is supported by the Grant-in-Aid of Ministry of Education, Science, Sports and Culture, of Japan, Grant-in-Aid for Scientific Research(C), 08680377, 1997, and Grant-in-Aid for Scientific Research(B), 10205214, 1998
2000
Computational geometry
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Given a planar point set, we consider three classes of optimal triangulations: (1) the minimum weight triangulation with angular constraints (constraints on the minimum angle and the maximum angle in a ...
With appropriate definition of local optimality for each class, a simple unified method is established for the computation of the subgraphs of optimal triangulations. ...
Manabu Sugai, Professor Kokichi Sugihara and Professor Masao Iri [23] for kindly providing us their programs for the implementation of our algorithms. ...
doi:10.1016/s0925-7721(00)00016-x
fatcat:7gfeqvbfafbctcjcvblc6eird4
A new asymmetric inclusion region for minimum weight triangulation
2009
Journal of Global Optimization
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In this paper, a new asymmetric graph called one-sided β-skeleton is introduced. We show that the one-sided circle-disconnected ( √ 2β)skeleton is a subgraph of a minimum weight triangulation. ...
The minimum weight triangulation, or MWT in short, is defined as a triangulation of P with the minimum weight. ...
A new asymmetric inclusion region for identifying a subgraph of the minimum weight triangulation is proposed. ...
doi:10.1007/s10898-009-9409-z
fatcat:ea2in3ygabd2dirdpqqzjryn2e
Optimal Triangulation Using an Evolutionary Algorithm
[article]
2021
figshare.com
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In the Minimum Weight Triangulation (MWT)problem, we want to draw a triangulation of a givenpoint set that minimizes the sum of the edges length.Recently, Mulzer and Rote have proved that thisproblem is ...
A triangulation of a point set in the plane is a maximal planar straight-line graph with the vertexset . ...
A Minimum Weight Triangulation of a point set is a triangulation with minimum weight. Figure 1 shows an example of such triangulations. ...
doi:10.6084/m9.figshare.14462076.v1
fatcat:4o4uhmwae5cplog7vnqgegmbjq
Optimal Triangulation Using an Evolutionary Algorithm
2010
Zenodo
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In the Minimum Weight Triangulation (MWT) problem, we want to draw a triangulation of a given point set that minimizes the sum of the edges length. ...
A triangulation of a point set S in the plane is a maximal planar straight-line graph with the vertex set S . ...
A Minimum Weight Triangulation of a point set is a triangulation with minimum weight. Figure 1 shows an example of such triangulations. ...
doi:10.5281/zenodo.3813451
fatcat:ve5d2dy66zgmnep6lyho4bxiz4
Minimum cuts and shortest homologous cycles
2009
Proceedings of the 25th annual symposium on Computational geometry - SCG '09
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A slight generalization of our minimum-cut algorithm computes a minimum-cost subgraph in every 2 -homology class. ...
We also prove that finding a minimum-cost subgraph homologous to a single input cycle is NP-hard. ...
A minimum (s, t)-cut is an (s, t)-cut of minimum size, or minimum total weight if the edges of G are weighted. ...
doi:10.1145/1542362.1542426
dblp:conf/compgeom/ChambersEN09
fatcat:77bdajq6i5ax7cpbzwxek26bve
Page 5330 of Mathematical Reviews Vol. , Issue 2000h
[page]
2000
Mathematical Reviews
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Ravi, R. (1-CMU-I; Pittsburgh, PA)
A new bound for the 2-edge connected subgraph problem. ...
We show that the minimum cost of a 2-edge connected subgraph is at most four-thirds the cost of the minimum cost 5-integral solution of the subtour relaxation. ...
Page 6251 of Mathematical Reviews Vol. , Issue 96j
[page]
1996
Mathematical Reviews
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channel.”
96j:68178 68U05 05C10
Yang, Bo-Ting (PRC-XJUS-SC; Xi’an)
A better subgraph of the minimum weight triangulation. ...
Summary: “Given a set S of n points in the plane, it is shown that the csc(27/7)-skeleton of S is a subgraph of the minimum weight triangulation of S. We improve the result in a paper by J. M. ...
A parallel algorithm for minimum weighted colouring of triangulated graphs
1992
Theoretical Computer Science
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In particular. there exist I '% algorithms for finding a largest clique, a minimum colouring. a largest stable set (independent set). and a minimum clique cover of a triangulated graph. ...
Howcler. there has been no parallel solution of the minimum weighted colouring problem (M WCOL for short) for triangulated graphs. ...
If S,=O then we think of the row i as being "free". Creating a new stable set is simply finding a free row. ...
doi:10.1016/0304-3975(92)90358-m
fatcat:i4t2ll3m6rchth27d5sxueeyyy
HT-graphs: centers, connected r-domination and Steiner trees
1993
Computer Science Journal of Moldova
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In this paper two new characterizations of these graphs are given and then it is shown that the central vertex, connected r-domination and Steiner trees problems are linear or almost linear time solvable ...
Lemma 13 A set D ⊂ V is a minimum connected r-dominating set of G with r(v) = 0 when v ∈ R and r(v) =2r(G) otherwise if and only if a spanning tree of a subgraph induced by D is a minimum cardinalitySteiner ...
G 2 is triangulated graph; F.Dragan 2. G does not contain a sun S k (k ≥ 4) as an isometric subgraph. ...
doaj:3a2788d6349f44849a41a470d36d9156
fatcat:q5ywbcc34zacbffnys6jbjx6fi
Page 1401 of Mathematical Reviews Vol. , Issue 86d
[page]
1986
Mathematical Reviews
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The applications are: (1) every triangulated graph without an infinite complete subgraph is perfect (conjectured by the reviewer); (2) a new proof of Lekkerkerker and Boland’s characterization of interval ...
1401
The circuit polynomial of a graph G is the polynomial }*[], wa where Wa is a weight associated with each component a of a spanning subgraph of G, whose components are nodes, edges and circuits, and ...
Page 4476 of Mathematical Reviews Vol. , Issue 95h
[page]
1995
Mathematical Reviews
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An undirected graph G is called triangulated if none of its induced subgraphs is a circuit of length at least 4. If both G and its complement G are triangulated, the graph G is called split. ...
A graph is called 7,,-universal if it contains every threshold graph with n vertices as its subgraph. T,-universal graphs with the minimum number of vertices are called minimum T,,-universal. ...
Page 3171 of Mathematical Reviews Vol. , Issue 95f
[page]
1995
Mathematical Reviews
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A minimum weight triangulation of S is a triangulation that minimizes the sum of the edge lengths. It is shown that the 2- skeleton of S is a subgraph of the minimum weight triangulation of S. ...
Mark (3-SK-C; Saskatoon, SK) Computing a subgraph of the minimum weight triangulation. (English summary) Comput. Geom. 4 (1994), no. 1, 13-26. ...
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