Minimum-weight triangulation (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Minimum-weight triangulation" in English language version.

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17doi.org

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14ams.org

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9semanticscholar.org

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2lth.se

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2handle.net

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ams.org (Global: 451^st place; English: 277^th place)

mathscinet.ams.org

For surveys of the problem, see Xu (1998), Levcopoulos (2008), and De Loera, Rambau & Santos (2010). Xu, Yin-Feng (1998), "Minimum weight triangulations", Handbook of Combinatorial Optimization, Vol. 2, Boston, MA: Kluwer Academic Publishers, pp. 617–634, MR 1665412. Levcopoulos, Christos (2008), "Minimum Weight Triangulation", in Kao, Ming-Yang (ed.), Encyclopedia of Algorithms, Springer, pp. 546–548, ISBN 978-0-387-30770-1. De Loera, Jesús A.; Rambau, Jörg; Santos, Francisco (2010), "3.2.3 Greedy and minimum weight triangulations", Triangulations: Structures for Algorithms and Applications, Algorithms and Computation in Mathematics, vol. 25, Springer, pp. 102–107, ISBN 978-3-642-12970-4.
See also Manacher & Zobrist (1979). Manacher, Glenn K.; Zobrist, Albert L. (1979), "Neither the greedy nor the Delaunay triangulation of a planar point set approximates the optimal triangulation", Information Processing Letters, 9 (1): 31–34, doi:10.1016/0020-0190(79)90104-2, MR 0537055.
Kirkpatrick (1980). A weaker bound was given by Manacher & Zobrist (1979). Kirkpatrick, David G. (1980), "A note on Delaunay and optimal triangulations", Information Processing Letters, 10 (3): 127–128, doi:10.1016/0020-0190(80)90062-9, MR 0566856. Manacher, Glenn K.; Zobrist, Albert L. (1979), "Neither the greedy nor the Delaunay triangulation of a planar point set approximates the optimal triangulation", Information Processing Letters, 9 (1): 31–34, doi:10.1016/0020-0190(79)90104-2, MR 0537055.
A family of examples proving that the approximation ratio is $\Omega ({\sqrt {n}})$ was given by Levcopoulos (1987), and the matching upper bound is by Levcopoulos & Krznaric (1998). As with the approximation ratio for Delaunay triangulation, a weaker bound was also given by Manacher & Zobrist (1979). Levcopoulos, Christos (1987), "An Ω(√n) lower bound for the nonoptimality of the greedy triangulation", Information Processing Letters, 25 (4): 247–251, doi:10.1016/0020-0190(87)90170-0, MR 0896144. Levcopoulos, C.; Krznaric, D. (1998), "Quasi-greedy triangulations approximating the minimum weight triangulation" (PDF), Journal of Algorithms, 27 (2): 303–338, doi:10.1006/jagm.1997.0918, MR 1622398, S2CID 13991653. Manacher, Glenn K.; Zobrist, Albert L. (1979), "Neither the greedy nor the Delaunay triangulation of a planar point set approximates the optimal triangulation", Information Processing Letters, 9 (1): 31–34, doi:10.1016/0020-0190(79)90104-2, MR 0537055.
Remy & Steger (2009). For earlier results on polynomial-time approximation algorithms, see Plaisted & Hong (1987) (log-factor approximation) and Levcopoulos & Krznaric (1998) (constant-factor approximation). Remy, Jan; Steger, Angelika (2009), "A quasi-polynomial time approximation scheme for minimum weight triangulation", Journal of the ACM, 56 (3), Article A15, doi:10.1145/1516512.1516517, S2CID 1781658. Plaisted, D. A.; Hong, J. (1987), "A heuristic triangulation algorithm", Journal of Algorithms, 8 (3): 405–437, doi:10.1016/0196-6774(87)90020-4. Levcopoulos, C.; Krznaric, D. (1998), "Quasi-greedy triangulations approximating the minimum weight triangulation" (PDF), Journal of Algorithms, 27 (2): 303–338, doi:10.1006/jagm.1997.0918, MR 1622398, S2CID 13991653.
