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Volumn , Issue , 2011, Pages 135-144

The least spanning area of a knot and the optimal bounding chain problem

Author keywords

Homology; Knot genus; Linear programming; Minimal surface; NP complete; Topology

Indexed keywords

3-DIMENSIONAL; 3-MANIFOLD; DESINGULARIZATION; HOMOLOGY; INTEGER COEFFICIENT; KNOT GENUS; KNOT THEORY; LINEAR PROGRAMMING FORMULATION; MINIMAL GENUS; MINIMAL SURFACE; NP-COMPLETE; NP-HARD; POLYNOMIAL-TIME;

EID: 79960195316     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1998196.1998218     Document Type: Conference Paper
Times cited : (25)

References (28)
  • 1
    • 33748297453 scopus 로고    scopus 로고
    • The computational complexity of knot genus and spanning area
    • DOI 10.1090/S0002-9947-05-03919-X, PII S000299470503919X
    • AGOL, I., HASS, J., AND THURSTON, W. The computational complexity of knot genus and spanning area. Trans. Amer. Math. Soc. 358, 9 (2006), 3821-3850. arXiv:math.GT/0205057, doi:10.1090/S0002-9947-05-03919-X. (Pubitemid 44328543)
    • (2006) Transactions of the American Mathematical Society , vol.358 , Issue.9 , pp. 3821-3850
    • Agol, I.1    Hass, J.2    Thurston, W.3
  • 2
    • 77954921903 scopus 로고    scopus 로고
    • The complexity of the normal surface solution space
    • New York, NY, USA, ACM, doi:10.1145/1810959.1810995
    • BURTON, B. A. The complexity of the normal surface solution space. In SoCG '10: Proceedings of the 2010 annual symposiumon computational geometry (New York, NY, USA, 2010), ACM, pp. 201-209. doi:10.1145/1810959.1810995.
    • (2010) SoCG '10: Proceedings of the 2010 Annual Symposiumon Computational Geometry , pp. 201-209
    • Burton, B.A.1
  • 4
    • 72949098392 scopus 로고    scopus 로고
    • Optimizing the double descriptionmethod for normal surface enumeration
    • doi:10.1090/S0025-5718-09-02282-0
    • BURTON, B. A. Optimizing the double descriptionmethod for normal surface enumeration. Math. Comp. 79, 269 (2010), 453-484. doi:10.1090/S0025-5718-09- 02282-0.
    • (2010) Math. Comp. , vol.79 , Issue.269 , pp. 453-484
    • Burton, B.A.1
  • 7
    • 77954735165 scopus 로고    scopus 로고
    • Optimal homologous cycles, total unimodularity, and linear programming
    • New York, NY, USA, June 6-8, ACM. Also available as preprint arXiv:1001.0338v1 [math.AT] on. http://doi.acm.org/10.1145/1806689.1806721,arXiv 1001.0338, doi:10.1145/1806689.1806721 2010
    • DEY, T. K., HIRANI, A. N., AND KRISHNAMOORTHY, B. Optimal homologous cycles, total unimodularity, and linear programming. In STOC '10: Proceedings of the 42nd ACM Symposiumon Theory of Computing (New York, NY, USA, June 6-8 2010), ACM, pp. 221-230. Also available as preprint arXiv:1001.0338v1 [math.AT] on http://arxiv.org/abs/1001.0338. URL http://doi.acm.org/10.1145/1806689. 1806721,arXiv:1001.0338, doi:10.1145/1806689.1806721.
    • STOC '10: Proceedings of the 42nd ACM Symposiumon Theory of Computing , pp. 221-230
    • Dey, T.K.1    Hirani, A.N.2    Krishnamoorthy, B.3
  • 8
    • 0001380055 scopus 로고
    • Exact solution of linear equations using p-adic expansions
    • doi:10.1007/BF01459082
    • DIXON, J. D. Exact solution of linear equations using p-adic expansions. Numer.Math. 40, 1 (1982), 137-141. URL http://dx.doi.org/10.1007/BF01459082, doi:10.1007/BF01459082.
    • (1982) Numer.Math , vol.40 , Issue.1 , pp. 137-141
    • Dixon, J.D.1
  • 9
    • 0041151682 scopus 로고
    • A method of numerical solution of the problem of Plateau
    • 1-4, doi:10.2307/1967991
    • DOUGLAS, J. A method of numerical solution of the problem of Plateau. Ann. ofMath. (2) 29, 1-4 (1927/28), 180-188. URL http://dx.doi.org/10.2307/ 1967991, doi:10.2307/1967991.
    • (1927) Ann. of Math , vol.29 , Issue.2 , pp. 180-188
    • Douglas, J.1
  • 12
    • 73849094741 scopus 로고    scopus 로고
    • Minimal surfaces extend shortest path segmentationmethods to 3D
    • February, doi:10.1109/TPAMI.2008.289
    • GRADY, L. Minimal surfaces extend shortest path segmentationmethods to 3D. IEEE Transactions on Pattern Analysis andMachine Intelligence 32, 2 (February 2010), 321-334. doi:10.1109/TPAMI.2008.289.
    • (2010) IEEE Transactions on Pattern Analysis AndMachine Intelligence , vol.32 , Issue.2 , pp. 321-334
    • Grady, L.1
  • 13
    • 84974001411 scopus 로고
    • Intersections of least area surfaces
    • HASS, J. Intersections of least area surfaces. Pacific J.Math. 152, 1 (1992), 119-123.
    • (1992) Pacific J. Math , vol.152 , Issue.1 , pp. 119-123
    • Hass, J.1
  • 14
    • 0038310144 scopus 로고    scopus 로고
    • The size of spanning disks for polygonal curves
    • DOI 10.1007/s00454-002-2707-6
    • HASS, J., SNOEYINK, J., AND THURSTON, W. P. The size of spanning disks for polygonal curves. Discrete and Computational Geometry 29, 1 (March 2003), 1-17. URL http://dx.doi.org/10.1007/s00454-002-2707-6, doi:10.1007/s00454-002- 2707-6. (Pubitemid 36820367)
    • (2003) Discrete and Computational Geometry , vol.29 , Issue.1 , pp. 1-17
    • Hass, J.1    Snoeyink, J.2    Thurston, W.P.3
  • 15
    • 34247517282 scopus 로고    scopus 로고
    • On the convergence ofmetric and geometric properties of polyhedral surfaces
    • December
    • HILDEBRANDT, K., POLTHIER, K., AND WARDETZKY, M. On the convergence ofmetric and geometric properties of polyhedral surfaces. Geometriae Dedicata 123, 1 (December 2006), 89-112.
    • (2006) Geometriae Dedicata , vol.123 , Issue.1 , pp. 89-112
    • Hildebrandt, K.1    Polthier, K.2    Wardetzky, M.3
  • 17
    • 0345292312 scopus 로고
    • Incompressible surfaces in knot spaces
    • LYON, H. C. Incompressible surfaces in knot spaces. Trans. Amer.Math. Soc. 157 (1971), 53-62. URL.
    • (1971) Trans. Amer.Math. Soc. , vol.157 , pp. 53-62
    • Lyon, H.C.1
  • 18
    • 7544227287 scopus 로고    scopus 로고
    • Algorithmic topology and classification of 3-manifolds
    • second ed, Springer, Berlin
    • MATVEEV, S. Algorithmic topology and classification of 3-manifolds, second ed., vol. 9 of Algorithms and Computation inMathematics. Springer, Berlin, 2007.
    • (2007) Algorithms and Computation in Mathematics , vol.9
    • Matveev, S.1
  • 19
    • 0003418230 scopus 로고    scopus 로고
    • fourth ed, Elsevier/Academic Press, Amsterdam,. A beginner's guide
    • MORGAN, F. Geometric measure theory, fourth ed. Elsevier/Academic Press, Amsterdam, 2009. A beginner's guide.
    • (2009) Geometric Measure Theory
    • Morgan, F.1
  • 21
    • 0040557532 scopus 로고
    • Explicit determination of area minimizinghypersurfaces, II
    • PARKS, H. R. Explicit determination of area minimizinghypersurfaces, II. Mem. Amer.Math. Soc. 60, 342 (1986),iv+90.
    • (1986) Mem. Amer.Math. Soc. , vol.60 , Issue.342
    • Parks, H.R.1
  • 22
    • 0005394726 scopus 로고
    • Numerical approximation of parametric oriented area-minimizing hypersurfaces
    • doi:10.1137/0913027
    • PARKS, H. R. Numerical approximation of parametric oriented area-minimizing hypersurfaces. SIAM J. Sci Statist. Comput. 13, 2 (1992), 499-511. doi:10.1137/0913027.
    • (1992) SIAM J. Sci Statist. Comput. , vol.13 , Issue.2 , pp. 499-511
    • Parks, H.R.1
  • 23
    • 0031129189 scopus 로고    scopus 로고
    • Computing least area hypersurfaces spanning arbitrary boundaries
    • PII S1064827594278903
    • PARKS, H. R., AND PITTS, J. T. Computing least area hypersurfaces spanning arbitrary boundaries. SIAM J. Sci. Comput. 18, 3 (1997), 886-917. doi:10.1137/S1064827594278903. (Pubitemid 127640888)
    • (1997) SIAM Journal of Scientific Computing , vol.18 , Issue.3 , pp. 886-917
    • Parks, H.R.1    Pitts, J.T.2
  • 24
    • 84950826016 scopus 로고
    • Computing discrete minimal surfaces and their conjugates
    • PINKALL, U., AND POLTHIER, K. Computing discrete minimal surfaces and their conjugates. Experiment.Math. 2, 1 (1993), 15-36. URL http://projecteuclid. org/getRecord?id=euclid.em/1062620735.
    • (1993) Experiment. Math , vol.2 , Issue.1 , pp. 15-36
    • Pinkall, U.1    Polthier, K.2
  • 25
    • 70349660725 scopus 로고    scopus 로고
    • Computational aspects of discrete minimal surfaces
    • Global theory of minimal surfaces. Amer.Math. Soc., Providence, RI
    • POLTHIER, K. Computational aspects of discrete minimal surfaces. In Global theory of minimal surfaces, vol. 2 of Clay Math. Proc. Amer.Math. Soc., Providence, RI, 2005, pp. 65-111..
    • (2005) Clay Math. Proc. , vol.2 , pp. 65-111
    • Polthier, K.1
  • 28
    • 0040774367 scopus 로고
    • Integral extreme points
    • VEINOTT, ARTHUR F., J., AND DANTZIG, G. B. Integral extreme points. SIAM Review 10, 3 (1968), 371-372. URL http://www.jstor.org/stable/2027662.
    • (1968) SIAM Review , vol.10 , Issue.3 , pp. 371-372
    • Veinott Arthur, F.J.1    Dantzig, G.B.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.