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Given any discrete allocation, for any agent i, define r(i) as the rank of agent i's bundle, so that r(i)=1 if i got his best bundle, r(i)=2 if i got his second-best bundle, etc. This r is a vector of size n (the number of agents). An ordinally-egalitarian allocation is one that minimizes the largest element in r.
Because the smallest circle is always determined by some three points, the smallest circle problem has combinatorial dimension three, even though it is defined using two-dimensional Euclidean geometry. [2] More generally, the smallest enclosing ball of points in d dimensions forms an LP-type problem of combinatorial dimension d + 1.
Python's standard library includes heapq.nsmallest and heapq.nlargest functions for returning the smallest or largest elements from a collection, in sorted order. The implementation maintains a binary heap , limited to holding k {\displaystyle k} elements, and initialized to the first k {\displaystyle k} elements in the collection.
The following list includes the continued fractions of some constants and is sorted by their representations. Continued fractions with more than 20 known terms have been truncated, with an ellipsis to show that they continue. Rational numbers have two continued fractions; the version in this list is the shorter one.
A minifloat is usually described using a tuple of four numbers, (S, E, M, B): S is the length of the sign field. It is usually either 0 or 1. E is the length of the exponent field.
Graphs of functions commonly used in the analysis of algorithms, showing the number of operations versus input size for each function. The following tables list the computational complexity of various algorithms for common mathematical operations.
In mathematics, the lowest common denominator or least common denominator (abbreviated LCD) is the lowest common multiple of the denominators of a set of fractions. It simplifies adding, subtracting, and comparing fractions.
In each iteration, select two k-tuples A and B in which the difference between the maximum and minimum sum is largest, and combine them in reverse order of sizes, i.e.: smallest subset in A with largest subset in B, second-smallest in A with second-largest in B, etc. Proceed in this way until a single partition remains. Examples: