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Pratik Agarwal and Edwin Olson University of Freiburg and University of Michigan Variable reordering strategies for SLAM

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Graph based SLAM Good ordering Bad ordering 24 times more zeros

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Graph based SLAM Reorder

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Reordering = =

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Reordering is essential for SLAM Bad ordering 10s Good ordering 0.1s Good ordering 100 times faster

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Contribution

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Exact minimum degree (EMD) Remove node with min edges Connect neighbors

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Our method: bucket heap AMD Advantage over EMD: Single query - multiple vertex elimination How? Lists of vertices with similar #edges

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BHAMD in action

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Multiple vertices eliminated

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BHAMD on a 10,000 node graph EMD - 10,000 steps BHAMD - 107 steps Max heap size in BHAMD 42

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State-of-the-art techniques AMD Approximate Minimum Degree COLAMD Column Approximate Minimum Degree NESDIS Nested Dissection METIS Serial Graph Partition

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Evaluation – reordering time EMD is slowest

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Evaluation – solve time

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Further room for improvement? maximum improvement of 0.5% (with 1 week compute time)

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Conclusion 1.All methods comparable EMD & COLAMD on A 2.BHAMD - simple yet competitive 3.Negligible improvement with small changes

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Questions

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Reordering matrix - P

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Toy example Good ordering Bad ordering

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Multiple Min Degree (MMD) vs BHAMD Similarity multiple elimination Difference MMD computes and eliminates independent nodes MMD is still exact unlike BHAMD

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But I use CSparse with COLAMD It calls AMD if the matrix is PSD Be careful when opening the box

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Graph based SLAM Good ordering Bad ordering 24 times sparser

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