Fixed-parameter tractability of graph modification problems for hereditary properties
Information Processing Letters
An Optimal Algorithm to Detect a Line Graph and Output Its Root Graph
Journal of the ACM (JACM)
Non-approximability results for optimization problems on bounded degree instances
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Node-and edge-deletion NP-complete problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
An efficient fixed-parameter algorithm for 3-hitting set
Journal of Discrete Algorithms
On the asymmetric representatives formulation for the vertex coloring problem
Discrete Applied Mathematics
A Class Representative Model for Pure Parsimony Haplotyping
INFORMS Journal on Computing
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We propose a novel graph theoretic method to estimate haplotype population size from genotype data. The method considers only the potential sharing of haplotypes between individuals and is based on transforming the graph of potential haplotype sharing into a line graph using a minimum number of edge and vertex deletions. We show that the problems are NP complete and provide exact integer programming solutions for them. We test our approach using extensive simulations of multiple population evolution and genotypes sampling scenarios. Our computational experiments show that when most of the sharings are true sharings the problem can be solved very fast and the estimated size is very close to the true size; when many of the potential sharings do not stem from true haplotype sharing, our method gives reasonable lower bounds on the underlying number of haplotypes. In comparison, a naive approach of phasing the input genotypes provides trivial upper bounds of twice the number of genotypes.