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arXiv · 1301.3946

Efficient Identification of Equivalences in Dynamic Graphs and Pedigree Structures

Hoyt Koepke·Elizabeth Thompson
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Abstract

We propose a new framework for designing test and query functions for complex structures that vary across a given parameter such as genetic marker position. The operations we are interested in include equality testing, set operations, isolating unique states, duplication counting, or finding equivalence classes under identifiability constraints. A motivating application is locating equivalence classes in identity-by-descent (IBD) graphs, graph structures in pedigree analysis that change over genetic marker location. The nodes of these graphs are unlabeled and identified only by their connecting edges, a constraint easily handled by our approach. The general framework introduced is powerful enough to build a range of testing functions for IBD graphs, dynamic populations, and other structures using a minimal set of operations. The theoretical and algorithmic properties of our approach are analyzed and proved. Computational results on several simulations demonstrate the effectiveness of our approach.

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Hoyt Koepke, Elizabeth Thompson. 2013-02-18. Efficient Identification of Equivalences in Dynamic Graphs and Pedigree Structures. https://arxiv.org/abs/1301.3946

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