With the rapidly expanding field of medical genetics and genetic counseling, genealogy information is becoming increasingly abundant. An important computation on pedigree data is the calculation of identity coefficients, which provide a complete description of the degree of relatedness of a pair of individuals. The areas of application of identity coefficients are numerous and diverse, from genetic counseling to disease tracking, and thus, the computation of identity coefficients merits special attention. However, the computation of identity coefficients is not done directly, but rather as the final step after computing a set of generalized kinship coefficients. In this paper, we first propose a novel Path-Counting Formula for calculating generalized kinship coefficients, which is motivated by Wright's path-counting method for computing inbreeding coefficient. We then present an efficient and scalable scheme for calculating generalized kinship coefficients on large pedigrees using NodeCodes, a special encoding scheme for expediting the evaluation of queries on pedigree graph structures. Furthermore, we propose an improved scheme using Family NodeCodes for the computation of generalized kinship coefficients, which is motivated by the significant improvement of using Family NodeCodes for inbreeding coefficient over the use of NodeCodes. We also perform experiments for evaluating the efficiency of our method, and compare it with the performance of the traditional recursive algorithm for three individuals. Experimental results demonstrate that the resulting scheme is more scalable and efficient than the traditional recursive methods for computing generalized kinship coefficients.
A Short Conceptual Proof of Narayana's Path-Counting Formula