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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.
Max-sum MSSP: for each subset j in 1,...,m, there is a capacity C j. The goal is to make the sum of all subsets as large as possible, such that the sum in each subset j is at most C j. [1] Max-min MSSP (also called bottleneck MSSP or BMSSP): again each subset has a capacity, but now the goal is to make the smallest subset sum as large as ...
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 .
Each possible sub-array is represented by a point on a colored line. That point's y-coordinate represents the sum of the sample, its x-coordinate represents the end of the sample, and the leftmost point on that colored line represents the start of the sample. In this case, the array from which samples are taken is [2, 3, -1, -20, 5, 10].
In the subset sum problem, the goal is to find a subset of S whose sum is a certain target number T given as input (the partition problem is the special case in which T is half the sum of S). In multiway number partitioning , there is an integer parameter k , and the goal is to decide whether S can be partitioned into k subsets of equal sum ...
18. Seattle Seahawks — Tyler Booker, OL, Alabama. Klint Kubiak’s scheme is going to run the damn ball and Seattle’s offensive line didn’t necessarily make that the easiest task this season.
The longest increasing subsequence problem is closely related to the longest common subsequence problem, which has a quadratic time dynamic programming solution: the longest increasing subsequence of a sequence is the longest common subsequence of and , where is the result of sorting.