Algorithms for comparing large pedigree graphs

Abstract

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.