title: Fast half-sibling population reconstruction: theory and algorithms.
abstract: BACKGROUND
  Kinship inference is the task of identifying genealogically related individuals. Kinship information is important for determining mating structures, notably in endangered populations. Although many solutions exist for reconstructing full sibling relationships, few exist for half-siblings.
  
  
  RESULTS
  We consider the problem of determining whether a proposed half-sibling population reconstruction is valid under Mendelian inheritance assumptions. We show that this problem is NP-complete and provide a 0/1 integer program that identifies the minimum number of individuals that must be removed from a population in order for the reconstruction to become valid. We also present SibJoin, a heuristic-based clustering approach based on Mendelian genetics, which is strikingly fast. The software is available at http://github.com/ddexter/SibJoin.git+.
  
  
  CONCLUSIONS
  Our SibJoin algorithm is reasonably accurate and thousands of times faster than existing algorithms. The heuristic is used to infer a half-sibling structure for a population which was, until recently, too large to evaluate.
authors.affiliation: David R Cheriton School of Computer Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada. browndg@uwaterloo.ca.
authors.forename: Daniel
authors.initials: D
authors.lastname: Dexter
authors.forename: Daniel G
authors.initials: DG
authors.lastname: Brown