The parameterized complexity of the shared center problem

Authors:
Zhi-Zhong Chen;Lusheng Wang;Wenji Ma
Affiliations:
Department of Information System Design, Tokyo Denki University, Hatoyama, Saitama, Japan;Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong SAR;Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong SAR
Venue:
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
Year:
2012

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Parameterized Complexity

Parameterized Complexity

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Abstract

Recently, the shared center (SC) problem has been proposed as a mathematical model for inferring the allele-sharing status of a given set of individuals using a database of confirmed haplotypes as reference. The problem was proved to be NP-complete and a ratio-2 polynomial-time approximation algorithm was designed for its minimization version (called the closest shared center (CSC) problem). In this paper, we consider the parameterized complexity of the SC problem. First, we show that the SC problem is W[1]-hard with parameters d and n, where d and n are the radius and the number of (diseased or normal) individuals in the input, respectively. Then, we present two asymptotically optimal parameterized algorithms for the problem.