Lingas (1987); Heath & Pemmaraju (1994). Lingas, Andrzej (1987), "A new heuristic for minimum weight triangulation", SIAM Journal on Algebraic and Discrete Methods, 8 (4): 646–658, doi:10.1137/0608053, MR 0918066. Heath, L. S.; Pemmaraju, S. V. (1994), "New results for the minimum weight triangulation problem", Algorithmica, 12 (6): 533–552, doi:10.1007/BF01188718, hdl:10919/19701, MR 1297812, S2CID 21160664.
Yang, Xu & You (1994). Yang, Bo Ting; Xu, Yin Feng; You, Zhao Yong (1994), "A chain decomposition algorithm for the proof of a property on minimum weight triangulations", in Du, Ding-Zhu; Zhang, Xiang-Sun (eds.), Algorithms and Computation: 5th International Symposium, ISAAC '94, Beijing, P. R. China, August 25–27, 1994, Proceedings, Lecture Notes in Computer Science, vol. 834, Berlin: Springer, pp. 423–427, doi:10.1007/3-540-58325-4_207, ISBN 978-3-540-58325-7, MR 1316441.
Keil (1994); Cheng, Golin & Tsang (1995); Cheng & Xu (2001); Hu (2010). Keil, J. Mark (1994), "Computing a subgraph of the minimum weight triangulation", Computational Geometry: Theory & Applications, 4 (1): 18–26, doi:10.1016/0925-7721(94)90014-0. Cheng, Siu-Wing; Golin, Mordecai; Tsang, J. (1995), "Expected case analysis of β-skeletons with applications to the construction of minimum weight triangulations", Proc. 7th Canadian Conference on Computational Geometry (CCCG 1995), pp. 279–284. Cheng, Siu-Wing; Xu, Yin-Feng (2001), "On β-skeleton as a subgraph of the minimum weight triangulation", Theoretical Computer Science, 262 (1–2): 459–471, doi:10.1016/S0304-3975(00)00318-2. Hu, Shiyan (2010), "A new asymmetric inclusion region for minimum weight triangulation", Journal of Global Optimization, 46 (1): 63–73, CiteSeerX 10.1.1.377.6164, doi:10.1007/s10898-009-9409-z, MR 2566136, S2CID 869128.
Kyoda et al. (1997). Kyoda, Yoshiaki; Imai, Keiko; Takeuchi, Fumihiko; Tajima, Akira (1997), "A branch-and-cut approach for minimum weight triangulation", Algorithms and Computation (Singapore, 1997), Lecture Notes in Computer Science, vol. 1350, Berlin: Springer, pp. 384–393, doi:10.1007/3-540-63890-3_41, ISBN 978-3-540-63890-2, MR 1651067.
Hoffmann & Okamoto (2004); Grantson, Borgelt & Levcopoulos (2005); Knauer & Spillner (2006). Hoffmann, M.; Okamoto, Y. (2004), "The minimum weight triangulation problem with few inner points", Proc. 1st International Workshop on Parameterized and Exact Computation, pp. 200–212. Grantson, M.; Borgelt, C.; Levcopoulos, C. (2005), "Minimum weight triangulation by cutting out triangles", Proc. 16th International Symposium on Algorithms and Computation, pp. 984–994. Knauer, Christian; Spillner, Andreas (2006), "A fixed-parameter algorithm for the minimum weight triangulation problem based on small graph separators", Graph-Theoretic Concepts in Computer Science, Lecture Notes in Computer Science, vol. 4271, Berlin: Springer, pp. 49–57, doi:10.1007/11917496_5, ISBN 978-3-540-48381-6, MR 2290717.
Anagnostou & Corneil (1993); Meijer & Rappaport (1992). Anagnostou, Efthymios; Corneil, Derek (1993), "Polynomial-time instances of the minimum weight triangulation problem", Computational Geometry. Theory and Applications, 3 (5): 247–259, doi:10.1016/0925-7721(93)90016-Y, MR 1251594. Meijer, Henk; Rappaport, David (1992), "Computing the minimum weight triangulation of a set of linearly ordered points", Information Processing Letters, 42 (1): 35–38, doi:10.1016/0020-0190(92)90129-J, MR 1160443.
Eppstein (1994). Eppstein, David (1994), "Approximating the minimum weight Steiner triangulation" (PDF), Discrete and Computational Geometry, 11 (2): 163–191, doi:10.1007/BF02574002, MR 1254088.
Gudmundsson & Levcopoulos (2007); Aichholzer et al. (2009). Gudmundsson, Joachim; Levcopoulos, Christos (2007), "Minimum weight pseudo-triangulations", Computational Geometry Theory and Applications, 38 (3): 139–153, doi:10.1016/j.comgeo.2007.05.004, MR 2352529.
Lenhart & Liotta (2002). Lenhart, William; Liotta, Giuseppe (2002), "The drawability problem for minimum weight triangulations", Theoretical Computer Science, 270 (1–2): 261–286, doi:10.1016/S0304-3975(00)00383-2, MR 1871072.

