Alternative graphical representations of genotypes in a pedigree

Three representations of the conditional independences due toMendelian segregation of genes in a pedigree are proposed. Thecomputational costs of performing calculations using the techniqueof peeling with each of these representations is compared byconsidering the weights of triangulations of the graph producedby each representation.     

A pedigree-based algorithm for finding efficient peeling sequences

The computational cost, in terms of both storage requirementsand calculation required, of performing an elimination orderingon a graph is considered as a function of the order in whichthe vertices of the moral graph are eliminated. Useful propertiesof the moral graph of a pedigree with respect to vertex eliminationare observed and these properties extended to define a k-pedigreeas a graph permitting allocation of one of k sexes to each vertexof the graph, such that the subgraph induced by vertices ofa single six contains no cycles. Properties of k-pedigrees includean upper bound of 2k on clique size. A novel algorithm, SEXY,based upon these properties is proposed and its performancecompared with other algorithms used to generate eliminationsequences. It is found to give a widely dispersed range of sequences,including some sequences requiring under a quarter of the storageand under a half of the computational time than had previouslybeen found using standard methods.