Figure 2
From: A linear-time algorithm for reconstructing zero-recombinant haplotype configuration on a pedigree
Two types of redundancy arise from linearly dependence. (a) A cycle c is decomposed into a tree path p2 and a path p1 that contains a non-tree edge e. So we have b c = b p + b t , where b c , b p , and b t are constraints of cycle c, path p1 and path p2, respectively. The dotted line represents the non-tree edge e. (b) n l is the node closest to n i on the path p3. Assume that the constraint of tree path p i is b i , 1 ≤ i ≤ 6. We have b1 = b4 + b6, b2 = b4 + b5, and b3 = b5 + b6, which conclude that b1 = b2 + b3 due to the addition over GF(2).