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The Closest String Problem (CSP) is an NP-Complete problem which seeks to find the geometrical center of a set of input strings: given <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> strings of length <inline-formula> <tex-math notation="LaTeX">$L$ </tex-math></inline-formula> and a non-negative integer <inline-formula> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula>, construct a solution string <inline-formula> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula>, if it exists, such that the Hamming distance between <inline-formula> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula> and each input string is no larger than <inline-formula> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula>. 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&#x2019;s performance was compared with multiple state-of-the-art algorithms including Gramm et al.&#x2019;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&#x005F;LSS algorithm by Liu et al., and a sequential version of the heuristic algorithm (Heuris&#x005F;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.

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