메뉴 건너뛰기




Volumn 93, Issue 1, 2002, Pages 57-70

Minimum networks for four points in space

Author keywords

Minimum network; Steiner ratio; Steiner tree; Unslovability

Indexed keywords


EID: 0036386751     PISSN: 00465755     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1020389712969     Document Type: Article
Times cited : (20)

References (22)
  • 3
    • 52449144884 scopus 로고
    • A proof of Gilbert and Pollak's conjecture on the Steiner ratio
    • Du, D. Z., and Hwang, F. K.: A proof of Gilbert and Pollak's conjecture on the Steiner ratio, Algorithmica, 7 (1992), 121-135.
    • (1992) Algorithmica , vol.7 , pp. 121-135
    • Du, D.Z.1    Hwang, F.K.2
  • 5
    • 0141805916 scopus 로고
    • A short proof of a result of Pollak on Steiner minimal trees
    • Du, D. Z., Yao, E. Y. and Hwang, F. K.: A short proof of a result of Pollak on Steiner minimal trees, J. Combin. Theory Ser. A, 32 (1982), 396-400.
    • (1982) J. Combin. Theory Ser. A , vol.32 , pp. 396-400
    • Du, D.Z.1    Yao, E.Y.2    Hwang, F.K.3
  • 6
    • 0141471115 scopus 로고
    • A simple proof for a result of Ollerenshaw on Steiner trees
    • Nonconvex Optim. Appl. 1, Kluwer Acad. Publ., Dordrecht
    • Du, X. F., Du, D. Z., Gao, B. and Lixue, Q.: A simple proof for a result of Ollerenshaw on Steiner trees, In: Advances in Optimization and Approximation, Nonconvex Optim. Appl. 1, Kluwer Acad. Publ., Dordrecht, 1994, pp. 68-71.
    • (1994) Advances in Optimization and Approximation , pp. 68-71
    • Du, X.F.1    Du, D.Z.2    Gao, B.3    Lixue, Q.4
  • 7
    • 0022662973 scopus 로고
    • A linear time algorithm for full Steiner trees
    • Hwang, F. K.: A linear time algorithm for full Steiner trees, Oper. Res. Lett. 5 (1986), 235-237.
    • (1986) Oper. Res. Lett. , vol.5 , pp. 235-237
    • Hwang, F.K.1
  • 8
    • 38249041136 scopus 로고
    • Hexagonal coordinate systems and Steiner minimal trees
    • Hwang, F. K. and Weng, J.F.: Hexagonal coordinate systems and Steiner minimal trees, Discrete Math. 62 (1986), 49-57.
    • (1986) Discrete Math. , vol.62 , pp. 49-57
    • Hwang, F.K.1    Weng, J.F.2
  • 10
    • 0011996378 scopus 로고
    • 'Steiner's' problem revisited
    • G. B. Dantzig and B. C. Eaves (eds), Math. Assoc. Amer., Washington
    • Kuhn, H. W.: 'Steiner's' problem revisited, In: G. B. Dantzig and B. C. Eaves (eds), Studies in Optimization, Math. Assoc. Amer., Washington, 1974, pp. 52-70.
    • (1974) Studies in Optimization , pp. 52-70
    • Kuhn, H.W.1
  • 11
    • 0141471109 scopus 로고    scopus 로고
    • Simple counter examples for the unsolvability of the Fermat- and Steiner-Weber-problem by compass and ruler
    • Mehlhos, St.: Simple counter examples for the unsolvability of the Fermat- and Steiner-Weber-problem by compass and ruler, Contrib. Algebra Geom. 41 (2000), 151-158.
    • (2000) Contrib. Algebra Geom. , vol.41 , pp. 151-158
    • Mehlhos, S.1
  • 12
    • 0000426814 scopus 로고
    • On the Steiner problem
    • Melzak, Z. A.: On the Steiner problem, Canad. Math. Bull. 4 (1961), 143-148.
    • (1961) Canad. Math. Bull. , vol.4 , pp. 143-148
    • Melzak, Z.A.1
  • 13
    • 0141694390 scopus 로고
    • Minimum networks linking four points in a plane
    • Ollerenshaw, K.: Minimum networks linking four points in a plane, Inst. Math. Appl. 15 (1978), 208-211.
    • (1978) Inst. Math. Appl. , vol.15 , pp. 208-211
    • Ollerenshaw, K.1
  • 14
    • 0000433950 scopus 로고
    • Some results on the Steiner problem
    • Pollak, H. O.: Some results on the Steiner problem, J. Combin. Theory Ser. A 24 (1978), 278-295.
    • (1978) J. Combin. Theory Ser. A , vol.24 , pp. 278-295
    • Pollak, H.O.1
  • 15
    • 0000693111 scopus 로고
    • A variational approach to the Steiner network problem
    • Rubinstein, J. H. and Thomas, D. A.: A variational approach to the Steiner network problem, Ann. Oper. Res. 33 (1991), 481-499.
    • (1991) Ann. Oper. Res. , vol.33 , pp. 481-499
    • Rubinstein, J.H.1    Thomas, D.A.2
  • 17
    • 0141471114 scopus 로고
    • The Steiner ratio conjecture for cocircular points
    • Rubinstein, J. H. and Thomas, D. A.: The Steiner ratio conjecture for cocircular points, J. Discrete Comput. Geom. 7 (1992), pp. 77-86.
    • (1992) J. Discrete Comput. Geom. , vol.7 , pp. 77-86
    • Rubinstein, J.H.1    Thomas, D.A.2
  • 18
    • 0026711351 scopus 로고
    • How to find Steiner minimal trees in Euclidean d-space
    • Smith, W. D.: How to find Steiner minimal trees in Euclidean d-space, Algorithmica 7 (1992), 137-177.
    • (1992) Algorithmica , vol.7 , pp. 137-177
    • Smith, W.D.1
  • 20
    • 0000259553 scopus 로고
    • Generalized Steiner problem and hexagonal coordinate system
    • Weng, J. F.: Generalized Steiner problem and hexagonal coordinate system (in Chinese), Acta Math. Appl. Sinica 8 (1985), 383-397.
    • (1985) Acta Math. Appl. Sinica , vol.8 , pp. 383-397
    • Weng, J.F.1
  • 21
    • 38149146649 scopus 로고
    • Symmetrization theorem of full Steiner trees
    • Weng, J. F.: Symmetrization theorem of full Steiner trees, J. Combin. Theory Ser. A 66 (1994), 185-191.
    • (1994) J. Combin. Theory Ser. A , vol.66 , pp. 185-191
    • Weng, J.F.1
  • 22
    • 0141471113 scopus 로고
    • Variational approach and Steiner minimal trees on four points
    • Weng, J. F.: Variational approach and Steiner minimal trees on four points, Discrete Math. 132 (1994), 349-362.
    • (1994) Discrete Math. , vol.132 , pp. 349-362
    • Weng, J.F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.