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  2. Floor and ceiling functions - Wikipedia

    en.wikipedia.org/wiki/Floor_and_ceiling_functions

    In mathematics, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor(x). Similarly, the ceiling function maps x to the least integer greater than or equal to x, denoted ⌈x⌉ or ceil(x). [1]

  3. Kempner function - Wikipedia

    en.wikipedia.org/wiki/Kempner_function

    The Kempner function () of an arbitrary number is the maximum, over the prime powers dividing , of (). [4] When n {\displaystyle n} is itself a prime power p e {\displaystyle p^{e}} , its Kempner function may be found in polynomial time by sequentially scanning the multiples of p {\displaystyle p} until finding the first one whose factorial ...

  4. Integer-valued function - Wikipedia

    en.wikipedia.org/wiki/Integer-valued_function

    In mathematics, an integer-valued function is a function whose values are integers.In other words, it is a function that assigns an integer to each member of its domain.. The floor and ceiling functions are examples of integer-valued functions of a real variable, but on real numbers and, generally, on (non-disconnected) topological spaces integer-valued functions are not especially useful.

  5. Median of medians - Wikipedia

    en.wikipedia.org/wiki/Median_of_medians

    If one instead groups the other way, say dividing the element list into 5 lists, computing the median of each, and then computing the median of these – i.e., grouping by a constant fraction, not a constant number – one does not as clearly reduce the problem, since it requires computing 5 medians, each in a list of elements, and then ...

  6. Min-max heap - Wikipedia

    en.wikipedia.org/wiki/Min-max_heap

    We assume in the next points that the root element is at the first level, i.e., 0. Example of Min-max heap. Each node in a min-max heap has a data member (usually called key) whose value is used to determine the order of the node in the min-max heap. The root element is the smallest element in the min-max heap.

  7. Shortest path problem - Wikipedia

    en.wikipedia.org/wiki/Shortest_path_problem

    Shortest path (A, C, E, D, F), blue, between vertices A and F in the weighted directed graph. In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.

  8. Graph partition - Wikipedia

    en.wikipedia.org/wiki/Graph_partition

    Division into a larger number of communities can be achieved by repeated bisection or by using multiple eigenvectors corresponding to the smallest eigenvalues. [12] The examples in Figures 1,2 illustrate the spectral bisection approach. Figure 1: The graph G = (5,4) is analysed for spectral bisection. The linear combination of the smallest two ...

  9. Graph property - Wikipedia

    en.wikipedia.org/wiki/Graph_property

    Informally, the term "graph invariant" is used for properties expressed quantitatively, while "property" usually refers to descriptive characterizations of graphs. For example, the statement "graph does not have vertices of degree 1" is a "property" while "the number of vertices of degree 1 in a graph" is an "invariant".