In-Place Algorithms for Computing (Layers of) Maxima

AbstractWe describe space-efficient algorithms for solving problems related to finding maxima among points in two and three dimensions. Our algorithms run in optimal $\mathcal{O}(n\log n)$ time and occupy only constant extra space in addition to the space needed for representing the input.

[1]  Timothy M. Chan,et al.  Towards in-place geometric algorithms and data structures , 2004, SCG '04.

[2]  Jeffrey S. Salowe,et al.  Stable Unmerging in Linear Time and Constant Space , 1987, Inf. Process. Lett..

[3]  Beng Chin Ooi,et al.  Efficient Progressive Skyline Computation , 2001, VLDB.

[4]  Pat Morin,et al.  Space-efficient planar convex hull algorithms , 2004, Theor. Comput. Sci..

[5]  Jan Vahrenhold Line-Segment Intersection Made In-Place , 2005, WADS.

[6]  Timothy M. Chan,et al.  A Space-Efficient Algorithm for Segment Intersection , 2003, CCCG.

[7]  Kenneth L. Clarkson,et al.  Fast linear expected-time algorithms for computing maxima and convex hulls , 1993, SODA '90.

[8]  Donald Kossmann,et al.  Shooting Stars in the Sky: An Online Algorithm for Skyline Queries , 2002, VLDB.

[9]  Jon Louis Bentley,et al.  Multidimensional divide-and-conquer , 1980, CACM.

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

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

[12]  Jingchao Chen Optimizing stable in-place merging , 2003, Theor. Comput. Sci..

[13]  Michael T. Goodrich,et al.  Three-Dimensional Layers of Maxima , 2004, Algorithmica.

[14]  H. K. Dai,et al.  Improved Linear Expected-Time Algorithms for Computing Maxima , 2004, LATIN.

[15]  Martin Farach-Colton LATIN 2006: Theoretical Informatics: 7th Latin American Symposium, Valdivia, Chile, March 20-24, 2006, Proceedings , 2004 .

[16]  Jyrki Katajainen,et al.  Stable minimum space partitioning in linear time , 1992, BIT.

[17]  Sanjiv Kapoor Dynamic Maintenance of Maxima of 2-d Point Sets , 2000, SIAM J. Comput..

[18]  Wm. Randolph Franklin Computational Geometry: An Introduction (Franco P. Preparata and Michael Ian Shamos) , 1988 .

[19]  Jyrki Katajainen,et al.  Asymptotically efficient in-place merging , 2000, Theor. Comput. Sci..

[20]  Jirí Matousek,et al.  Computing Dominances in E^n , 1991, Inf. Process. Lett..

[21]  Jing-Chao Chen A simple algorithm for in-place merging , 2006, Inf. Process. Lett..

[22]  Donald Kossmann,et al.  The Skyline operator , 2001, Proceedings 17th International Conference on Data Engineering.

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

[24]  Bernard Chazelle,et al.  On the convex layers of a planar set , 1985, IEEE Trans. Inf. Theory.

[25]  J. IAN MUNRO,et al.  An Implicit Data Structure Supporting Insertion, Deletion, and Search in O(log² n) Time , 1986, J. Comput. Syst. Sci..

[26]  Franco P. Preparata,et al.  Computational Geometry , 1985, Texts and Monographs in Computer Science.

[27]  Michiel H. M. Smid,et al.  Space-efficient geometric divide-and-conquer algorithms , 2007, Comput. Geom..

[28]  Timothy M. Chan,et al.  Space-efficient algorithms for computing the convex hull of a simple polygonal line in linear time , 2004, Comput. Geom..

[29]  Bernhard Seeger,et al.  Progressive skyline computation in database systems , 2005, TODS.