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If ′ =, then for large the set is expected to have the fraction (1 - 1/e) (~63.2%) of the unique samples of , the rest being duplicates. [1] This kind of sample is known as a bootstrap sample. Sampling with replacement ensures each bootstrap is independent from its peers, as it does not depend on previous chosen samples when sampling.
Set-Union Knapsack Problem: SUKP is defined by Kellerer et al [ 2 ] (on page 423) as follows: Given a set of n {\displaystyle n} items N = { 1 , … , n } {\displaystyle N=\{1,\ldots ,n\}} and a set of m {\displaystyle m} so-called elements P = { 1 , … , m } {\displaystyle P=\{1,\ldots ,m\}} , each item j {\displaystyle j} corresponds to a ...
Pandas (styled as pandas) is a software library written for the Python programming language for data manipulation and analysis. In particular, it offers data structures and operations for manipulating numerical tables and time series .
For example, for the array of values [−2, 1, −3, 4, −1, 2, 1, −5, 4], the contiguous subarray with the largest sum is [4, −1, 2, 1], with sum 6. Some properties of this problem are: If the array contains all non-negative numbers, then the problem is trivial; a maximum subarray is the entire array.
The aggregation problem is the difficult problem of finding a valid way to treat an empirical or theoretical aggregate as if it reacted like a less-aggregated measure, say, about behavior of an individual agent as described in general microeconomic theory [1] (see representative agent and heterogeneity in economics).
Interval scheduling is a class of problems in computer science, particularly in the area of algorithm design. The problems consider a set of tasks. Each task is represented by an interval describing the time in which it needs to be processed by some machine (or, equivalently, scheduled on some resource).
The strip packing problem contains the bin packing problem as a special case when all the items have the same height 1. For this reason, it is strongly NP-hard, and there can be no polynomial time approximation algorithm that has an approximation ratio smaller than 3 / 2 {\displaystyle 3/2} unless P = N P {\displaystyle P=NP} .
In computational complexity theory, Karp's 21 NP-complete problems are a set of computational problems which are NP-complete.In his 1972 paper, "Reducibility Among Combinatorial Problems", [1] Richard Karp used Stephen Cook's 1971 theorem that the boolean satisfiability problem is NP-complete [2] (also called the Cook-Levin theorem) to show that there is a polynomial time many-one reduction ...