On the total perimeter of homothetic convex bodies in a convex container
Tóm tắt
Từ khóa
Tài liệu tham khảo
Apostol, T.M.: Introduction to Analytic Number Theory. Springer, New York (1976)
Arora, S.: Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems. J. ACM 45(5), 753–782 (1998)
Bern, M., Eppstein, D.: Approximation algorithms for geometric problems. In: Hochbaum, D.S. (ed.) Approximation Algorithms for NP-hard Problems, pp. 296–345. PWS Publishing Company, Boston (1997)
Brass, P., Moser, W.O.J., Pach, J.: Research Problems in Discrete Geometry. Springer, New York (2005)
de Berg, M., Gudmundsson, J., Katz, M.J., Levcopoulos, C., Overmars, M.H., van der Stappen, A.F.: TSP with neighborhoods of varying size. J. Algorithms 57(1), 22–36 (2005)
Dumitrescu, A., Mitchell, J.S.B.: Approximation algorithms for TSP with neighborhoods in the plane. J. Algorithms 48(1), 135–159 (2003)
Dumitrescu, A., Tóth, C.D.: Minimum weight convex Steiner partitions. Algorithmica 60(3), 627–652 (2011)
Dumitrescu, A., Tóth, C.D.: The traveling salesman problem for lines, balls and planes. In: Proceedings of 24th ACM-SIAM Symposium on Discrete Algorithms, 2013, SIAM, pp. 828–843
Glazyrin, A., Morić, F.: Upper bounds for the perimeter of plane convex bodies. Acta Mathematica Hungarica 142(2), 366–383 (2014)
Graham, R.L., Lagarias, J.C., Mallows, C.L., Wilks, A.R., Yan, C.H.: Apollonian circle packings: geometry and group theory I: the Apollonian group. Discret. Comput. Geom. 34, 547–585 (2005)
Hales, T.C.: The strong dodecahedral conjecture and Fejes Tóth’s conjecture on sphere packings with kissing number twelve. In: Discrete Geometry and Optimization, vol. 69 of Fields Communications, pp. 121–132, Springer, Switzerland (2013)
Levcopoulos, C., Lingas, A.: Bounds on the length of convex partitions of polygons. In: Proceedings of 4th Annual Conference on Foundations of Software Technology and Theoretical Computer Science, LNCS 181, pp. 279–295, Springer (1984)
Mata, C., Mitchell, J.S.B.: Approximation algorithms for geometric tour and network design problems. In: Proceedings of 11th ACM Symposium on Computational Geometry, ACM, pp. 360–369 (1995)