cccg.ca (Global: low place; English: low place)

Lingas (1998). Lingas, Andrzej (1998), "Subexponential-time algorithms for minimum weight triangulations and related problems", Proceedings of the 10th Canadian Conference on Computational Geometry (CCCG'98).
Bose, Devroye & Evans (1996). Bose, Prosenjit; Devroye, Luc; Evans, William (1996), "Diamonds are not a minimum weight triangulation's best friend", Proc. 8th Canadian Conference on Computational Geometry (CCCG 1996) (PDF), pp. 68–73.

core.ac.uk (Global: 1,734^th place; English: 1,312^th place)

Keil (1994); Cheng, Golin & Tsang (1995); Cheng & Xu (2001); Hu (2010). Keil, J. Mark (1994), "Computing a subgraph of the minimum weight triangulation", Computational Geometry: Theory & Applications, 4 (1): 18–26, doi:10.1016/0925-7721(94)90014-0. Cheng, Siu-Wing; Golin, Mordecai; Tsang, J. (1995), "Expected case analysis of β-skeletons with applications to the construction of minimum weight triangulations", Proc. 7th Canadian Conference on Computational Geometry (CCCG 1995), pp. 279–284. Cheng, Siu-Wing; Xu, Yin-Feng (2001), "On β-skeleton as a subgraph of the minimum weight triangulation", Theoretical Computer Science, 262 (1–2): 459–471, doi:10.1016/S0304-3975(00)00318-2. Hu, Shiyan (2010), "A new asymmetric inclusion region for minimum weight triangulation", Journal of Global Optimization, 46 (1): 63–73, CiteSeerX 10.1.1.377.6164, doi:10.1007/s10898-009-9409-z, MR 2566136, S2CID 869128.

doi.org (Global: 2^nd place; English: 2^nd place)

