A Heuristic Solution to the Closest String Problem Using Wave Function Collapse Techniques

A Heuristic Solution to the Closest String Problem Using Wave Function Collapse Techniques

The Closest String Problem (CSP) is an NP-Complete problem which seeks to find the geometrical center of a set of input strings: given k strings of length L and a non-negative integer d , construct a solution string t , if it exists, such that the Hamming distance between t and each input st...

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Bibliographic Details
Published in:IEEE access 2022, Vol.10, p.115869-115883
Main Authors: Xu, Shirley, Perkins, David
Format: Article
Language:eng
Subjects:
Algorithms
Approximation algorithms
closest string problem
Entropy
Games
Hamming distances
Heuristic
Heuristic algorithms
Heuristic methods
NP-complete
NP-hard
Strings
Time complexity
Wave functions
WaveFunctionCollapse
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Summary:The Closest String Problem (CSP) is an NP-Complete problem which seeks to find the geometrical center of a set of input strings: given k strings of length L and a non-negative integer d , construct a solution string t , if it exists, such that the Hamming distance between t and each input string is no larger than d . This paper proposes WFC-CSP, a novel heuristic algorithm inspired by Wave Function Collapse (WFC) techniques to solve CSP. Experimental results show that WFC-CSP is highly reliable and efficient in solving CSP across different configurations and instance sizes. Using extensive test data sets, WFC-CSP's performance was compared with multiple state-of-the-art algorithms including Gramm et al.'s Fixed-parameter algorithm (FP-CSP), the Ant-CSP algorithm by Faro and Pappalardo using metaheuristic techniques, the third IP formation algorithm by Meneses et al., the LDDA_LSS algorithm by Liu et al., and a sequential version of the heuristic algorithm (Heuris_Seq) by Gomes et al. We observe that WFC-CSP outperforms the other algorithms in solution quality or run time or both metrics. The WFC-CSP algorithm has wide applications in solving CSP in the fields of computational biology and coding theory.
ISSN:2169-3536
2169-3536