A Non-iterative Parallelizable Eigenbasis Algorithm for Johnson Graphs
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We present a new O(k^2 nk^2) method for generating an orthogonal basis of eigenvectors for the Johnson graph J(n,k). Unlike standard methods for computing a full eigenbasis of sparse symmetric matrices, the algorithm presented here is non-iterative, and produces exact results under an infinite-precision computation model. In addition, our method is highly parallelizable; given access to unlimited parallel processors, the eigenbasis can be constructed in only O(n) time given n and k. We also present an algorithm for computing projections onto the eigenspaces of J(n,k) in parallel time O(n).
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