See also Manacher & Zobrist (1979). Manacher, Glenn K.; Zobrist, Albert L. (1979), "Neither the greedy nor the Delaunay triangulation of a planar point set approximates the optimal triangulation", Information Processing Letters, 9 (1): 31–34, doi:10.1016/0020-0190(79)90104-2, MR 0537055.
Kirkpatrick (1980). A weaker bound was given by Manacher & Zobrist (1979). Kirkpatrick, David G. (1980), "A note on Delaunay and optimal triangulations", Information Processing Letters, 10 (3): 127–128, doi:10.1016/0020-0190(80)90062-9, MR 0566856. Manacher, Glenn K.; Zobrist, Albert L. (1979), "Neither the greedy nor the Delaunay triangulation of a planar point set approximates the optimal triangulation", Information Processing Letters, 9 (1): 31–34, doi:10.1016/0020-0190(79)90104-2, MR 0537055.
A family of examples proving that the approximation ratio is $\Omega ({\sqrt {n}})$ was given by Levcopoulos (1987), and the matching upper bound is by Levcopoulos & Krznaric (1998). As with the approximation ratio for Delaunay triangulation, a weaker bound was also given by Manacher & Zobrist (1979). Levcopoulos, Christos (1987), "An Ω(√n) lower bound for the nonoptimality of the greedy triangulation", Information Processing Letters, 25 (4): 247–251, doi:10.1016/0020-0190(87)90170-0, MR 0896144. Levcopoulos, C.; Krznaric, D. (1998), "Quasi-greedy triangulations approximating the minimum weight triangulation" (PDF), Journal of Algorithms, 27 (2): 303–338, doi:10.1006/jagm.1997.0918, MR 1622398, S2CID 13991653. Manacher, Glenn K.; Zobrist, Albert L. (1979), "Neither the greedy nor the Delaunay triangulation of a planar point set approximates the optimal triangulation", Information Processing Letters, 9 (1): 31–34, doi:10.1016/0020-0190(79)90104-2, MR 0537055.
Lingas (1986). Lingas, Andrzej (1986), "The Greedy and Delaunay triangulations are not bad in the average case", Information Processing Letters, 22 (1): 25–31, doi:10.1016/0020-0190(86)90038-4.
Remy & Steger (2009). For earlier results on polynomial-time approximation algorithms, see Plaisted & Hong (1987) (log-factor approximation) and Levcopoulos & Krznaric (1998) (constant-factor approximation). Remy, Jan; Steger, Angelika (2009), "A quasi-polynomial time approximation scheme for minimum weight triangulation", Journal of the ACM, 56 (3), Article A15, doi:10.1145/1516512.1516517, S2CID 1781658. Plaisted, D. A.; Hong, J. (1987), "A heuristic triangulation algorithm", Journal of Algorithms, 8 (3): 405–437, doi:10.1016/0196-6774(87)90020-4. Levcopoulos, C.; Krznaric, D. (1998), "Quasi-greedy triangulations approximating the minimum weight triangulation" (PDF), Journal of Algorithms, 27 (2): 303–338, doi:10.1006/jagm.1997.0918, MR 1622398, S2CID 13991653.
Lingas (1987); Heath & Pemmaraju (1994). Lingas, Andrzej (1987), "A new heuristic for minimum weight triangulation", SIAM Journal on Algebraic and Discrete Methods, 8 (4): 646–658, doi:10.1137/0608053, MR 0918066. Heath, L. S.; Pemmaraju, S. V. (1994), "New results for the minimum weight triangulation problem", Algorithmica, 12 (6): 533–552, doi:10.1007/BF01188718, hdl:10919/19701, MR 1297812, S2CID 21160664.
Yang, Xu & You (1994). Yang, Bo Ting; Xu, Yin Feng; You, Zhao Yong (1994), "A chain decomposition algorithm for the proof of a property on minimum weight triangulations", in Du, Ding-Zhu; Zhang, Xiang-Sun (eds.), Algorithms and Computation: 5th International Symposium, ISAAC '94, Beijing, P. R. China, August 25–27, 1994, Proceedings, Lecture Notes in Computer Science, vol. 834, Berlin: Springer, pp. 423–427, doi:10.1007/3-540-58325-4_207, ISBN 978-3-540-58325-7, MR 1316441.
Keil (1994); Cheng, Golin & Tsang (1995); Cheng & Xu (2001); Hu (2010). Keil, J. Mark (1994), "Computing a subgraph of the minimum weight triangulation", Computational Geometry: Theory & Applications, 4 (1): 18–26, doi:10.1016/0925-7721(94)90014-0. Cheng, Siu-Wing; Golin, Mordecai; Tsang, J. (1995), "Expected case analysis of β-skeletons with applications to the construction of minimum weight triangulations", Proc. 7th Canadian Conference on Computational Geometry (CCCG 1995), pp. 279–284. Cheng, Siu-Wing; Xu, Yin-Feng (2001), "On β-skeleton as a subgraph of the minimum weight triangulation", Theoretical Computer Science, 262 (1–2): 459–471, doi:10.1016/S0304-3975(00)00318-2. Hu, Shiyan (2010), "A new asymmetric inclusion region for minimum weight triangulation", Journal of Global Optimization, 46 (1): 63–73, CiteSeerX 10.1.1.377.6164, doi:10.1007/s10898-009-9409-z, MR 2566136, S2CID 869128.
