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Klee's Measure Problem
In computational geometry, Klee's measure problem is the problem of determining how efficiently the measure of a union of ( multidimensional) rectangular ranges can be computed. Here, a ''d''-dimensional rectangular range is defined to be a Cartesian product of ''d'' intervals of real numbers, which is a subset of R''d''. The problem is named after Victor Klee, who gave an algorithm for computing the length of a union of intervals (the case ''d'' = 1) which was later shown to be optimally efficient in the sense of computational complexity theory. The computational complexity of computing the area of a union of 2-dimensional rectangular ranges is now also known, but the case ''d'' ≥ 3 remains an open problem. History and algorithms In 1977, Victor Klee considered the following problem: given a collection of ''n'' intervals in the real line, compute the length of their union. He then presented an algorithm to solve this problem with computational complexity (or "running ti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Set A Rectangles (Klee's Trevis)
Set, The Set, SET or SETS may refer to: Science, technology, and mathematics Mathematics *Set (mathematics), a collection of elements *Category of sets, the category whose objects and morphisms are sets and total functions, respectively Electronics and computing *Set (abstract data type), a data type in computer science that is a collection of unique values ** Set (C++), a set implementation in the C++ Standard Library * Set (command), a command for setting values of environment variables in Unix and Microsoft operating-systems * Secure Electronic Transaction, a standard protocol for securing credit card transactions over insecure networks * Single-electron transistor, a device to amplify currents in nanoelectronics * Single-ended triode, a type of electronic amplifier * Set!, a programming syntax in the scheme programming language Biology and psychology * Set (psychology), a set of expectations which shapes perception or thought *Set or sett, a badger's den *Set, a small tuber ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |