Dynamically computing the maxima of decomposable functions, with applications

The authors present a general technique for updating the maximum (minimum) value of a decomposable function as elements are inserted into and deleted from the set S. Applications of this technique include efficient algorithms for dynamically computing the diameter or closest pair of a set of points, minimum separation among a set of rectangles, smallest distance between a set of points and a set of hyperplanes, and largest or smallest area (perimeter) rectangles determined by a set of points. The main appeal of the approach lies in its generality. Several research directions suggested by the work are noted.<<ETX>>

[1]  Jon Louis Bentley,et al.  Decomposable Searching Problems I: Static-to-Dynamic Transformation , 1980, J. Algorithms.

[2]  Richard Cole,et al.  Geometric retrieval problems , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[3]  Robert E. Tarjan,et al.  A Linear-Time Algorithm for a Special Case of Disjoint Set Union , 1985, J. Comput. Syst. Sci..

[4]  Mark H. Overmars,et al.  Batched Dynamic Solutions to Decomposable Searching Problems , 1985, J. Algorithms.

[5]  Alok Aggarwal,et al.  Fast algorithms for computing the largest empty rectangle , 1987, SCG '87.

[6]  Mark H. Overmars,et al.  Dynamization of Order Decomposable Set Problems , 1981, J. Algorithms.

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

[8]  D. T. Lee,et al.  The Power of Geometric Duality Revisited , 1985, Inf. Process. Lett..

[9]  Bernard Chazelle,et al.  How to Search in History , 1983, Inf. Control..

[10]  Bernard Chazelle,et al.  A deterministic view of random sampling and its use in geometry , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[11]  Richard Cole,et al.  On k-Hulls and Related Problems , 1987, SIAM J. Comput..

[12]  Andrew Chi-Chih Yao,et al.  On Constructing Minimum Spanning Trees in k-Dimensional Spaces and Related Problems , 1977, SIAM J. Comput..

[13]  Bernard Chazelle,et al.  Computing the Largest Empty Rectangle , 1986, SIAM J. Comput..