Additive Schur Complement Approximation for Graphs

Abstract

This thesis deals with the approximation of the Schur complement on graphs represented by a graph Laplacian. The Schur complement of a graph eliminates selected vertices while preserving its properties. The approximation algorithm is based on splitting the graph into smaller parts (subgraphs) and computing the Schur complement on them, the resulting approximation is then constructed as the sum of the Schur complements of the individual subgraphs. This algorithm is also implemented in the Python programming language and is available at https://github.com/jn-flk/asca. Different methods and parameters can be used for graph splitting and selecting the eliminated vertices, their influence on the accuracy of the approximation is tested on selected graphs using the implementation. These tests showed that the approximation is effective.