Reporting and counting maximal points in a query orthogonal rectangle

In this work we show that given a set S of n points with coordinates on an n × n grid, we can construct data structures for (i) reporting and (ii) counting the maximal points in an axes-parallel query rectangle in sub-logarithmic time. We assume our model of computation to be the word RAM with size of each word being log ź n bits.

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

[2]  K. Srinathan,et al.  Counting Maximal Points in a Query Orthogonal Rectangle , 2013, WALCOM.

[3]  David R. Clark,et al.  Efficient suffix trees on secondary storage , 1996, SODA '96.

[4]  Johannes Fischer,et al.  Optimal Succinctness for Range Minimum Queries , 2008, LATIN.

[5]  J. Ian Munro,et al.  Efficient Suffix Trees on Secondary Storage (extended Abstract) , 1996, SODA.

[6]  Mikhail J. Atallah,et al.  Data structures for range minimum queries in multidimensional arrays , 2010, SODA '10.

[7]  K. Srinathan,et al.  Range Aggregate Maximal Points in the Plane , 2012, WALCOM.

[8]  Robert E. Tarjan,et al.  Fast Algorithms for Finding Nearest Common Ancestors , 1984, SIAM J. Comput..

[9]  Gonzalo Navarro,et al.  Sorted Range Reporting , 2012, SWAT.

[10]  Yufei Tao,et al.  I/O-efficient planar range skyline and attrition priority queues , 2013, PODS '13.

[11]  Gerth Stølting Brodal,et al.  Dynamic Planar Range Maxima Queries , 2011, ICALP.

[12]  Yakov Nekrich.  A Linear Space Data Structure for Orthogonal Range Reporting and Emptiness Queries , 2009, Int. J. Comput. Geom. Appl..

[13]  Anthony K. H. Tung,et al.  Finding k-dominant skylines in high dimensional space , 2006, SIGMOD Conference.

[14]  K. Srinathan,et al.  On Finding Skyline Points for Range Queries in Plane , 2011, CCCG.

[15]  Wing-Kai Hon,et al.  Improved data structures for the orthogonal range successor problem , 2011, Comput. Geom..

[16]  Kasper Green Larsen,et al.  Optimal Planar Orthogonal Skyline Counting Queries , 2014, SWAT.

[17]  S. Srinivasa Rao,et al.  On Space Efficient Two Dimensional Range Minimum Data Structures , 2011, Algorithmica.

[18]  Peter van Emde Boas,et al.  Preserving order in a forest in less than logarithmic time , 1975, 16th Annual Symposium on Foundations of Computer Science (sfcs 1975).

[19]  Ananda Swarup Das,et al.  On Counting Range Maxima Points in Plane , 2012, IWOCA.