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The Art of Computer Programming, Volume III: Sorting and Searching

The Art of Computer Programming, Volume III: Sorting and Searching,Donald E. Knuth

The Art of Computer Programming, Volume III: Sorting and Searching   (Citations: 2428)
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Published in 1973.
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    • ...A numeral system is a linguistic system and mathematical notation for representing numbers of a given set by symbols in a consistent manner [13]...
    • ...The most commonly used numeral systems are positional numeral systems [13], where given a positive natural number , a string represents a number . For example, the binary and decimal numeral systems use powers of two and powers of ten, respectively, as bases...

    Xuebin Wuet al. Efficient CODEC Designs for Crosstalk Avoidance Codes Based on Numeral...

    • ...2) Memory Units: The memory units are designed as binary heap [11] data structures, which keep the stored elements in order according to the selected cost metric...
    • ...The storing of a new element requires a time complexity of in the worst case [11], where is the size of the memory...
    • ...The possible new partial candidate(s) (child and father) are first compared to the minimum candidate, and if the candidate on the top of the heap has the minimum PED, the first stored candidate is located at the top of the heap and sorted via the down-heap operation [11]...
    • ...new candidate is added to the next free memory address and the heap is sorted via the up-heap operation [11]...

    Markus Myllyläet al. Architecture Design and Implementation of the Metric First List Sphere...

    • ... of S(F, F ) is dominated by (7), yielding a complexity of O(nc · nc · m). In a retrieval operation over a fingerprint database, the time needed to compute a single score S(F, F ) can be assumed constant since it is independent of the number of fingerprints N . The computational complexity is then dominated by the selection of the top NT scores, which can be performed in O(N + NT logNT ) using a specialized partial sorting algorithm ...

    Raffaele Cappelli. Fast and Accurate Fingerprint Indexing Based on Ridge Orientation and ...

    • ...It can even be computed using floatingpoint operations [24]...
    • ...The genericity of the theorem with respect to formats can be seen on Figure 2: the Fprop plus error file does not depend on the specialized formats defined in Fcore FIX, FLX, and so on. 4) Error of the multiplication: It is also well-known that the error of a floating-point multiplication is a floating-point number, whatever the rounding, but provided no underflow occur [24]...

    Sylvie Boldoet al. Flocq: A Unified Library for Proving Floating-Point Algorithms in Coq

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