Randomized Fixed-Parameter Algorithms for the Closest String Problem - Chen, Zhi-Zhong; Ma, Bin; Wang, Lusheng (Algorithmica, 2016)
Given a set S = { s 1 , s 2 , … , s n } of strings of equal length L and an integer d , the closest string problem (CSP) requires the computation of a string s of length L such that d ( s , s i ) ≤ d for each s i ∈ S , where d ( s , s i ) is the Hamming distance between s and s i . The problem is NP-hard and has been extensively studied in the context of approximation algorithms and fixed-parameter algorithms. Fixed-parameter algorithms provide the most practical solutions to its real-life applications in bioinformatics. In this paper we develop the first randomized fixed-parameter algorithms for CSP. Not only are the randomized algorithms much simpler than their deterministic counterparts, their time complexities are also significantly better than the previously best known (deterministic) algorithms.