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The current [needs update] record for integers modulo prime numbers, set in December 2019, is a discrete logarithm computation modulo a prime with 240 digits. For characteristic 2, the current record for finite fields, set in July 2019, is a discrete logarithm over G F ( 2 30750 ) {\displaystyle \mathrm {GF} (2^{30750})} .
For example, log 10 10000 = 4, and log 10 0.001 = −3. These are instances of the discrete logarithm problem. Other base-10 logarithms in the real numbers are not instances of the discrete logarithm problem, because they involve non-integer exponents. For example, the equation log 10 53 = 1.724276… means that 10 1.724276… = 53.
The set may contain different objects with their sizes specified, or a single object of a fixed dimension that can be used repeatedly. Usually the packing must be without overlaps between goods and other goods or the container walls. In some variants, the aim is to find the configuration that packs a single container with the maximal packing ...
The pancake sorting problem and the problem to obtain the diameter of the pancake graph are equivalent. [ 16 ] The pancake graph of dimension n , P n can be constructed recursively from n copies of P n−1 , by assigning a different element from the set {1, 2, …, n} as a suffix to each copy.
The graph shows the running time vs. problem size for a knapsack problem of a state-of-the-art, specialized algorithm. The quadratic fit suggests that the algorithmic complexity of the problem is O((log(n)) 2). [24] All of the above discussion has assumed that P means "easy" and "not in P" means "difficult", an assumption known as Cobham's ...
The zig-zagging entails starting from the point (n, 0) and iteratively moving to (n, log b (n) ), to (0, log b (n) ), to (log b (n), 0 ). In computer science , the iterated logarithm of n {\displaystyle n} , written log * n {\displaystyle n} (usually read " log star "), is the number of times the logarithm function must be iteratively applied ...
In mathematics, the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number.For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the 3 rd power: 1000 = 10 3 = 10 × 10 × 10.
In the online version of the bin packing problem, the items arrive one after another and the (irreversible) decision where to place an item has to be made before knowing the next item or even if there will be another one. A diverse set of offline and online heuristics for bin-packing have been studied by David S. Johnson on his Ph.D. thesis. [11]