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Maximum subarray problems arise in many fields, such as genomic sequence analysis and computer vision.. Genomic sequence analysis employs maximum subarray algorithms to identify important biological segments of protein sequences that have unusual properties, by assigning scores to points within the sequence that are positive when a motif to be recognized is present, and negative when it is not ...
The multiple subset sum problem is an optimization problem in computer science and operations research. It is a generalization of the subset sum problem . The input to the problem is a multiset S {\displaystyle S} of n integers and a positive integer m representing the number of subsets.
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.
Qualitatively, the sum-product problem has been solved over finite fields: Theorem (Bourgain, Katz, Tao (2004)): [23] Let p be prime and let A ⊂ 픽 p with p δ < | A | < p 1−δ for some 0 < δ < 1. Then max(| A + A |, | AA |) ≥ c δ | A | 1+ε for some ε = ε(δ) > 0. Bourgain, Katz, and Tao extended this theorem to arbitrary fields ...
A random permutation on : is equivalently generated by uniformly sampling points in a square, then find the longest increasing subsequence of that. Now, define the Poisson point process with density 1 on [ 0 , ∞ ) 2 {\displaystyle [0,\infty )^{2}} , and define the random variables M k ∗ {\displaystyle M_{k}^{*}} to be the length of the ...
A longest common subsequence (LCS) is the longest subsequence common to all sequences in a set of sequences (often just two sequences). It differs from the longest common substring : unlike substrings, subsequences are not required to occupy consecutive positions within the original sequences.
The subset sum problem (SSP) is a decision problem in computer science. In its most general formulation, there is a multiset S {\displaystyle S} of integers and a target-sum T {\displaystyle T} , and the question is to decide whether any subset of the integers sum to precisely T {\displaystyle T} . [ 1 ]
Longest common subsequence problem: Find the longest subsequence common to all sequences in a set of sequences; Longest increasing subsequence problem: Find the longest increasing subsequence of a given sequence; Ruzzo–Tompa algorithm: Find all non-overlapping, contiguous, maximal scoring subsequences in a sequence of real numbers