Dickerson & Montague (1996); Cheng, Katoh & Sugai (1996); Beirouti & Snoeyink (1998); Aichholzer, Aurenhammer & Hainz (1999). Dickerson, Matthew T.; Montague, Mark H. (1996), "A (usually?) connected subgraph of the minimum weight triangulation", Proc. 12th ACM Symposium on Computational Geometry, pp. 204–213, doi:10.1145/237218.237364, S2CID 18962760. Cheng, Siu-Wing; Katoh, Naoki; Sugai, Manabu (1996), "A study of the LMT-skeleton", Algorithms and Computation, Lecture Notes in Computer Science, vol. 1178, pp. 256–265, doi:10.1007/BFb0009502, ISBN 978-3-540-62048-8. Beirouti, Ronald; Snoeyink, Jack (1998), "Implementations of the LMT heuristic for minimum weight triangulation", Proc. 14th ACM Symposium on Computational Geometry, pp. 96–105, doi:10.1145/276884.276895, S2CID 15102126. Aichholzer, Oswin; Aurenhammer, Franz; Hainz, Reinhard (1999), "New results on MWT subgraphs", Information Processing Letters, 69 (5): 215–219, doi:10.1016/S0020-0190(99)00018-6.
Qin, Wang & Gong (1997); Capp & Julstrom (1998). Qin, Kaihuai; Wang, Wenping; Gong, Minglun (1997), "A genetic algorithm for the minimum weight triangulation", IEEE International Conference on Evolutionary Computation, pp. 541–546, doi:10.1109/ICEC.1997.592370, hdl:10722/45578, S2CID 18775737, Semantic Scholar. Capp, Kerry; Julstrom, Bryant A. (1998), "A weight-coded genetic algorithm for the minimum weight triangulation problem", Proc. ACM Symposium on Applied Computing, Atlanta, Georgia, United States, pp. 327–331, doi:10.1145/330560.330833, S2CID 13589205, Semantic Scholar{{citation}}: CS1 maint: location missing publisher (link).
Kyoda et al. (1997). Kyoda, Yoshiaki; Imai, Keiko; Takeuchi, Fumihiko; Tajima, Akira (1997), "A branch-and-cut approach for minimum weight triangulation", Algorithms and Computation (Singapore, 1997), Lecture Notes in Computer Science, vol. 1350, Berlin: Springer, pp. 384–393, doi:10.1007/3-540-63890-3_41, ISBN 978-3-540-63890-2, MR 1651067.
Jahani, Bigham & Askari (2010). Jahani, M.; Bigham, B.S.; Askari, A. (2010), "An ant colony algorithm for the minimum weight triangulation", International Conference on Computational Science and Its Applications (ICCSA), pp. 81–85, doi:10.1109/ICCSA.2010.38, S2CID 11790811, Semantic Scholar.
Hoffmann & Okamoto (2004); Grantson, Borgelt & Levcopoulos (2005); Knauer & Spillner (2006). Hoffmann, M.; Okamoto, Y. (2004), "The minimum weight triangulation problem with few inner points", Proc. 1st International Workshop on Parameterized and Exact Computation, pp. 200–212. Grantson, M.; Borgelt, C.; Levcopoulos, C. (2005), "Minimum weight triangulation by cutting out triangles", Proc. 16th International Symposium on Algorithms and Computation, pp. 984–994. Knauer, Christian; Spillner, Andreas (2006), "A fixed-parameter algorithm for the minimum weight triangulation problem based on small graph separators", Graph-Theoretic Concepts in Computer Science, Lecture Notes in Computer Science, vol. 4271, Berlin: Springer, pp. 49–57, doi:10.1007/11917496_5, ISBN 978-3-540-48381-6, MR 2290717.
Anagnostou & Corneil (1993); Meijer & Rappaport (1992). Anagnostou, Efthymios; Corneil, Derek (1993), "Polynomial-time instances of the minimum weight triangulation problem", Computational Geometry. Theory and Applications, 3 (5): 247–259, doi:10.1016/0925-7721(93)90016-Y, MR 1251594. Meijer, Henk; Rappaport, David (1992), "Computing the minimum weight triangulation of a set of linearly ordered points", Information Processing Letters, 42 (1): 35–38, doi:10.1016/0020-0190(92)90129-J, MR 1160443.
Eppstein (1994). Eppstein, David (1994), "Approximating the minimum weight Steiner triangulation" (PDF), Discrete and Computational Geometry, 11 (2): 163–191, doi:10.1007/BF02574002, MR 1254088.
Gudmundsson & Levcopoulos (2007); Aichholzer et al. (2009). Gudmundsson, Joachim; Levcopoulos, Christos (2007), "Minimum weight pseudo-triangulations", Computational Geometry Theory and Applications, 38 (3): 139–153, doi:10.1016/j.comgeo.2007.05.004, MR 2352529.
Lenhart & Liotta (2002). Lenhart, William; Liotta, Giuseppe (2002), "The drawability problem for minimum weight triangulations", Theoretical Computer Science, 270 (1–2): 261–286, doi:10.1016/S0304-3975(00)00383-2, MR 1871072.

