Isomorphism and Similarity for 2-Generation Pedigrees

We consider the emerging problem of comparing the similarity between (unlabeled) pedigrees. More specifically, we focus on the simplest pedigrees, namely, the 2-generation pedigrees. We show that the isomorphism testing for two 2-generation pedigrees is GI-hard. If the 2-generation pedigrees are monogamous (i.e., each individual at level-1 can mate with exactly one partner) then the isomorphism testing problem can be solved in polynomial time. We then consider the problem by relaxing it into an NP-complete decomposition problem which can be formulated as the Minimum Common Integer Pair Partition (MCIPP) problem, which we show to be FPT by exploiting a property of the optimal solution. While there is still some difficulty to overcome, this lays down a solid foundation for this research

Algorithms for comparing large pedigree graphs

The importance of pedigrees is translated by geneticists as a tool for diagnosing genetic diseases. Errors resulting during collection of data and missing information of individuals are considered obstacles in deducing pedigrees, especially larger ones. Therefore, the reconstructed pedigree graph evaluation needs to be undertaken for relevant diagnosis. This requires a comparison between the derived and the original data. The present study discusses the isomorphism of huge pedigrees with labeled and unlabeled leaves, where a pedigree has hundreds of families, which are monogamous and generational. The algorithms presented in this paper are based on a set of bipartite graphs covering the pedigree and the problem addressed is parameter tractable. The Bipartite graphs Covering the Pedigree (BCP) problem is said to possess a time complexity of $f(k).mod(X)^{O(1)}$ where $f$ is the computing function that grows exponentially. The study presents an algorithm for the BCP problem that can be categorized as a polynomial-time-tractable evaluation of the reconstructed pedigree. The paper considers pedigree graphs that consist of both labeled and unlabeled leaves that make use of parameterized and kernelization algorithms to solve the problem. The kernelization algorithm executes in $O(k^3)$ for the BCP graphs

Isomorphism and similarity for 2-generation pedigrees

We consider the emerging problem of comparing the similarity between (unlabeled) pedigrees. More specifically, we focus on the simplest pedigrees, namely, the 2-generation pedigrees. We show that the isomorphism testing for two 2-generation pedigrees is GI-hard. If the 2-generation pedigrees are monogamous (i.e., each individual at level-1 can mate with exactly one partner) then the isomorphism testing problem can be solved in polynomial time. We then consider the problem by relaxing it into an NP-complete decomposition problem which can be formulated as the Minimum Common Integer Pair Partition (MCIPP) problem, which we show to be FPT by exploiting a property of the optimal solution. While there is still some difficulty to overcome, this lays down a solid foundation for this research