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Closest String
In theoretical computer science, the closest string is an NP-hard computational problem, which tries to find the geometrical center of a set of input strings. To understand the word "center", it is necessary to define a distance between two strings. Usually, this problem is studied with the Hamming distance in mind. Formal definition More formally, given ''n'' strings ''s''1, ''s''2, ..., ''s''''n'' of length ''m'', the closest string problem seeks a new string ''s'' of length ''m'' such that ''d''(''s'',''s''''i'') ≤ ''k'' for all ''i'', where ''d'' is the Hamming distance, and where ''k'' is as small as possible. A decision problem version of the closest string problem, which is NP-complete, instead takes ''k'' as another input and questions whether there is a string within Hamming distance ''k'' of all the input strings. The closest string problem can be seen as a special case of the generic 1-center problem in which the distances between elements are measured using Hamming di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theoretical Computer Science
Theoretical computer science is a subfield of computer science and mathematics that focuses on the Abstraction, abstract and mathematical foundations of computation. It is difficult to circumscribe the theoretical areas precisely. The Association for Computing Machinery, ACM's Special Interest Group on Algorithms and Computation Theory (SIGACT) provides the following description: History While logical inference and mathematical proof had existed previously, in 1931 Kurt Gödel proved with his incompleteness theorem that there are fundamental limitations on what statements could be proved or disproved. Information theory was added to the field with A Mathematical Theory of Communication, a 1948 mathematical theory of communication by Claude Shannon. In the same decade, Donald Hebb introduced a mathematical model of Hebbian learning, learning in the brain. With mounting biological data supporting this hypothesis with some modification, the fields of neural networks and para ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
