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The maximum subarray problem was proposed by Ulf Grenander in 1977 as a simplified model for maximum likelihood estimation of patterns in digitized images. [5]Grenander was looking to find a rectangular subarray with maximum sum, in a two-dimensional array of real numbers.
For separate items: the price-of-fairness of max-min fairness is unbounded. For example, suppose Alice has two items with values 1 and e, for some small e>0. George has two items with value e. The capacity is 1. The maximum sum is 1 - when Alice gets the item with value 1 and George gets nothing. But the max-min allocation gives both agents ...
The subset sum problem (SSP) is a decision problem in computer science. In its most general formulation, there is a multiset of integers and a target-sum , and the question is to decide whether any subset of the integers sum to precisely . [1] The problem is known to be NP-complete.
The maximum scoring subsequence from the set produced by the algorithm is also a solution to the maximum subarray problem. The Ruzzo–Tompa algorithm has applications in bioinformatics , [ 4 ] web scraping , [ 5 ] and information retrieval .
In the limit as approaches infinity, the Baik-Deift-Johansson theorem says, that the length of the longest increasing subsequence of a randomly permuted sequence of items has a distribution approaching the Tracy–Widom distribution, the distribution of the largest eigenvalue of a random matrix in the Gaussian unitary ensemble.
Ulf Grenander (23 July 1923 – 12 May 2016) was a Swedish statistician and professor of applied mathematics at Brown University.. His early research was in probability theory, stochastic processes, time series analysis, and statistical theory (particularly the order-constrained estimation of cumulative distribution functions using his sieve estimator).
A sum-free set is said to be maximal if it is not a proper subset of another sum-free set. Let f : [ 1 , ∞ ) → [ 1 , ∞ ) {\displaystyle f:[1,\infty )\to [1,\infty )} be defined by f ( n ) {\displaystyle f(n)} is the largest number k {\displaystyle k} such that any subset of [ 1 , ∞ ) {\displaystyle [1,\infty )} with size n has a sum ...
Similarly, a normal subgroup N of G is said to be a maximal normal subgroup (or maximal proper normal subgroup) of G if N < G and there is no normal subgroup K of G such that N < K < G. We have the following theorem: Theorem: A normal subgroup N of a group G is a maximal normal subgroup if and only if the quotient G/N is simple.