handle.net (Global: 102^nd place; English: 76^th place)

hdl.handle.net

Lingas (1987); Heath & Pemmaraju (1994). Lingas, Andrzej (1987), "A new heuristic for minimum weight triangulation", SIAM Journal on Algebraic and Discrete Methods, 8 (4): 646–658, doi:10.1137/0608053, MR 0918066. Heath, L. S.; Pemmaraju, S. V. (1994), "New results for the minimum weight triangulation problem", Algorithmica, 12 (6): 533–552, doi:10.1007/BF01188718, hdl:10919/19701, MR 1297812, S2CID 21160664.
Qin, Wang & Gong (1997); Capp & Julstrom (1998). Qin, Kaihuai; Wang, Wenping; Gong, Minglun (1997), "A genetic algorithm for the minimum weight triangulation", IEEE International Conference on Evolutionary Computation, pp. 541–546, doi:10.1109/ICEC.1997.592370, hdl:10722/45578, S2CID 18775737, Semantic Scholar. Capp, Kerry; Julstrom, Bryant A. (1998), "A weight-coded genetic algorithm for the minimum weight triangulation problem", Proc. ACM Symposium on Applied Computing, Atlanta, Georgia, United States, pp. 327–331, doi:10.1145/330560.330833, S2CID 13589205, Semantic Scholar{{citation}}: CS1 maint: location missing publisher (link).

lth.se (Global: low place; English: low place)

