Journal of KIISE:Computer Systems and Theory (한국정보과학회논문지:시스템및이론)

Korean Institute of Information Scientists and Engineers (한국정보과학회)
권호 표지

Computing Symmetric Angle Restricted Nearest Neighbors using Monotone Matrix Search

단조 행렬 탐색을 이용한 양방향 각도제한 근접점 계산방법

  • 위영철 (아주대학교 정보 및 컴퓨터공학부)
  • Published : 2001.02.01
Download PDF
⟨ Previous Next ⟩

Abstract

이 논문은 행렬 탐색 방법을 이용하여 평면상의 η개의 점에 대한 모든 L$_{p}$, 1$\leq$P$\leq$$\infty$ 거리의 양방향 각도제한 근접 점 문제를 0(nlogn) 시간에 계산하는 알고리즘을 고안한다. 이 방법은 최적의 시간 복잡도를 가지며 궤적추적 법을 쓰지 않기 때문에 수치오차가 적으며 구현이 용이하고 실용적이다.

Keywords

References

  1. A. Aggarwal, M .M. Klawe, S. Moran, P. Shor, and R. Wilber, 'Geometric Applications of a Matrix-Searching Algorithm,' Algorithmica vol. 2, 1987, pp. 195-208 https://doi.org/10.1007/BF01840359
  2. A. Aggarwal, S. Moran, P. W. Shor, and S . Sur, Computing the Minimum Visible Vertex Distance Between Two Polygons,' in: in Proc. on the Workshop on Algorithms and Data Structures, Lecture Notes in Computer Science, (Eds. F. Dehne, J. R. Sack, and N. Santoro), Springer-Verlag, 1989, pp. 115-134 https://doi.org/10.1007/3-540-51542-9_11
  3. M. Ben-Or, 'Lower Bounds for Algebraic Computation Trees,' in: Proc. of 15th Annual ACM Symposium on Theory of Computing, 1983, pp. 80-86 https://doi.org/10.1145/800061.808735
  4. D. Chriton and R. E. Tarjan, 'Finding Minimum Spanning Trees,' SIAM J. on Computing Vol. 5, No. 4, 1976, pp. 724-742 https://doi.org/10.1137/0205051
  5. K. Clarkson, 'Approximation Problems for Shortest Path Motion Planning,' in Proc. 19th Ann. ACM Symp. Theory of Computing. 1987, pp. 56-65
  6. L. J. Guibas and J. Stolfi, 'On Computing all North-east Nearest Neighbors in The $L_p$ metric,' Info. Process. Lett. Vol. 17, 1983, pp. 219-223 https://doi.org/10.1016/0020-0190(83)90045-5
  7. J. Katajainen, 'The Region Neighborhood Graphs, in the $L_p$ metric,' Computing Vol. 40, 1988, pp. 147-161 https://doi.org/10.1007/BF02247943
  8. K. J. Supowit, 'The Relative Neighborhood Graphs with an Application to Minimum Spanning Trees,' J. of ACM, Vol. 30, 1983, pp. 428-447 https://doi.org/10.1145/2402.322386
  9. Y. C. Wee and S. Chaiken and S. S. Ravi, 'Rectilinear Steiner Tree Heuristics and Minimum Spanning Tree Algorithms Using Geographic Nearest Neighbors,' Algorithmica 12, 1994, pp. 421-435 https://doi.org/10.1007/BF01188713
  10. Y. C. Wee, S. Chaiken and D. E. Willard, 'On the Angle Restricted Nearest Neighbor Problem,' Information Processing Letters, Vol 34. 1990, pp. 71-76 https://doi.org/10.1016/0020-0190(90)90139-O
  11. A. C. Yao, 'On constructing Minimum Spanning Trees in k-dimensional Spaces and Related Problems,' SIAM J. on Computing, Vol. 11, 1982, pp. 721-736 https://doi.org/10.1137/0211059