Table 1.

Overview of common notation

Notation	Meaning	Example
$\mathcal{I}$	Set of individuals	$\{1,2,3,4\}$
$\mathcal{T}$	Set of trio relationships	$\{(1,2,3),(1,2,4)\}$
${\mathcal{F}}_i\in {\{0,1,-\}}^{R_i\times M}$	Input SNP matrix for individual $i\in \mathcal{I}$	$\left[\begin{array}{ccccc}-& -& 1& 0& 1\\ 0& 1& 1& 1& -\end{array}\right]$
${\mathcal{W}}_i\in {\mathbb{N}}^{R_i\times M}$	Matrix of weights for individual $i\in \mathcal{I}$	$\left[\begin{array}{ccccc}0& 0& 10& 21& 7\\ 13& 9& 31& 25& 0\end{array}\right]$
$\mathcal{X}\in {\mathbb{N}}^M$	Recombination cost vector	$(0,20,12,23,11)$
$g_i\in {\{0,1,2\}}^M$	Input genotypes for individual i	$(0,2,2,1,1)$
A(k)	Set of reads active in column k	$\{[\text{\hspace{0.17em}-\hspace{0.17em}-\hspace{0.17em}}101],[0111\text{\hspace{0.17em}-\hspace{0.17em}}]\}$
${\Delta }_C(k,B,t)$	Local cost incurred for column k, bipartition B and transmission tuple t	10
$C(k,B,t)$	DP table entry for column k, bipartition B and transmission tuple t	37
$h_i^0,h_i^1\in {\{0,1\}}^M$	Sought haplotypes for individual i	$(0,1,1,1,0),(0,1,1,0,1)$
$t_{m\to c},t_{f\to c}\in {\{0,1\}}^M$	Sought transmission vectors for trio $(m,f,c)\in \mathcal{T}$	$(0,0,0,1,1)$