fileadmin.cs.lth.se

A family of examples proving that the approximation ratio is $\Omega ({\sqrt {n}})$ was given by Levcopoulos (1987), and the matching upper bound is by Levcopoulos & Krznaric (1998). As with the approximation ratio for Delaunay triangulation, a weaker bound was also given by Manacher & Zobrist (1979). Levcopoulos, Christos (1987), "An Ω(√n) lower bound for the nonoptimality of the greedy triangulation", Information Processing Letters, 25 (4): 247–251, doi:10.1016/0020-0190(87)90170-0, MR 0896144. Levcopoulos, C.; Krznaric, D. (1998), "Quasi-greedy triangulations approximating the minimum weight triangulation" (PDF), Journal of Algorithms, 27 (2): 303–338, doi:10.1006/jagm.1997.0918, MR 1622398, S2CID 13991653. Manacher, Glenn K.; Zobrist, Albert L. (1979), "Neither the greedy nor the Delaunay triangulation of a planar point set approximates the optimal triangulation", Information Processing Letters, 9 (1): 31–34, doi:10.1016/0020-0190(79)90104-2, MR 0537055.
Remy & Steger (2009). For earlier results on polynomial-time approximation algorithms, see Plaisted & Hong (1987) (log-factor approximation) and Levcopoulos & Krznaric (1998) (constant-factor approximation). Remy, Jan; Steger, Angelika (2009), "A quasi-polynomial time approximation scheme for minimum weight triangulation", Journal of the ACM, 56 (3), Article A15, doi:10.1145/1516512.1516517, S2CID 1781658. Plaisted, D. A.; Hong, J. (1987), "A heuristic triangulation algorithm", Journal of Algorithms, 8 (3): 405–437, doi:10.1016/0196-6774(87)90020-4. Levcopoulos, C.; Krznaric, D. (1998), "Quasi-greedy triangulations approximating the minimum weight triangulation" (PDF), Journal of Algorithms, 27 (2): 303–338, doi:10.1006/jagm.1997.0918, MR 1622398, S2CID 13991653.

psu.edu (Global: 207^th place; English: 136^th place)

citeseerx.ist.psu.edu

Keil (1994); Cheng, Golin & Tsang (1995); Cheng & Xu (2001); Hu (2010). Keil, J. Mark (1994), "Computing a subgraph of the minimum weight triangulation", Computational Geometry: Theory & Applications, 4 (1): 18–26, doi:10.1016/0925-7721(94)90014-0. Cheng, Siu-Wing; Golin, Mordecai; Tsang, J. (1995), "Expected case analysis of β-skeletons with applications to the construction of minimum weight triangulations", Proc. 7th Canadian Conference on Computational Geometry (CCCG 1995), pp. 279–284. Cheng, Siu-Wing; Xu, Yin-Feng (2001), "On β-skeleton as a subgraph of the minimum weight triangulation", Theoretical Computer Science, 262 (1–2): 459–471, doi:10.1016/S0304-3975(00)00318-2. Hu, Shiyan (2010), "A new asymmetric inclusion region for minimum weight triangulation", Journal of Global Optimization, 46 (1): 63–73, CiteSeerX 10.1.1.377.6164, doi:10.1007/s10898-009-9409-z, MR 2566136, S2CID 869128.

semanticscholar.org (Global: 11^th place; English: 8^th place)

