Computational geometry: an introduction
Computational geometry: an introduction
Information and Control
Information and Control
Computing the largest empty rectangle
SIAM Journal on Computing
Optimal point location in a monotone subdivision
SIAM Journal on Computing
On k-hulls and related problems
SIAM Journal on Computing
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Fast algorithms for computing the largest empty rectangle
SCG '87 Proceedings of the third annual symposium on Computational geometry
Two-Dimensional Voronoi Diagrams in the Lp-Metric
Journal of the ACM (JACM)
Divide-and-conquer in multidimensional space
STOC '76 Proceedings of the eighth annual ACM symposium on Theory of computing
A Convex Hull Algorithm Optimal for Point Sets in Even Dimensions
A Convex Hull Algorithm Optimal for Point Sets in Even Dimensions
A deterministic view of random sampling and its use in geometry
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Fast hierarchical clustering and other applications of dynamic closest pairs
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Fast hierarchical clustering and other applications of dynamic closest pairs
Journal of Experimental Algorithmics (JEA)
Dynamic subgraph connectivity with geometric applications
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Semi-online maintenance of geometric optima and measures
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Extreme Distances in Multicolored Point Sets
ICCS '02 Proceedings of the International Conference on Computational Science-Part III
A dynamic data structure for 3-d convex hulls and 2-d nearest neighbor queries
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A dynamic data structure for 3-D convex hulls and 2-D nearest neighbor queries
Journal of the ACM (JACM)
FIFO indexes for decomposable problems
Proceedings of the thirtieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Three problems about dynamic convex hulls
Proceedings of the twenty-seventh annual symposium on Computational geometry
| Hi-index | 0.01 |
Let S be a set, f: S×S→R+ a bivariate function, and f(x,S) the maximum value of f(x,y) over all elements y∈S. We say that f is decomposable with respect with the maximum if f(x,S) = max {f(x,S1),f(x,S2),…,f(x,Sk)} for any decomposition S = &mgr;i=1i=kSi. Computing the maximum (minimum) value of a decomposable function is inherent in many problems of computational geometry and robotics. In this paper, a general technique is presented for updating the maximum (minimum) value of a decomposable function as elements are inserted into and deleted from the set S. Our result holds for a semi-online model of dynamization: When an element is inserted, we are told how long it will stay. 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) retangles determined by a set of points. These problems are fundamental to application areas such as robotics, VLSI masking, and optimization.