Space-efficient planar convex hull algorithms

A space-efficient algorithm is one in which the output is given in the same location as the input and only a small amount of additional memory is used by the algorithm. We describe four space-efficient algorithms for computing the convex hull of a planar point set.

[1]  M. Chial,et al.  in simple , 2003 .

[2]  F. Frances Yao,et al.  Computational Geometry , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

[3]  Thomas Ottmann,et al.  Enumerating Extreme Points in Higher Dimensions , 2001, Nord. J. Comput..

[4]  William F. Eddy,et al.  A New Convex Hull Algorithm for Planar Sets , 1977, TOMS.

[5]  Edsger W. Dijkstra,et al.  Smoothsort, an Alternative for Sorting In Situ , 1982, Sci. Comput. Program..

[6]  Jan van Leeuwen,et al.  Maintenance of Configurations in the Plane , 1981, J. Comput. Syst. Sci..

[7]  Hans-Werner Six,et al.  Sorting a Random Access File in Situ , 1984, Comput. J..

[8]  Ray A. Jarvis,et al.  On the Identification of the Convex Hull of a Finite Set of Points in the Plane , 1973, Inf. Process. Lett..

[9]  David S. L. Wei,et al.  Computer Algorithms , 1998, Scalable Computing : Practice and Experience.

[10]  Raimund Seidel,et al.  Small-dimensional linear programming and convex hulls made easy , 1991, Discret. Comput. Geom..

[11]  Kenneth L. Clarkson,et al.  Applications of random sampling in computational geometry, II , 1988, SCG '88.

[12]  F. P. Preparata,et al.  Convex hulls of finite sets of points in two and three dimensions , 1977, CACM.

[13]  Nimrod Megiddo,et al.  Linear Programming in Linear Time When the Dimension Is Fixed , 1984, JACM.

[14]  Timothy M. Chan.  Output-sensitive results on convex hulls, extreme points, and related problems , 1995, SCG '95.

[15]  Jeffrey S. Salowe,et al.  Simplified Stable Merging Tasks , 1987, J. Algorithms.

[16]  Timothy M. Chan.  Output-sensitive results on convex hulls, extreme points, and related problems , 1996, Discret. Comput. Geom..

[17]  A. J. M. van Gasteren,et al.  An Introduction to Three Algorithms for Sorting in Situ , 1982, Inf. Process. Lett..

[18]  Edsger W. Dijkstra,et al.  A Discipline of Programming , 1976 .

[19]  Franco P. Preparata,et al.  An optimal real-time algorithm for planar convex hulls , 1979, CACM.

[20]  Jukka Teuhola,et al.  Practical In-Place Mergesort , 1996, Nord. J. Comput..

[21]  Derick Wood,et al.  Implicit Selection , 1988, SWAT.

[22]  Heikki Mannila,et al.  A Simple Linear-Time Algorithm for in Situ Merging , 1984, Inf. Process. Lett..

[23]  Michael A. Langston,et al.  Fast Stable Merging and Sorting in Constant Extra Space , 1992, Comput. J..

[24]  Bernard Chazelle,et al.  Intersection of convex objects in two and three dimensions , 1987, JACM.

[25]  S. Dvorák,et al.  Stable Linear Time Sublinear Space Merging , 1987, Comput. J..

[26]  Jyrki Katajainen,et al.  In-Place Sorting with Fewer Moves , 1999, Inf. Process. Lett..

[27]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[28]  Ronald L. Graham,et al.  An Efficient Algorithm for Determining the Convex Hull of a Finite Planar Set , 1972, Inf. Process. Lett..

[29]  A. M. Andrew,et al.  Another Efficient Algorithm for Convex Hulls in Two Dimensions , 1979, Inf. Process. Lett..

[30]  Antonios Symvonis,et al.  Optimal Stable Merging , 1995, Comput. J..

[31]  Michael A. Langston,et al.  Practical in-place merging , 1987, CACM.

[32]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[33]  Timothy M. Chan.  Optimal output-sensitive convex hull algorithms in two and three dimensions , 1996, Discret. Comput. Geom..

[34]  Timothy M. Chan,et al.  Primal Dividing and Dual Pruning: Output-Sensitive Construction of Four-Dimensional Polytopes and Three-Dimensional Voronoi Diagrams , 1997, Discret. Comput. Geom..

[35]  S. Dvorák,et al.  Unstable Linear Time O(1) Space Merging , 1988, Comput. J..

[36]  Jyrki Katajainen,et al.  Stable minimum space partitioning in linear time , 1992, BIT Comput. Sci. Sect..

[37]  Binay K. Bhattacharya,et al.  On a Simple, Practical, Optimal, Output-Sensitive Randomized Planar Convex Hull Algorithm , 1997, J. Algorithms.

[38]  Venkatesh Raman,et al.  Stable in situ sorting and minimum data movement , 1990, BIT.

[39]  David G. Kirkpatrick,et al.  The Ultimate Planar Convex Hull Algorithm? , 1986, SIAM J. Comput..

[40]  R. Wenger,et al.  Randomized Quick Hull , 1995 .

[41]  Kenneth L. Clarkson.  More output-sensitive geometric algorithms , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.