Figure 1

Example of TDS. We process three trios sequentially. In each trio the first two genotypes are the genotypes of the parents and the third genotype is the genotype of the child. The possible solutions of each trio are given exactly next to it and numbered 1, 2. In each of the possible solutions for each trio the first two genotypes are the transmitted and the untransmitted haplotype from the first parent and similarly the remaining two for the second parent. At each step we are willing to keep only K = 2 streams which would be called "surviving streams". 1) The first trio has two possible solutions. 2) a) The second trio has two possible solutions. We have four possible combinations of a solution from the first trio to a solution from the second. The indices below the solutions show from which solutions from each trio this stream was created. For example stream s_1-2 as illustrated, was created from the first solution in the first trio and from the second in the second. In each stream we associate a weight as described in method section. b) We keep only the K = 2 streams with the highest weights (surviving streams) so at this point we consider them as the most probable and keep them. 3) The third trio has 2 possible solutions. a) Each one of them is appended in the end of each of the two solutions that we have kept. The definition of the streams is similar as before with stream s_2-1-1 coming from appending solution 1 of the third trio to stream s_2-1. b) Again we keep only two of the streams the ones with the highest weights s_2-1-1 and s_2-1-2.