api.semanticscholar.org

A family of examples proving that the approximation ratio is $\Omega ({\sqrt {n}})$ was given by Levcopoulos (1987), and the matching upper bound is by Levcopoulos & Krznaric (1998). As with the approximation ratio for Delaunay triangulation, a weaker bound was also given by Manacher & Zobrist (1979). Levcopoulos, Christos (1987), "An Ω(√n) lower bound for the nonoptimality of the greedy triangulation", Information Processing Letters, 25 (4): 247–251, doi:10.1016/0020-0190(87)90170-0, MR 0896144. Levcopoulos, C.; Krznaric, D. (1998), "Quasi-greedy triangulations approximating the minimum weight triangulation" (PDF), Journal of Algorithms, 27 (2): 303–338, doi:10.1006/jagm.1997.0918, MR 1622398, S2CID 13991653. Manacher, Glenn K.; Zobrist, Albert L. (1979), "Neither the greedy nor the Delaunay triangulation of a planar point set approximates the optimal triangulation", Information Processing Letters, 9 (1): 31–34, doi:10.1016/0020-0190(79)90104-2, MR 0537055.
Remy & Steger (2009). For earlier results on polynomial-time approximation algorithms, see Plaisted & Hong (1987) (log-factor approximation) and Levcopoulos & Krznaric (1998) (constant-factor approximation). Remy, Jan; Steger, Angelika (2009), "A quasi-polynomial time approximation scheme for minimum weight triangulation", Journal of the ACM, 56 (3), Article A15, doi:10.1145/1516512.1516517, S2CID 1781658. Plaisted, D. A.; Hong, J. (1987), "A heuristic triangulation algorithm", Journal of Algorithms, 8 (3): 405–437, doi:10.1016/0196-6774(87)90020-4. Levcopoulos, C.; Krznaric, D. (1998), "Quasi-greedy triangulations approximating the minimum weight triangulation" (PDF), Journal of Algorithms, 27 (2): 303–338, doi:10.1006/jagm.1997.0918, MR 1622398, S2CID 13991653.
Lingas (1987); Heath & Pemmaraju (1994). Lingas, Andrzej (1987), "A new heuristic for minimum weight triangulation", SIAM Journal on Algebraic and Discrete Methods, 8 (4): 646–658, doi:10.1137/0608053, MR 0918066. Heath, L. S.; Pemmaraju, S. V. (1994), "New results for the minimum weight triangulation problem", Algorithmica, 12 (6): 533–552, doi:10.1007/BF01188718, hdl:10919/19701, MR 1297812, S2CID 21160664.
Keil (1994); Cheng, Golin & Tsang (1995); Cheng & Xu (2001); Hu (2010). Keil, J. Mark (1994), "Computing a subgraph of the minimum weight triangulation", Computational Geometry: Theory & Applications, 4 (1): 18–26, doi:10.1016/0925-7721(94)90014-0. Cheng, Siu-Wing; Golin, Mordecai; Tsang, J. (1995), "Expected case analysis of β-skeletons with applications to the construction of minimum weight triangulations", Proc. 7th Canadian Conference on Computational Geometry (CCCG 1995), pp. 279–284. Cheng, Siu-Wing; Xu, Yin-Feng (2001), "On β-skeleton as a subgraph of the minimum weight triangulation", Theoretical Computer Science, 262 (1–2): 459–471, doi:10.1016/S0304-3975(00)00318-2. Hu, Shiyan (2010), "A new asymmetric inclusion region for minimum weight triangulation", Journal of Global Optimization, 46 (1): 63–73, CiteSeerX 10.1.1.377.6164, doi:10.1007/s10898-009-9409-z, MR 2566136, S2CID 869128.
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Qin, Wang & Gong (1997); Capp & Julstrom (1998). Qin, Kaihuai; Wang, Wenping; Gong, Minglun (1997), "A genetic algorithm for the minimum weight triangulation", IEEE International Conference on Evolutionary Computation, pp. 541–546, doi:10.1109/ICEC.1997.592370, hdl:10722/45578, S2CID 18775737, Semantic Scholar. Capp, Kerry; Julstrom, Bryant A. (1998), "A weight-coded genetic algorithm for the minimum weight triangulation problem", Proc. ACM Symposium on Applied Computing, Atlanta, Georgia, United States, pp. 327–331, doi:10.1145/330560.330833, S2CID 13589205, Semantic Scholar{{citation}}: CS1 maint: location missing publisher (link).
Jahani, Bigham & Askari (2010). Jahani, M.; Bigham, B.S.; Askari, A. (2010), "An ant colony algorithm for the minimum weight triangulation", International Conference on Computational Science and Its Applications (ICCSA), pp. 81–85, doi:10.1109/ICCSA.2010.38, S2CID 11790811, Semantic Scholar.

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Eppstein (1994). Eppstein, David (1994), "Approximating the minimum weight Steiner triangulation" (PDF), Discrete and Computational Geometry, 11 (2): 163–191, doi:10.1007/BF02574002, MR 1254088.

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eprints.cs.vt.edu

Lingas (1987); Heath & Pemmaraju (1994). Lingas, Andrzej (1987), "A new heuristic for minimum weight triangulation", SIAM Journal on Algebraic and Discrete Methods, 8 (4): 646–658, doi:10.1137/0608053, MR 0918066. Heath, L. S.; Pemmaraju, S. V. (1994), "New results for the minimum weight triangulation problem", Algorithmica, 12 (6): 533–552, doi:10.1007/BF01188718, hdl:10919/19701, MR 1297812, S2CID 21160664.