Computation of matrix chain products. Part II
SIAM Journal on Computing
Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Application-controlled demand paging for out-of-core visualization
VIS '97 Proceedings of the 8th conference on Visualization '97
Interactive out-of-core isosurface extraction
Proceedings of the conference on Visualization '98
Multidimensional binary search trees used for associative searching
Communications of the ACM
Introduction to algorithms
Speeding Up Isosurface Extraction Using Interval Trees
IEEE Transactions on Visualization and Computer Graphics
The Visual Computer: International Journal of Computer Graphics
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Given a set of 1D intervals and a desired partition number, in this paper, the author examines how to make an optimal partitioning of these intervals, such that the number of intervals between the largest partition and smallest partition is minimal among all possible partitioning schemes. This problem has its difficulty due to the fact that an interval "striding" multiple partitions should be counted multiple times. Previously the author proposed an approximated solution to this problem by employing a simulated annealing approach (Yang & Chiueh, 2006), which could give satisfactory results in most cases; however, there is no theoretical guarantee on its optimality. This paper proposes a method that could both optimally and deterministically partition a given set of 1D intervals into a given number of partitions. The author shows that some load balancing problems could also be formulated as a balanced interval partitioning problem.