The Closest String Problem (CSP) is an NP-hard problem, which arises in computational molecular biology and coding theory.
We call this problem the Closest String with Wildcards problem, and we analyze it in the framework of parameterized complexity.
In this paper we describe and implement a parallel algorithm to find approximate solutions for the Closest String Problem (CSP).
Given a set of n strings of length L and a radius d, the closest string problem (CSP for short) asks for a string tsol that is within a Hamming distance of d to each of the given strings.
The Closest String problem asks to find a string s which is not too far from each string in a set of m input strings, where the distance is taken as the Hamming distance.
In this paper, we introduce a new variant of Closest String where the input strings can contain wildcards that can match any letter in the alphabet, and the goal is to find a solution string without wildcards.
A related problem, with Hamming distance instead of Manhattan distance, is called Hamming String Consensus (HSC), also known under the names of string center problem or closest string problem.
His dissertation, titled "Open-closed String Duality and Topological Theories," sheds new light on the relationship between gauge theory and gravity and, ultimately, on the fundamental workings of the universe.
For the general CSP, we design a polynomial heuristic which is a combination of our proposed approximation algorithm LDDA ([10] Liu Xiaolan, Fu Keqiang, Shao Renxiang. Largest distance decreasing algorithm for the Closest String Problem. Journal of Information & Computational Science 2004; 1(2): 287–92) and local search strategies.
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